Distance Calculus Course Curricula |
The LiveMath-based e-texts feature notebooks, screencast recordings discussing the topics in the LiveMath notebooks, which also serve as a tutorial on using LiveMath, and "by hand" videos as complimentary instruction for certain topics where hand calculations are important for mathematical literacy.
A subset selection of notebooks and movies are presented for students considering enrolling in a Distance Calculus course.
When Distance Calculus was launched back in 1997, the first
courses were Calculus I and higher. As enrollment grew, it became clear that a number of students needed
more Precalculus practice before jumping into the Calculus curriculum.
Out of this necessity was born the comprehensive (and exhaustive!) The Primitives of Precalculus, bridging the gap between a varied high school math background and the core skill requirements of the Calculus I course. We begin with hand-calculations of solving basic equations from Algebra I level, all the way through conic sections, series, vectors, and polar equations - topics usually found in a precalculus textbook but never actually covered in class. The pedagogical approach is dual in nature:
Using both hand-skills and LiveMath skills as the foundation, we then advance through the Precalculus curriculum eventually leaning towards LiveMath and advanced and unique topics that cannot be studied without a technological tool. ![]()
Such unique and advanced topics include:
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>>>Hide Table of Contents (With Demo Sections & Content)
- P1: Solving Equations
- P1.1: Solving Equations in 1 Variable
- P1.1a: 3x + 5 = 14
- P1.1b: 1/4 x - 6 = 2
- P1.1c: 2x + 9 = 4x - 7
- LiveMath Video: P1.1.c-Video.mp4
- LiveMath Video: P1.1.c-LMVideo.mp4
- LiveMath Notebook: P1.1.c.the
- P1.1d: 8(2-x) + 4 = -3(2x+1) - 2
- LiveMath Video: P1.1.d-Video.mp4
- LiveMath Video: P1.1.d-LMVideo.mp4
- LiveMath Notebook: P1.1.d.the
- P1.1e: 0.2x - 4pi = 7.62 - 3.87(x-5)
- LiveMath Video: P1.1.e-Video.mp4
- LiveMath Video: P1.1.e-LMVideo.mp4
- LiveMath Notebook: P1.1.e.the
- P1.1f: 6(x)^(2) - 3 = 21
- LiveMath Video: P1.1.f-Video.mp4
- LiveMath Video: P1.1.f-LMVideo.mp4
- LiveMath Notebook: P1.1.f.the
- P1.1g: 5(x)^(2)+4 = 17
- LiveMath Video: P1.1.g-Video.mp4
- LiveMath Video: P1.1.g-LMVideo.mp4
- LiveMath Notebook: P1.1.g.the
- P1.1h: 7(x)^(3)+6 = 62
- LiveMath Video: P1.1.h-Video.mp4
- LiveMath Video: P1.1.h-LMVideo.mp4
- LiveMath Notebook: P1.1.h.the
- P1.1i: 4((x-1))^(2)- 13 = 35
- LiveMath Video: P1.1.i-Video.mp4
- LiveMath Video: P1.1.i-LMVideo.mp4
- LiveMath Notebook: P1.1.i.the
- P1.1j: (2)/(x-1)+6 = (3)/(x-1)
- P1.1k: (x)/(x - 2) = (- 2 x - 3)/(x + 1)
- P1.1l: Homework Problems
- LiveMath Video: P1.1.l-Video.mp4
- LiveMath Notebook: P1.1.l.the
- P1.1m: Solving Equations in LiveMath
- LiveMath Notebook: P1.1.m.the
- P1.2: What If You Can't Solve For x?
- P1.2a: Trying To Isolate The Variable
- LiveMath Video: P1.2.a-Video.mp4
- LiveMath Video: P1.2.a-LMVideo.mp4
- LiveMath Notebook: P1.2.a.the
- P1.2b: Many Variables, Only 1 Solution
- LiveMath Video: P1.2.b-Video.mp4
- LiveMath Video: P1.2.b-LMVideo.mp4
- LiveMath Notebook: P1.2.b.the
- P1.2c: Multiple Solutions
- LiveMath Video: P1.2.c-Video.mp4
- LiveMath Video: P1.2.c-LMVideo.mp4
- LiveMath Notebook: P1.2.c.the
- P1.2d: Very Complicated, Only 1 Solution
- LiveMath Video: P1.2.d-Video.mp4
- LiveMath Video: P1.2.d-LMVideo.mp4
- LiveMath Notebook: P1.2.d.the
- P1.2e: No Real Solutions, But Imaginary Solutions
- LiveMath Video: P1.2.e-Video.mp4
- LiveMath Video: P1.2.e-LMVideo.mp4
- LiveMath Notebook: P1.2.e.the
- P1.2f: Homework Problems
- LiveMath Notebook: P1.2.f.the
- P1.3: Finding Solutions Numerically
- P1.3a: Experimenting With Substitution Values
- LiveMath Video: P1.3.a-Video.mp4
- LiveMath Video: P1.3.a-LMVideo.mp4
- LiveMath Notebook: P1.3.a.the
- P1.3b: Numerical Tables
- LiveMath Video: P1.3.b-LMVideo.mp4
- LiveMath Notebook: P1.3.b.the
- P1.3c: Reduce Equation To: LHS = 0
- LiveMath Video: P1.3.c-LMVideo.mp4
- LiveMath Notebook: P1.3.c.the
- P1.3d: Homework Problems
- LiveMath Notebook: P1.3.d.the
- P1.4: Finding Solutions Graphically
- P1.4a: Algebraic Setup and Graphing
- P1.4b: Converting to LHS=0 and Graph
- P1.4c: Looking Around For Solutions
- P1.4d: Homework Problems
- LiveMath Notebook: P1.4.d.the
- P1.5: What About Equations With More Than 1 Variable?
- P1.5a: Sample Equation With 2 Variables
- LiveMath Video: P1.5.a-Video.mp4
- LiveMath Video: P1.5.a-LMVideo.mp4
- LiveMath Notebook: P1.5.a.the
- P1.5b: Graphing in 3D To Help Find Solutions
- LiveMath Video: P1.5.b-LMVideo.mp4
- LiveMath Notebook: P1.5.b.the
- P1.5c: Homework Problems
- LiveMath Notebook: P1.5.c.the
- P1.6: Conclusion
- P1.6a: Literacy Sheet
- P1.6b: P1 LiveMath Quiz
- LiveMath Notebook: P1.6.b.the
- P1.6c: P1 Video Quiz
- LiveMath Video: P1.6.c-Video.mp4
- P2: Functions
- P2.1: What is a Function?
- P2.1a: Notation
- LiveMath Video: P2.1.a-Video.mp4
- P2.1b: Data Sets & Functional Notation
- LiveMath Video: P2.1.b-Video.mp4
- P2.1c: More Data Sets
- LiveMath Video: P2.1.c-Video.mp4
- P2.1d: When is a Data Set NOT a Function?
- LiveMath Video: P2.1.d-Video.mp4
- P2.1e: Algebraic Formulae
- LiveMath Video: P2.1.e-Video.mp4
- P2.1f: Massachusetts Lunatics
- LiveMath Video: P2.1.f-Video.mp4
- P2.1g: Hurricane Katrina Data
- LiveMath Video: P2.1.g-Video.mp4
- P2.1h: Formal Definition of Function
- LiveMath Video: P2.1.h-Video.mp4
- P2.1i: Homework Problems
- LiveMath Video: P2.1.i-Video.mp4
- LiveMath Notebook: P2.1.i.the
- P2.2: Graphing Data Functions
- P2.2a: Input vs. Output
- LiveMath Video: P2.2.a-Video.mp4
- LiveMath Notebook: P2.2.a.the
- P2.2b: Graphing Data in LiveMath Manually
- LiveMath Video: P2.2.b-LMVideo.mp4
- LiveMath Notebook: P2.2.b.the
- P2.2c: Graphing Multiple Data Sets
- LiveMath Video: P2.2.c-LMVideo.mp4
- LiveMath Notebook: P2.2.c.the
- P2.2d: Graphing 3D Data
- LiveMath Video: P2.2.d-LMVideo.mp4
- LiveMath Notebook: P2.2.d.the
- P2.2e: Not a Function?
- LiveMath Video: P2.2.e-LMVideo.mp4
- LiveMath Notebook: P2.2.e.the
- P2.3: Functions from Algebraic Formulae
- P2.3a: Generating Data
- LiveMath Video: P2.3.a-Video.mp4
- LiveMath Video: P2.3.a-LMVideo.mp4
- LiveMath Notebook: P2.3.a.the
- P2.3b: Graphing Generated Data
- LiveMath Video: P2.3.b-Video.mp4
- LiveMath Video: P2.3.b-LMVideo.mp4
- LiveMath Notebook: P2.3.b.the
- P2.3c: Increasing Resolution
- LiveMath Video: P2.3.c-LMVideo.mp4
- LiveMath Notebook: P2.3.c.the
- P2.3d: Smooth Curves
- LiveMath Video: P2.3.d-LMVideo.mp4
- LiveMath Notebook: P2.3.d.the
- P2.3e: Graphing Without Data
- LiveMath Video: P2.3.e-LMVideo.mp4
- LiveMath Notebook: P2.3.e.the
- P2.3f: Graph Multiple Functions Together
- LiveMath Video: P2.3.f-LMVideo.mp4
- LiveMath Notebook: P2.3.f.the
- P2.3g: Functions in 3D
- P2.4: Bad Inputs?
- P2.4a: Undefined Input Values
- LiveMath Video: P2.4.a-Video.mp4
- LiveMath Video: P2.4.a-LMVideo.mp4
- LiveMath Notebook: P2.4.a.the
- P2.4b: All Good Input Values = Domain
- LiveMath Video: P2.4.b-Video.mp4
- LiveMath Video: P2.4.b-LMVideo.mp4
- LiveMath Notebook: P2.4.b.the
- P2.4c: All Realized Output Values = Range
- LiveMath Video: P2.4.c-LMVideo.mp4
- LiveMath Notebook: P2.4.c.the
- P2.5: Combinations of Functions
- P2.5a: Add, Subtract Functions
- LiveMath Video: P2.5.a-Video.mp4
- LiveMath Video: P2.5.a-LMVideo.mp4
- LiveMath Notebook: P2.4.a.the
- P2.5b: Multiply Functions
- LiveMath Video: P2.5.b-Video.mp4
- LiveMath Video: P2.5.b-LMVideo.mp4
- LiveMath Notebook: P2.5.b.the
- P2.5c: Divide Functions
- LiveMath Video: P2.5.c-Video.mp4
- LiveMath Video: P2.5.c-LMVideo.mp4
- LiveMath Notebook: P2.5.c.the
- P2.5d: Abstract Substitution
- LiveMath Video: P2.5.d-Video.mp4
- LiveMath Video: P2.5.d-LMVideo.mp4
- LiveMath Notebook: P2.5.d.the
- P2.5e: Composition of Functions
- LiveMath Video: P2.5.e-Video.mp4
- LiveMath Video: P2.5.e-LMVideo.mp4
- LiveMath Notebook: P2.5.d.the
- P2.6: Functions Without Algebraic Formulae
- P3: Linear Functions
- P3.1: Data Functions With Linearity Property
- P3.1a: Fixed Output Increase
- P3.1b: Input Intervals Constant
- P3.1c: Input Intervals Vary
- P3.1d: Slope of a Data Set
- P3.1e: Checking All Points for Linearity Property
- LiveMath Video: P3.1.e-LMVideo.mp4
- LiveMath Notebook: P3.1.e.the
- P3.1f: Which Function Grows Faster?
- P3.2: Algebraic Formula For Linear Data Sets
- P3.2a: Finding Linear Formula
- LiveMath Video: P3.2.a-LMVideo.mp4
- LiveMath Notebook: P3.2.a.the
- P3.2b: Slope
- LiveMath Video: P3.2.b-LMVideo.mp4
- LiveMath Notebook: P3.2.b.the
- P3.2c: Output Axis Intercept
- LiveMath Video: P3.2.c-LMVideo.mp4
- LiveMath Notebook: P3.2.c.the
- P3.2d: Almost Linear Data Sets
- LiveMath Video: P3.2.d-LMVideo.mp4
- LiveMath Notebook: P3.2.d.the
- P3.2e: Homework Problems
- LiveMath Notebook: P3.2.e.the
- P3.3: Classical Linear Functions
- P3.3a: y = m x + b
- P3.3b: Given 2 Points, Find Linear Function
- P3.3c: Parallel Lines
- LiveMath Video: P3.3.c-Video.mp4
- LiveMath Video: P3.3.c-LMVideo.mp4
- LiveMath Notebook: P3.3.c.the
- P3.3d: Perpendicularity
- LiveMath Video: P3.3.d-LMVideo.mp4
- LiveMath Notebook: P3.3.d.the
- P3.3e: Point-Slope Form
- LiveMath Video: P3.3.e-LMVideo.mp4
- LiveMath Notebook: P3.3.e.the
- P3.3f: Finding x-Intercept
- P3.3g: Homework Problems
- LiveMath Notebook: P3.3.g.the
- P3.4: Solving Problems Involving Linear Functions
- P3.4a: Gas Mileage and Hybrids
- LiveMath Video: P3.4.a-LMVideo.mp4
- LiveMath Notebook: P3.4.a.the
- P3.4b: Purchasing MP3 Music Files
- LiveMath Video: P3.4.b-LMVideo.mp4
- LiveMath Notebook: P3.4.b.the
- P3.4c: Tivo vs. NetFlix
- LiveMath Video: P3.4.c-LMVideo.mp4
- LiveMath Notebook: P3.4.c.the
- P3.4d: Homework Problems
- LiveMath Notebook: P3.4.d.the
- P3.4e: Homework Problems
- LiveMath Notebook: P3.4.e.the
- P4: Quadratic Functions
- P4.1: Quadratic Algebraic Functions
- P4.1a: Power Function
- LiveMath Video: P4.1.a-Video.mp4
- P4.1b: Power Function & Lower Terms
- LiveMath Video: P4.1.b-Video.mp4
- P4.1c: General Form
- LiveMath Video: P4.1.c-Video.mp4
- P4.2: Quadratic Data
- P4.2a: Generate Data From Algebraic Formula
- LiveMath Video: P4.2.a-Video.mp4
- LiveMath Video: P4.2.a-LMVideo.mp4
- LiveMath Notebook: P4.2.a.the
- P4.2b: Graphing Quadratic Functions
- LiveMath Video: P4.2.b-LMVideo.mp4
- LiveMath Notebook: P4.2.b.the
- P4.2c: Playing with Coefficients
- LiveMath Video: P4.2.c-LMVideo.mp4
- LiveMath Notebook: P4.2.c.the
- P4.2d: Given Data, Match Formula
- LiveMath Video: P4.2.d-Video.mp4
- LiveMath Video: P4.2.d-LMVideo.mp4
- LiveMath Notebook: P4.2.d.the
- P4.2e: Given Small Amount of Data, Match Graph
- LiveMath Video: P4.2.e-Video.mp4
- LiveMath Video: P4.2.e-LMVideo.mp4
- LiveMath Notebook: P4.2.e.the
- P4.2f: Best Fit Formula
- LiveMath Video: P4.2.f-LMVideo.mp4
- LiveMath Notebook: P4.2.f.the
- P4.2g: Quadratic Data
- LiveMath Notebook: P4.2.g.the
- P4.3: Quadratic Equations
- P4.3a: Solve By Guessing
- LiveMath Video: P4.3.a-Video.mp4
- LiveMath Video: P4.3.a-LMVideo.mp4
- LiveMath Notebook: P4.3.a.the
- P4.3b: Solve Graphically
- LiveMath Video: P4.3.b-LMVideo.mp4
- LiveMath Notebook: P4.3.b.the
- P4.3c: Solve Algebraically: Factoring
- LiveMath Video: P4.3.c-Video.mp4
- LiveMath Video: P4.3.c-LMVideo.mp4
- LiveMath Notebook: P4.3.c.the
- P4.3d: Complications with Factoring
- LiveMath Video: P4.3.d-Video.mp4
- LiveMath Video: P4.3.d-LMVideo.mp4
- LiveMath Notebook: P4.3.d.the
- P4.3e: Quadratic Formula
- LiveMath Video: P4.3.e-Video.mp4
- LiveMath Notebook: P4.3.e.the
- P4.3f: Using Quadratic Formula
- LiveMath Video: P4.3.f-Video.mp4
- LiveMath Video: P4.3.f-LMVideo.mp4
- LiveMath Notebook: P4.3.f.the
- P4.3g: Imaginary Numbers
- LiveMath Video: P4.3.g-Video.mp4
- LiveMath Video: P4.3.g-LMVideo.mp4
- LiveMath Notebook: P4.3.g.the
- P4.3h: Solve Numerically
- LiveMath Video: P4.3.h-LMVideo.mp4
- LiveMath Notebook: P4.3.h.the
- P4.3i: Homework on Solving Quadratic Equations
- LiveMath Video: P4.3.i-Video.mp4
- LiveMath Notebook: P4.3.i.the
- P4.3j: Homework Problems
- LiveMath Notebook: P4.3.j.the
- P4.4: Quadratic Graphs
- P4.4a: Translations Vertical
- LiveMath Video: P4.4.a-LMVideo.mp4
- LiveMath Notebook: P4.4.a.the
- P4.4b: Translations Horizontal
- LiveMath Video: P4.4.b-LMVideo.mp4
- LiveMath Notebook: P4.4.b.the
- P4.4c: Standard Graphing Form
- LiveMath Video: P4.4.c-LMVideo.mp4
- LiveMath Notebook: P4.4.c.the
- P4.4d: Completing the Square
- LiveMath Video: P4.4.d-LMVideo.mp4
- LiveMath Notebook: P4.4.d.the
- P4.4e: Parabolic Geometry Properties
- LiveMath Video: P4.4.e-LMVideo.mp4
- LiveMath Notebook: P4.4.e.the
- P4.4f: Homework Problems
- LiveMath Notebook: P4.4.f.the
- P5: Polynomial Functions
- P5.1: Algebraic Development
- P5.1a: Cubic Functions
- LiveMath Video: P5.1.a-Video.mp4
- LiveMath Video: P5.1.a-LMVideo.mp4
- LiveMath Notebook: P5.1.a.the
- P5.1b: Quartic Functions
- LiveMath Video: P5.1.b-Video.mp4
- LiveMath Video: P5.1.b-LMVideo.mp4
- LiveMath Notebook: P5.1.b.the
- P5.1c: Power Functions
- LiveMath Video: P5.1.c-Video.mp4
- LiveMath Video: P5.1.c-LMVideo.mp4
- LiveMath Notebook: P5.1.c.the
- P5.1d: General Polynomial Functions
- LiveMath Video: P5.1.d-Video.mp4
- LiveMath Video: P5.1.d-LMVideo.mp4
- LiveMath Notebook: P5.1.d.the
- P5.1e: Graph Identification
- LiveMath Video: P5.1.e-LMVideo.mp4
- LiveMath Notebook: P5.1.e.the
- P5.1f: Homework Problems
- LiveMath Notebook: P5.1.f.the
- P5.2: Polynomial Data
- P5.2a: Generate Data from Algebraic Formula
- LiveMath Video: P5.2.a-LMVideo.mp4
- LiveMath Notebook: P5.2.a.the
- P5.2b: Roots
- LiveMath Video: P5.2.b-LMVideo.mp4
- LiveMath Notebook: P5.2.b.the
- P5.2c: Factored Form
- LiveMath Video: P5.2.c-LMVideo.mp4
- LiveMath Notebook: P5.2.c.the
- P5.2d: Given Data, Match Formula
- LiveMath Video: P5.2.d-LMVideo.mp4
- LiveMath Notebook: P5.2.d.the
- P5.2e: Best Fit Formula
- LiveMath Video: P5.2.e-LMVideo.mp4
- LiveMath Notebook: P5.2.e.the
- P5.2f: Homework Problems
- LiveMath Notebook: P5.2.f.the
- P5.3: Polynomial Equations
- P5.3a: Solve By Guessing
- LiveMath Video: P5.3.a-Video.mp4
- LiveMath Video: P5.3.a-LMVideo.mp4
- LiveMath Notebook: P5.3.a.the
- P5.3b: Solve Graphically
- LiveMath Video: P5.3.b-LMVideo.mp4
- LiveMath Notebook: P5.3.b.the
- P5.3c: Solve By Polynomial Division
- LiveMath Video: P5.3.c-Video.mp4
- LiveMath Video: P5.3.c-LMVideo.mp4
- LiveMath Notebook: P5.3.c.the
- P5.3d: Solve by Factoring
- LiveMath Video: P5.3.d-LMVideo.mp4
- LiveMath Notebook: P5.3.d.the
- P5.3e: Solve Numerically
- LiveMath Video: P5.3.e-LMVideo.mp4
- LiveMath Notebook: P5.3.e.the
- P5.3f: Homework Problems
- LiveMath Video: P5.3.f-Video.mp4
- LiveMath Notebook: P5.3.f.the
- P5.3g: Homework Problems
- LiveMath Notebook: P5.3.g.the
- P5.4: Polynomial Graphs
- P5.4a: Vertical Translations
- P5.4b: Horizontal Translations
- P5.4c: Roots are Key
- P5.4d: Given Graph, Match Formula
- P5.4e: Complex Roots and Graphs
- LiveMath Video: P5.4.e-LMVideo.mp4
- LiveMath Notebook: P5.4.e.the
- P5.4f: Homework Problems
- LiveMath Notebook: P5.4.f.the
- P5.5: Fundamental Theorem of Algebra
- P5.5a: FTOA
- LiveMath Video: P5.5.a-LMVideo.mp4
- LiveMath Notebook: P5.5.a.the
- P5.5b: Module Recap
- LiveMath Notebook: P5.5.b.the
- P6: Rational Polynomial Functions
- P6.1: Reciprocating
- P6.1a: Reciprocals of Linear Functions
- P6.1b: Reciprocals of Power Functions
- P6.1c: Reciprocals of Quadratic Functions
- P6.1d: Reciprocals of Polynomial Functions
- LiveMath Video: P6.1.d-LMVideo.mp4
- LiveMath Notebook: P6.1.d.the
- P6.1e: Roots and Asymptotes
- LiveMath Video: P6.1.e-LMVideo.mp4
- LiveMath Notebook: P6.1.e.the
- P6.1f: Homework Problems
- LiveMath Notebook: P6.1.f.the
- P6.2: Polynomial Over Polynomial
- P6.2a: Initial Graphs
- LiveMath Video: P6.2.a-LMVideo.mp4
- LiveMath Notebook: P6.2.a.the
- P6.2b: Roots on Top, Roots on Bottom
- LiveMath Video: P6.2.b-LMVideo.mp4
- LiveMath Notebook: P6.2.b.the
- P6.2c: Common Roots
- LiveMath Video: P6.2.c-LMVideo.mp4
- LiveMath Notebook: P6.2.c.the
- P6.2d: Degree Top Heavy
- LiveMath Video: P6.2.d-LMVideo.mp4
- LiveMath Notebook: P6.2.d.the
- P6.2e: Degree Bottom Heavy
- LiveMath Video: P6.2.e-LMVideo.mp4
- LiveMath Notebook: P6.2.e.the
- P6.2f: Degree Balanced
- LiveMath Video: P6.2.f-LMVideo.mp4
- LiveMath Notebook: P6.2.f.the
- P6.2g: Homework Problems
- LiveMath Notebook: P6.2.g.the
- P6.3: Rational Polynomial Equations
- P6.3a: Solve Graphically
- LiveMath Video: P6.3.a-LMVideo.mp4
- LiveMath Notebook: P6.3.a.the
- P6.3b: Solve By Cross Multiplication
- LiveMath Video: P6.3.b-Video.mp4
- LiveMath Video: P6.3.b-LMVideo.mp4
- LiveMath Notebook: P6.3.b.the
- P6.3c: Solving Via Factoring
- LiveMath Video: P6.3.c-LMVideo.mp4
- LiveMath Notebook: P6.3.c.the
- P6.3d: Land Mines To Watch Out For
- LiveMath Video: P6.3.d-LMVideo.mp4
- LiveMath Notebook: P6.3.d.the
- P6.3e: Homework Problems
- LiveMath Video: P6.3.e-Video.mp4
- LiveMath Notebook: P6.3.e.the
- P7: Exponential Functions
- P7.1: What Is An Exponential Function?
- P7.1a: Power Functions
- LiveMath Video: P7.1.a-Video.mp4
- LiveMath Video: P7.1.a-LMVideo.mp4
- LiveMath Notebook: P7.1.a.the
- P7.1b: Fractional Exponents
- LiveMath Video: P7.1.b-Video.mp4
- LiveMath Video: P7.1.b-LMVideo.mp4
- LiveMath Notebook: P7.1.b.the
- P7.1c: Roots
- LiveMath Video: P7.1.c-LMVideo.mp4
- LiveMath Notebook: P7.1.c.the
- P7.1d: Finite Decimal Exponents
- LiveMath Video: P7.1.d-LMVideo.mp4
- LiveMath Notebook: P7.1.d.the
- P7.1e: Infinite Decimal Exponents
- LiveMath Video: P7.1.e-LMVideo.mp4
- LiveMath Notebook: P7.1.e.the
- P7.1f: Definition of Exponential Function
- LiveMath Video: P7.1.f-LMVideo.mp4
- LiveMath Notebook: P7.1.f.the
- P7.1g: Famous Bases
- LiveMath Video: P7.1.g-LMVideo.mp4
- LiveMath Notebook: P7.1.g.the
- P7.1h: Homework Problems
- LiveMath Notebook: P7.1.h.the
- P7.2: Graphs of Exponential Functions
- P7.2a: Basic Graphs and Data
- LiveMath Video: P7.2.a-LMVideo.mp4
- LiveMath Notebook: P7.2.a.the
- P7.2b: Comparison of Graphs
- LiveMath Video: P7.2.b-LMVideo.mp4
- LiveMath Notebook: P7.2.b.the
- P7.2c: Exponential Function Through Specified Points
- LiveMath Video: P7.2.c-Video.mp4
- LiveMath Video: P7.2.c-LMVideo.mp4
- LiveMath Notebook: P7.2.c.the
- P7.2d: Horseracing: Exponentials
- LiveMath Video: P7.2.d-LMVideo.mp4
- LiveMath Notebook: P7.2.d.the
- P7.2e: Horseracing: Power vs. Exponential
- LiveMath Video: P7.2.e-LMVideo.mp4
- LiveMath Notebook: P7.2.e.the
- P7.2f: Best Fit Formula for Exponential Functions
- LiveMath Video: P7.2.f-LMVideo.mp4
- LiveMath Notebook: P7.2.f.the
- P7.2g: Homework Problems
- LiveMath Notebook: P7.2.g.the
- P8: Logarithmic Functions
- P8.1: What is a Logarithm?
- P8.1a: Solving Power Function Equations: Roots
- LiveMath Video: P8.1.a-Video.mp4
- P8.1b: Solving Exponential Equations: ??
- LiveMath Video: P8.1.b-Video.mp4
- P8.1c: Manufacturing a Logarithm Function
- LiveMath Video: P8.1.c-LMVideo.mp4
- LiveMath Notebook: P8.1.c.the
- P8.1d: Inverse Functions
- LiveMath Video: P8.1.d-Video.mp4
- LiveMath Video: P8.1.d-LMVideo.mp4
- LiveMath Notebook: P8.1.d.the
- P8.1e: Definition of the Logarithm Function
- LiveMath Video: P8.1.e-Video.mp4
- P8.1f: Logarithm Dictionary
- LiveMath Video: P8.1.f-Video.mp4
- LiveMath Video: P8.1.f-LMVideo.mp4
- LiveMath Notebook: P8.1.f.the
- P8.1g: Homework Problems
- LiveMath Video: P8.1.g-Video.mp4
- LiveMath Notebook: P8.1.g.the
- P8.1h: Homework Problems
- LiveMath Notebook: P8.1.h.the
- P8.1i: Homework Problems
- P8.2: Examples of Logarithms
- P8.2a: Different Bases
- LiveMath Video: P8.2.a-Video.mp4
- LiveMath Video: P8.2.a-LMVideo.mp4
- LiveMath Notebook: P8.2.a.the
- P8.2b: Natural Base: Natural Logarithm
- LiveMath Video: P8.2.b-Video.mp4
- LiveMath Video: P8.2.b-LMVideo.mp4
- LiveMath Notebook: P8.2.b.the
- P8.2c: Converting To Different Bases
- LiveMath Video: P8.2.c-Video.mp4
- LiveMath Video: P8.2.c-LMVideo.mp4
- LiveMath Notebook: P8.2.c.the
- P8.2d: Laws of Exponents
- LiveMath Video: P8.2.d-Video.mp4
- LiveMath Video: P8.2.d-LMVideo.mp4
- LiveMath Notebook: P8.2.d.the
- P8.2e: Not Laws
- LiveMath Video: P8.2.e-Video.mp4
- LiveMath Video: P8.2.e-LMVideo.mp4
- LiveMath Notebook: P8.2.e.the
- P8.2f: Homework Problems
- LiveMath Notebook: P8.2.f.the
- P8.3: Graphs of Logarithmic Functions
- P8.3a: Basic Graphs
- LiveMath Video: P8.3.a-LMVideo.mp4
- LiveMath Notebook: P8.3.a.the
- P8.3b: Comparing Graphs
- LiveMath Video: P8.3.b-LMVideo.mp4
- LiveMath Notebook: P8.3.b.the
- P8.3c: Horserace: The Slowest Horse
- LiveMath Video: P8.3.c-LMVideo.mp4
- LiveMath Notebook: P8.3.c.the
- P8.4: Solving Logarithmic and Exponential Equations
- P8.4a: Solving by Graphing
- LiveMath Video: P8.4.a-LMVideo.mp4
- LiveMath Notebook: P8.4.a.the
- P8.4b: Applying Logarithms
- LiveMath Video: P8.4.b-Video.mp4
- LiveMath Video: P8.4.b-LMVideo.mp4
- LiveMath Notebook: P8.4.b.the
- P8.4c: Homework Problems
- LiveMath Video: P8.4.c-Video.mp4
- LiveMath Notebook: P8.4.c.the
- P8.4d: Homework Problems
- P8.5: Managing Exponential Data
- P9: Trigonometric Functions
- P9.1: Periodicity
- P9.1a: Periodic Data in Nature
- LiveMath Video: P9.1.a-LMVideo.mp4
- LiveMath Notebook: P9.1.a.the
- P9.1b: Measuring Data Periods
- LiveMath Video: P9.1.b-LMVideo.mp4
- LiveMath Notebook: P9.1.b.the
- P9.1c: Converting to a Circular Model
- LiveMath Video: P9.1.c-LMVideo.mp4
- LiveMath Notebook: P9.1.c.the
- P9.1d: Converting to a Translated Circular Model
- LiveMath Video: P9.1.d-LMVideo.mp4
- LiveMath Notebook: P9.1.d.the
- P9.1e: Homework Problems
- LiveMath Notebook: P9.1.e.the
- P9.2: Triangles and Circles
- P9.2a: Similar Triangles
- P9.2b: Triangle Embedded in a Circle
- P9.2c: The Ratios
- P9.2d: Primary Trigonometric Functions
- LiveMath Video: P9.2.d-Video.mp4
- LiveMath Video: P9.2.d-LMVideo.mp4
- LiveMath Notebook: P9.2.d.the
- P9.2e: Secondary Trigonometric Functions
- LiveMath Video: P9.2.e-LMVideo.mp4
- LiveMath Notebook: P9.2.e.the
- P9.2f: Degrees and Radians
- LiveMath Video: P9.2.f-LMVideo.mp4
- LiveMath Notebook: P9.2.f.the
- P9.2g: Most Important Triangles
- LiveMath Video: P9.2.g-Video.mp4
- LiveMath Notebook: P9.2.g.the
- P9.2h: Homework Problems
- LiveMath Video: P9.2.h-Video.mp4
- LiveMath Notebook: P9.2.h.the
- P9.3: Graphs of Trigonometric Functions
- P9.3a: Sine and Cosine
- LiveMath Video: P9.3.a-Video.mp4
- LiveMath Video: P9.3.a-LMVideo.mp4
- LiveMath Notebook: P9.3.a.the
- P9.3b: Tangent and Cotangent
- LiveMath Video: P9.3.b-LMVideo.mp4
- LiveMath Notebook: P9.3.b.the
- P9.3c: Secant and Cosecant
- LiveMath Video: P9.3.c-LMVideo.mp4
- LiveMath Notebook: P9.3.c.the
- P9.3d: Changing Periods
- LiveMath Video: P9.3.d-LMVideo.mp4
- LiveMath Notebook: P9.3.d.the
- P9.3e: Frequency
- LiveMath Video: P9.3.e-LMVideo.mp4
- LiveMath Notebook: P9.3.e.the
- P9.3f: Amplification
- LiveMath Video: P9.3.f-LMVideo.mp4
- LiveMath Notebook: P9.3.f.the
- P9.3g: Horizontal and Vertical Shifting
- LiveMath Video: P9.3.g-LMVideo.mp4
- LiveMath Notebook: P9.3.g.the
- P9.3h: General Sine and Cosine Functions
- LiveMath Video: P9.3.h-LMVideo.mp4
- LiveMath Notebook: P9.3.h.the
- P9.3i: Homework Problems
- LiveMath Notebook: P9.3.i.the
- P9.4: Identities
- P9.4a: Identities and Graphing
- LiveMath Video: P9.4.a-Video.mp4
- LiveMath Video: P9.4.a-LMVideo.mp4
- LiveMath Notebook: P9.4.a.the
- P9.4b: Basic Identities
- LiveMath Video: P9.4.b-LMVideo.mp4
- LiveMath Notebook: P9.4.b.the
- P9.4c: Pythagorean Identities
- LiveMath Video: P9.4.c-LMVideo.mp4
- LiveMath Notebook: P9.4.c.the
- P9.4d: Double Angle Identities
- LiveMath Video: P9.4.d-LMVideo.mp4
- LiveMath Notebook: P9.4.d.the
- P9.4e: Half-Angle Identities
- LiveMath Video: P9.4.e-LMVideo.mp4
- LiveMath Notebook: P9.4.e.the
- P9.4f: Applying Identities
- LiveMath Video: P9.4.f-LMVideo.mp4
- LiveMath Notebook: P9.4.f.the
- P9.4g: Homework Problems
- LiveMath Notebook: P9.4.g.the
- P9.5: Solving Trigonometric Equations
- P9.5a: Solving by Graphing
- LiveMath Video: P9.5.a-LMVideo.mp4
- LiveMath Notebook: P9.5.a.the
- P9.5b: Inverse Trigonometric Functions
- LiveMath Video: P9.5.b-Video.mp4
- LiveMath Video: P9.5.b-LMVideo.mp4
- LiveMath Notebook: P9.5.b.the
- P9.5c: Applying Inverses
- LiveMath Video: P9.5.c-LMVideo.mp4
- LiveMath Notebook: P9.5.c.the
- P9.5d: Homework Problems
- LiveMath Notebook: P9.5.d.the
- P9.6: Applications of Right Triangles
- P9.6a: Given Angle & Side, Solve Triangle
- LiveMath Video: P9.6.a-Video.mp4
- LiveMath Video: P9.6.a-LMVideo.mp4
- LiveMath Notebook: P9.6.a.the
- P9.6b: Given Sides, Find Angles
- LiveMath Video: P9.6.b-LMVideo.mp4
- LiveMath Notebook: P9.6.b.the
- P9.6c: Given Angles, Find Sides
- LiveMath Video: P9.6.c-LMVideo.mp4
- LiveMath Notebook: P9.6.c.the
- P9.6d: Find the Height of a Building
- LiveMath Video: P9.6.d-LMVideo.mp4
- LiveMath Notebook: P9.6.d.the
- P9.6e: Find the Height of a Mountain
- LiveMath Video: P9.6.e-LMVideo.mp4
- LiveMath Notebook: P9.6.e.the
- P9.6f: Find the Distance to a Star
- LiveMath Video: P9.6.f-Video.mp4
- P9.6g: Homework Problems
- LiveMath Notebook: P9.6.g.the
- P9.7: Laws of Sines and Cosines
- P9.7a: Non-Right Triangles
- LiveMath Video: P9.7.a-Video.mp4
- LiveMath Video: P9.7.a-LMVideo.mp4
- LiveMath Notebook: P9.7.a.the
- P9.7b: Law of Sines
- LiveMath Video: P9.7.b-Video.mp4
- LiveMath Video: P9.7.b-LMVideo.mp4
- LiveMath Notebook: P9.7.b.the
- P9.7c: Law of Cosines
- LiveMath Video: P9.7.c-Video.mp4
- LiveMath Video: P9.7.c-LMVideo.mp4
- LiveMath Notebook: P9.7.c.the
- P9.7d: Applications to Baseball
- P9.7e: More Applications
- P9.7f: Homework Problems
- LiveMath Notebook: P9.7.f.the
- P10: Systems of Equations
- P10.1: Systems of Linear 2D Equations
- P10.1a: Graphing
- LiveMath Video: P10.1.a-LMVideo.mp4
- LiveMath Notebook: P10.1.a.the
- P10.1b: Solving by Substitution
- LiveMath Video: P10.1.b-LMVideo.mp4
- LiveMath Notebook: P10.1.b.the
- P10.1c: Using Matrix Notation
- LiveMath Video: P10.1.c-LMVideo.mp4
- LiveMath Notebook: P10.1.c.the
- P10.1d: Homework Problems
- LiveMath Notebook: P10.1.d.the
- P10.2: Matrices
- P10.2a: Matrix Addition
- LiveMath Video: P10.2.a-LMVideo.mp4
- LiveMath Notebook: P10.2.a.the
- P10.2b: Matrix Multiplication
- LiveMath Video: P10.2.b-LMVideo.mp4
- LiveMath Notebook: P10.2.b.the
- P10.2c: Determinants
- LiveMath Video: P10.2.c-LMVideo.mp4
- LiveMath Notebook: P10.2.c.the
- P10.2d: Matrix Inverse
- LiveMath Video: P10.2.d-LMVideo.mp4
- LiveMath Notebook: P10.2.d.the
- P10.2e: Solving Linear Matrix Equation
- LiveMath Video: P10.2.e-LMVideo.mp4
- LiveMath Notebook: P10.2.e.the
- P10.2f: Homework Problems
- LiveMath Notebook: P10.2.f.the
- P10.3: Systems of Linear 3D Equations
- P10.3a: Graphing
- LiveMath Video: P10.3.a-LMVideo.mp4
- LiveMath Notebook: P10.3.a.the
- P10.3b: Solve via Substitution
- LiveMath Video: P10.3.b-LMVideo.mp4
- LiveMath Notebook: P10.3.b.the
- P10.3c: Solve Using Matrix Methods
- LiveMath Video: P10.3.c-LMVideo.mp4
- LiveMath Notebook: P10.3.c.the
- P10.3d: Different Solution Cases in 3D
- LiveMath Video: P10.3.d-LMVideo.mp4
- LiveMath Notebook: P10.3.d.the
- P10.3e: Homework Problems
- LiveMath Notebook: P10.3.e.the
- P10.4: Non-Linear Systems
- P10.4a: Non-Linear 2D Systems
- LiveMath Video: P10.4.a-LMVideo.mp4
- LiveMath Notebook: P10.4.a.the
- P10.4b: Non-Linear 3D Systems
- LiveMath Video: P10.4.b-LMVideo.mp4
- LiveMath Notebook: P10.4.b.the
- P10.4c: Homework Problems
- LiveMath Notebook: P10.4.c.the
- P11: Inequalities & Absolute Value
- P11.1: 1D Inequalities
- P11.1a: Basic 1D Inequalities
- LiveMath Video: P11.1.a-LMVideo.mp4
- LiveMath Notebook: P11.1.a.the
- P11.1b: Algebraic Operations on Inequalities
- LiveMath Video: P11.1.b-LMVideo.mp4
- LiveMath Notebook: P11.1.b.the
- P11.1c: Linear 1D Inequalities
- LiveMath Video: P11.1.c-LMVideo.mp4
- LiveMath Notebook: P11.1.c.the
- P11.1d: Quadratic 1D Inequalities
- LiveMath Video: P11.1.d-LMVideo.mp4
- LiveMath Notebook: P11.1.d.the
- P11.1e: Polynomial 1D Inequalities
- LiveMath Video: P11.1.e-LMVideo.mp4
- LiveMath Notebook: P11.1.e.the
- P11.1f: General 1D Inequalities
- LiveMath Video: P11.1.f-LMVideo.mp4
- LiveMath Notebook: P11.1.f.the
- P11.1g: Homework Problems
- LiveMath Notebook: P11.1.g.the
- P11.2: 2D Inequalities
- P11.2a: Linear 2D Inequality
- LiveMath Video: P11.2.a-LMVideo.mp4
- LiveMath Notebook: P11.2.a.the
- P11.2b: Quadratic 2D Inequality
- LiveMath Video: P11.2.b-LMVideo.mp4
- LiveMath Notebook: P11.2.b.the
- P11.2c: Polynomial 2D Inequality
- LiveMath Video: P11.2.c-LMVideo.mp4
- LiveMath Notebook: P11.2.c.the
- P11.2d: General 2D Inequality
- LiveMath Video: P11.2.d-LMVideo.mp4
- LiveMath Notebook: P11.2.d.the
- P11.2e: Homework Problems
- LiveMath Notebook: P11.2.e.the
- P11.3: Systems of 2D Inequalities
- P11.3a: System of 2D Linear Inequalities
- LiveMath Video: P11.3.a-LMVideo.mp4
- LiveMath Notebook: P11.3.a.the
- P11.3b: System of 2D General Inequalities
- LiveMath Video: P11.3.b-LMVideo.mp4
- LiveMath Notebook: P11.3.b.the
- P11.3c: Homework Problems
- LiveMath Notebook: P11.3.c.the
- P11.4: Absolute Value
- P11.4a: 1D Absolute Value Equations
- LiveMath Video: P11.4.a-LMVideo.mp4
- LiveMath Notebook: P11.4.a.the
- P11.4b: 1D General Absolute Value Equations
- LiveMath Video: P11.4.b-LMVideo.mp4
- LiveMath Notebook: P11.4.b.the
- P11.4c: 1D Linear Absolute Value Inequality
- LiveMath Video: P11.4.c-LMVideo.mp4
- LiveMath Notebook: P11.4.c.the
- P11.4d: 1D General Absolute Value Inequalities
- LiveMath Video: P11.4.d-LMVideo.mp4
- LiveMath Notebook: P11.4.d.the
- P11.4e: 2D Linear Absolute Value
- LiveMath Video: P11.4.e-LMVideo.mp4
- LiveMath Notebook: P11.4.e.the
- P11.4f: 2D General Absolute Value Inequalities
- LiveMath Video: P11.4.f-LMVideo.mp4
- LiveMath Notebook: P11.4.f.the
- P11.4g: Homework Problems
- LiveMath Notebook: P11.4.g.the
- P11.5: 3D Inequalities
- P12: Complex Numbers & Vectors
- P12.1: Complex Numbers Part Deux
- P12.1a: General Properties
- LiveMath Video: P12.1.a-Video.mp4
- LiveMath Video: P12.1.a-LMVideo.mp4
- LiveMath Notebook: P12.1.a.the
- P12.1b: Addition/Subtraction of Complex Numbers
- LiveMath Video: P12.1.b-Video.mp4
- LiveMath Video: P12.1.b-LMVideo.mp4
- LiveMath Notebook: P12.1.b.the
- P12.1c: Multiplication/Division of Complex Numbers
- LiveMath Video: P12.1.c-Video.mp4
- LiveMath Video: P12.1.c-LMVideo.mp4
- LiveMath Notebook: P12.1.c.the
- P12.1d: Plotting Complex Numbers
- LiveMath Video: P12.1.d-Video.mp4
- LiveMath Video: P12.1.d-LMVideo.mp4
- LiveMath Notebook: P12.1.d.the
- P12.1e: Homework Problems
- LiveMath Notebook: P12.1.e.the
- P12.1f: DeMoivre's Theorem
- P12.2: Vectors
- P12.2a: Vector Basics
- LiveMath Video: P12.2.a-LMVideo.mp4
- LiveMath Notebook: P12.2.a.the
- P12.2b: Notation
- LiveMath Video: P12.2.b-LMVideo.mp4
- LiveMath Notebook: P12.2.b.the
- P12.2c: Adding Vectors
- LiveMath Video: P12.2.c-LMVideo.mp4
- LiveMath Notebook: P12.2.c.the
- P12.2d: Subtracting Vectors
- LiveMath Video: P12.2.d-LMVideo.mp4
- LiveMath Notebook: P12.2.d.the
- P12.2e: Vectors in 3D
- LiveMath Video: P12.2.e-LMVideo.mp4
- LiveMath Notebook: P12.2.e.the
- P12.2f: Homework Problems
- LiveMath Notebook: P12.2.f.the
- P12.2g: Dot Product
- P12.3: Polar Coordinates
- P12.3a: Point in 2D in Polar Coordinates
- LiveMath Video: P12.3.a-LMVideo.mp4
- LiveMath Notebook: P12.3.a.the
- P12.3b: Conversion Formula
- LiveMath Video: P12.3.b-LMVideo.mp4
- LiveMath Notebook: P12.3.b.the
- P12.3c: Polar Equation
- LiveMath Video: P12.3.c-LMVideo.mp4
- LiveMath Notebook: P12.3.c.the
- P12.3d: Graphing Polar Equations
- LiveMath Video: P12.3.d-LMVideo.mp4
- LiveMath Notebook: P12.3.d.the
- P12.3e: Homework Problems
- LiveMath Notebook: P12.3.e.the
- P13: Analytic Geometry
- P13.1: Slice The Cone
- P13.1a: The Cone
- LiveMath Video: P13.1.a-LMVideo.mp4
- LiveMath Notebook: P13.1.a.the
- P13.1b: Slice to Parabola
- LiveMath Video: P13.1.b-LMVideo.mp4
- LiveMath Notebook: P13.1.b.the
- P13.1c: Slice To Ellipse
- LiveMath Video: P13.1.c-LMVideo.mp4
- LiveMath Notebook: P13.1.c.the
- P13.1d: Slice to Hyperbola
- LiveMath Video: P13.1.d-LMVideo.mp4
- LiveMath Notebook: P13.1.d.the
- P13.1e: Slice To Line
- LiveMath Video: P13.1.e-LMVideo.mp4
- LiveMath Notebook: P13.1.e.the
- P13.1f: Homework Problems
- LiveMath Notebook: P13.1.f.the
- P13.2: Ellipsi
- P13.2a: General Equation of the Simple Ellipse
- LiveMath Video: P13.2.a-LMVideo.mp4
- LiveMath Notebook: P13.2.a.the
- P13.2b: Foci
- LiveMath Video: P13.2.b-Video.mp4
- LiveMath Video: P13.2.b-LMVideo.mp4
- LiveMath Notebook: P13.2.b.the
- P13.2c: Rotated Axes
- LiveMath Video: P13.2.c-LMVideo.mp4
- LiveMath Notebook: P13.2.c.the
- P13.2d: Conic Slice to Rotated Axis Ellipse
- LiveMath Video: P13.2.d-LMVideo.mp4
- LiveMath Notebook: P13.2.d.the
- P13.2e: Homework Problems
- LiveMath Notebook: P13.2.e.the
- P13.3: Hyperbolae
- P13.3a: General Equation of the Simple Hyperbola
- LiveMath Video: P13.3.a-LMVideo.mp4
- LiveMath Notebook: P13.3.a.the
- P13.3b: Foci
- LiveMath Video: P13.3.b-LMVideo.mp4
- LiveMath Notebook: P13.3.b.the
- P13.3c: Rotated Axes
- LiveMath Video: P13.3.c-LMVideo.mp4
- LiveMath Notebook: P13.3.c.the
- P13.3d: Hyperbolae in Nature
- LiveMath Video: P13.3.d-LMVideo.mp4
- LiveMath Notebook: P13.3.d.the
- P13.3e: Homework Problems
- LiveMath Notebook: P13.3.e.the
- P13.4: Parabolae
- P13.4a: General Equation of the Simple Parabola
- LiveMath Video: P13.4.a-LMVideo.mp4
- LiveMath Notebook: P13.4.a.the
- P13.4b: Focus and Directrix
- LiveMath Video: P13.4.b-LMVideo.mp4
- LiveMath Notebook: P13.4.b.the
- P13.4c: Rotation of Axes
- LiveMath Video: P13.4.c-LMVideo.mp4
- LiveMath Notebook: P13.4.c.the
- P13.4d: Geometric Properties of Parabolae
- LiveMath Video: P13.4.d-LMVideo.mp4
- LiveMath Notebook: P13.4.d.the
- P13.4e: Homework Problems
- LiveMath Notebook: P13.4.e.the
- P13.5: Polar Equations of Conics
- P13.5a: General Polar Equation of a Simple Conic
- P13.5b: Rotation of Axes
- P13.5c: Homework Problems
- LiveMath Notebook: P13.5.c.the
- P13.6: Parametric Equations
- P13.6a: General 2D Parametric Curves
- LiveMath Video: P13.6.a-LMVideo.mp4
- LiveMath Notebook: P13.6.a.the
- P13.6b: Parametric Description of Parabolae
- LiveMath Video: P13.6.b-LMVideo.mp4
- LiveMath Notebook: P13.6.b.the
- P13.6c: Parametric Description of Ellipsi
- LiveMath Video: P13.6.c-LMVideo.mp4
- LiveMath Notebook: P13.6.c.the
- P13.6d: Parametric Description of Hyperbolae
- LiveMath Video: P13.6.d-LMVideo.mp4
- LiveMath Notebook: P13.6.d.the
- P13.6e: Projectile Motion
- LiveMath Video: P13.6.e-LMVideo.mp4
- LiveMath Notebook: P13.6.e.the
- P13.6f: Interesting Parametric Curves
- LiveMath Video: P13.6.f-LMVideo.mp4
- LiveMath Notebook: P13.6.f.the
- P13.6g: 3D Parametric Curves
- LiveMath Video: P13.6.g-LMVideo.mp4
- LiveMath Notebook: P13.6.g.the
- P13.6h: Homework Problems
- LiveMath Notebook: P13.6.h.the
- P14: Sequences and Series
- P14.1: Sequences
- P14.1a: Basic Sequences
- LiveMath Video: P14.1.a-LMVideo.mp4
- LiveMath Notebook: P14.1.a.the
- P14.1b: Recursive Sequences
- LiveMath Video: P14.1.b-LMVideo.mp4
- LiveMath Notebook: P14.1.b.the
- P14.1c: Arithmetic Sequences
- LiveMath Video: P14.1.c-LMVideo.mp4
- LiveMath Notebook: P14.1.c.the
- P14.1d: Geometric Sequences
- LiveMath Video: P14.1.d-LMVideo.mp4
- LiveMath Notebook: P14.1.d.the
- P14.1e: Sequence Limits
- LiveMath Video: P14.1.e-LMVideo.mp4
- LiveMath Notebook: P14.1.e.the
- P14.1f: Homework Problems
- LiveMath Notebook: P14.1.f.the
- P14.2: Summation of Sequences
- P14.2a: Summation Notation
- LiveMath Video: P14.2.a-LMVideo.mp4
- LiveMath Notebook: P14.2.a.the
- P14.2b: Numerical Experiments & Conclusive Formulae
- LiveMath Video: P14.2.b-LMVideo.mp4
- LiveMath Notebook: P14.2.b.the
- P14.2c: Arithmetic Series
- LiveMath Video: P14.2.c-LMVideo.mp4
- LiveMath Notebook: P14.2.c.the
- P14.2d: Geometric Series
- LiveMath Video: P14.2.d-LMVideo.mp4
- LiveMath Notebook: P14.2.d.the
- P14.2e: When Computers Fail
- LiveMath Video: P14.2.e-LMVideo.mp4
- LiveMath Notebook: P14.2.e.the
- P14.2f: Homework Problems
- LiveMath Notebook: P14.2.f.the
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One of the original Calculus Reform projects is the Calculus&Mathematica series from The
Ohio State University and The University of Illinois at Champaign-Urbana. Developed nearly 40 years ago,
C&M remains one of the most ground-breaking and non-traditional calculus reform project, and still in
active use in the NetMath program at UIUC.
Calculus&LiveMath is an e-text ported (with some enhancments) from the original Mathematica to LiveMath format, with additional commentary screencast movies, and a few hand-based calculation movies for key topics. This e-text serves as the core curriculum for the Distance Calculus Engineering-based first year calculus curriculum. This first book in the C&LM series is entitled: Growth, concentrating on differential calculus. Non-standard topics include a concentration on Percentage Growth Rate, a topic not found in most textbooks. Limits - usually the cornerstone of Calculus I - are not to be found, which is a fundamental tenet of C&M, interested instead to study patterns of growth, families of functions, and physical applications. |
>>>Show Table of Contents (With Demo Sections & Content)
- M1: 1.01: Growth
- M1.1: 1.01 - Basics
- M1.1a: 1.01.B1: Growth of Line Functions
- M1.1b: 1.01.B2: Growth of Power Functions
- M1.1c: 1.01.B3: Growth of Exponential Functions
- M1.1d: 1.01.B4: Dominance in the Global Scale
- M1.1e: 1.01.B5: Percentage Growth Rate and Dominance in the Global Scale
- LiveMath Video: M1.1.e-LMVideo.mp4
- LiveMath Video: 1.01.B5.mp4
- LiveMath Notebook: 1.01.B5.the
- M1.2: 1.01 - Tutorials
- M1.2a: 1.01.T1: Global Scale
- LiveMath Video: M1.2.a-LMVideo.mp4
- LiveMath Video: 1.01.T1.mp4
- LiveMath Notebook: 1.01.T1.the
- M1.2b: 1.01.T2: Linear Models
- LiveMath Video: M1.2.b-LMVideo.mp4
- LiveMath Video: 1.01.T2.mp4
- LiveMath Notebook: 1.01.T2.the
- M1.2c: 1.01.T3: Data Analysis and Compromise Lines
- LiveMath Video: M1.2.c-LMVideo.mp4
- LiveMath Video: 1.01.T3.mp4
- LiveMath Notebook: 1.01.T3.the
- M1.2d: 1.01.T4: Functions Given by Data Lists: Interpolation and Analysis
- LiveMath Video: M1.2.d-LMVideo.mp4
- LiveMath Video: 1.01.T4.mp4
- LiveMath Notebook: 1.01.T4.the
- M1.2e: 1.01.T5: The Trig Functions sin(x) and cos(x)
- LiveMath Video: M1.2.e-LMVideo.mp4
- LiveMath Video: 1.01.T5.mp4
- LiveMath Notebook: 1.01.T5.the
- M1.2f: 1.01.T6: Another Linear Model: Drinking and Driving
- LiveMath Video: M1.2.f-LMVideo.mp4
- LiveMath Video: 1.01.T6.mp4
- LiveMath Notebook: 1.01.T6.the
- M1.3: 1.01 - Give It A Try
- M1.3a: 1.01.G1: Line Fundamentals
- LiveMath Video: M1.3.a-LMVideo.mp4
- LiveMath Video: 1.01.G1.e-Help.mp4
- LiveMath Notebook: M1.3.a.the
- M1.3b: 1.01.G2: Global Scale
- LiveMath Notebook: 1.01.G2.the
- M1.3c: 1.01.G3: Linear Models
- LiveMath Notebook: 1.01.G3.the
- M1.3d: 1.01.G4: Compromise lines through data
- LiveMath Notebook: 1.01.G4.the
- M1.3e: 1.01.G5: Green Globs
- LiveMath Notebook: 1.01.G5.the
- M1.3f: 1.01.G6: Percentage Growth
- LiveMath Notebook: 1.01.G6.the
- M1.3g: 1.01.G7: Functions given by data lists: Interpolation and analysis
- LiveMath Notebook: M1.3.g.the
- M1.3h: 1.01.G8: Another linear model: Drinking and Driving
- LiveMath Notebook: 1.01.G8.the
- M1.3i: 1.01.G9: Interpolation and Approximation
- LiveMath Notebook: 1.01.G9.the
- M1.4: 1.04 - Literacy
- M2: 1.02: Exponential
- M2.1: 1.02 - Basics
- M2.1a: 1.02.B1: The natural base e and the natural logarithm
- LiveMath Video: 1.02.B1.mp4
- LiveMath Notebook: 1.02.B1.the
- M2.1b: 1.02.B2: Percentage growth of exponential functions: Doubling time and half life
- LiveMath Video: 1.02.B2.mp4
- LiveMath Notebook: 1.02.B2.the
- M2.1c: 1.02.B3: Unnatural bases
- LiveMath Video: 1.02.B3.mp4
- LiveMath Notebook: 1.02.B3.the
- M2.2: 1.02 - Tutorials
- M2.2a: 1.02.T1: Exponential models
- LiveMath Video: 1.02.T1.mp4
- LiveMath Notebook: 1.02.T1.the
- M2.2b: 1.02.T2: Exponential data
- LiveMath Video: 1.02.T2.mp4
- LiveMath Notebook: 1.02.T2.the
- M2.2c: 1.02.T3: e and Finance
- LiveMath Video: 1.02.T3.mp4
- LiveMath Notebook: 1.02.T3.the
- M2.3: 1.02 - Give It A Try
- M2.3a: 1.02.G1: Exponential growth
- LiveMath Notebook: 1.02.G1.the
- M2.3b: 1.02.G2: Steady growth versus steady percentage growth
- LiveMath Notebook: 1.02.G2.the
- M2.3c: 1.02.G3: Exponential models
- LiveMath Notebook: 1.02.G3.the
- M2.3d: 1.02.G4: Exponential data analysis
- LiveMath Video: M2.3.d-LMVideo.mp4
- LiveMath Video: 1.02.G4-Help1.mp4
- LiveMath Notebook: 1.02.G4.the
- M2.3e: 1.02.G5: Your money
- LiveMath Notebook: 1.02.G5.the
- M2.3f: 1.02.G6: Compounding every instant
- LiveMath Notebook: 1.02.G6.the
- M2.3g: 1.02.G7: Law and order
- LiveMath Notebook: 1.02.G7.the
- M2.3h: 1.02.G8: Unnatural bases
- LiveMath Notebook: 1.02.G8.the
- M2.3i: 1.02.G9: Reflecting patterns and wandering points
- LiveMath Notebook: 1.02.G9.the
- M2.4: 1.02 - Literacy
- M2.4a: 1.02 - Literacy Sheet 2-4, 9-12, 17
- LiveMath Notebook: 1.02.Literacy.the
- M3: 1.03: Growth Rates
- M3.1: 1.03 - Basics
- M3.1a: 1.03.B1: Instantaneous growth rates
- LiveMath Video: 1.03.B1.mp4
- LiveMath Notebook: 1.03.B1.the
- M3.1b: 1.03.B2: Instantaneous Growth Rate of Power Functions
- LiveMath Video: 1.03.B2.mp4
- LiveMath Notebook: 1.03.B2.the
- M3.1c: 1.03.B3: The Instantaneous Growth Rate of Trig Functions
- LiveMath Video: 1.03.B3.mp4
- LiveMath Notebook: 1.03.B3.the
- M3.1d: 1.03.B4: The Instantaneous Growth Rate of Exponential and Log Functions
- LiveMath Video: 1.03.B4.mp4
- LiveMath Notebook: 1.03.B4.the
- M3.2: 1.03 - Tutorials
- M3.2a: 1.03.T1: Average growth rate versus instantaneous growth rate
- M3.2b: 1.03.T2: Using the instantaneous growth rate f'(x) to predict the plot of f(x)
- M3.2c: 1.03.T3: Spread of disease
- LiveMath Video: 1.03.T3.mp4
- LiveMath Notebook: 1.03.T3.the
- M3.2d: 1.03.T4: Instantaneous growth rates in context
- LiveMath Video: 1.03.T4.mp4
- LiveMath Notebook: 1.03.T4.the
- M3.3: 1.03 - GiveItATry
- M3.3a: 1.03.G1: Relating f(x) and f'(x)
- LiveMath Notebook: 1.03.G1.the
- M3.3b: 1.03.G2: Explaining LiveMath Derivative Output
- LiveMath Notebook: 1.03.G2.the
- M3.3c: 1.03.G3: Approximation of the instantaneous growth rate f'(x) by average growth rates
- LiveMath Notebook: 1.03.G3.the
- M3.3d: 1.03.G4: Using the instantaneous growth rate f'(x) to predict the plot of f(x)
- LiveMath Video: 1.03.G4.mp4
- LiveMath Notebook: 1.03.G4.the
- M3.3e: 1.03.G5: Graphics action
- LiveMath Notebook: 1.03.G5.the
- M3.3f: 1.03.G6: Up and down, maximum and minimum
- LiveMath Video: M3.3.f-LMVideo.mp4
- LiveMath Video: 1.03.G6.Help.mp4
- LiveMath Notebook: 1.03.G6.the
- M3.3g: 1.03.G7: Spread of disease
- LiveMath Notebook: 1.03.G7.the
- M3.3h: 1.03.G8: Average growth rate versus instantaneous growth rate
- LiveMath Notebook: 1.03.G8.the
- M3.3i: 1.03.G9: Why folks study the instantaneous growth rate instead of instantaneous growth
- LiveMath Notebook: 1.03.G9.the
- M3.4: 1.03 - Literacy
- M3.4a: 1.03.LiteracySheet
- LiveMath Notebook: 1.03.Literacy.the
- M4: 1.04: Rules
- M4.1: 1.04 - Basics
- M4.1a: 1.04.B1: Derivatives, instantaneous growth rates, f'(x) and d/dx (f(x))
- LiveMath Video: 1.04.B1.mp4
- LiveMath Notebook: 1.04.B1.the
- M4.1b: 1.04.B2: The Chain Rule
- LiveMath Video: 1.04.B2.mp4
- LiveMath Notebook: 1.04.B2.the
- M4.1c: 1.04.B3: General rules for taking derivatives
- LiveMath Video: 1.04.B3.mp4
- LiveMath Notebook: 1.04.B3.the
- M4.1d: 1.04.B4: Using the logarithm to calculational advantage
- LiveMath Video: 1.04.B4.mp4
- LiveMath Notebook: 1.04.B4.the
- M4.1e: 1.04.B5: The instantaneous percentage growth rate of a positive function
- LiveMath Video: 1.04.B5.mp4
- LiveMath Notebook: 1.04.B5.the
- M4.1f: 1.04.B6: Exponential growth dominates power growth and power growth dominates logarithmic growth
- LiveMath Video: 1.04.B6.mp4
- LiveMath Notebook: 1.04.B6.the
- M4.2: 1.04 - Tutorials
- M4.2a: 1.04.T1: Practicing with the chain rule
- LiveMath Video: M4.2.a-LMVideo.mp4
- LiveMath Video: M4.2.a-Video.mp4
- LiveMath Video: M4.2.b-LMVideo.mp4
- LiveMath Video: 1.04.T1-Video.mp4
- LiveMath Video: 1.04.T1-LMVideo.mp4
- LiveMath Notebook: 1.04.T1.the
- M4.2b: 1.04.T2: Practicing with the chain rule, the product rule, and the power rule
- LiveMath Video: M4.2.b-Video.mp4
- LiveMath Video: M4.2.b-LMVideo.mp4
- LiveMath Video: 1.04.T2-Video.mp4
- LiveMath Video: 1.04.T2-LMVideo.mp4
- LiveMath Notebook: 1.04.T2.the
- M4.2c: 1.04.T3: Linear dimension: length, area, volume and weight
- LiveMath Notebook: 1.04.T3.the
- M4.3: 1.04 - Give It A Try
- M4.3a: 1.04.G1: Practicing with the chain rule
- LiveMath Notebook: 1.04.G1.the
- M4.3b: 1.04.G2: Practicing with the chain rule, the product rule, and the power rule
- LiveMath Notebook: M4.3.b.the
- M4.3c: 1.04.G3: Global scale
- LiveMath Notebook: 1.04.G3.the
- M4.3d: 1.04.G4: Exponential functions and their constant percentage growth rate
- LiveMath Notebook: 1.04.G4.the
- M4.3e: 1.04.G5: Relating the plots of f(x) and f'(x)
- LiveMath Notebook: 1.04.G5.the
- M4.3f: 1.04.G6: 100 ln(f(x)) and the instantaneous percentage growth rate
- LiveMath Notebook: 1.04.G6.the
- M4.3g: 1.04.G7: Linear dimension: Length, area, volume, and weight
- LiveMath Notebook: 1.04.G7.the
- M4.3h: 1.04.G8: Interest compounded every instant versus interest compounded every month
- LiveMath Notebook: 1.04.G8.the
- M4.4: 1.04 - Literacy
- M4.4a: 1.04.LiteracySheet
- LiveMath Notebook: 1.04.Literacy.the
- M5: 1.05: Tools
- M5.1: 1.05 - Basics
- M5.1a: 1.05.B1: Using the derivative for finding maximum values and minimum values
- LiveMath Video: 1.05.B1.mp4
- LiveMath Notebook: 1.05.B1.the
- M5.1b: 1.05.B2: Using the derivative to help to get a good representative plot
- LiveMath Notebook: 1.05.B2.the
- M5.1c: 1.05.B3: Using the derivative to fit data by curves: Line fit and Sine and Cosine wave fit
- LiveMath Notebook: 1.05.B3.the
- M5.2: 1.05 - Tutorials
- M5.2a: 1.05.T1: Highest and lowest points on the graph
- LiveMath Video: M5.2.a-LMVideo.mp4
- LiveMath Video: 1.05-FindRootFix-H264.mp4
- LiveMath Notebook: 1.05.T1.the
- M5.2b: 1.05.T2: Approximations by polynomials; Approximations by Sine and Cosine waves
- LiveMath Notebook: 1.05.T2.the
- M5.2c: 1.05.T3: Fish gotta swim: The least energy
- LiveMath Notebook: 1.05.T3.the
- M5.2d: 1.05.T4: Designing a box
- LiveMath Notebook: 1.05.T4.the
- M5.2e: 1.05.T5: Largest and smallest
- LiveMath Notebook: 1.05.T5.the
- M5.3: 1.05 - Give It A Try
- M5.3a: 1.05.G1: Good representative plots
- LiveMath Notebook: 1.05.G1.the
- M5.3b: 1.05.G2: Highest and lowest points on the graph
- M5.3c: 1.05.G3: Approximations by polynomials and approximations by Sine and Cosine waves
- M5.3d: 1.05.G4: Oil slicks
- LiveMath Video: 1.05.G3.Help.mp4
- LiveMath Notebook: 1.05.G4.the
- M5.3e: 1.05.G5: The second derivative, f''(x)
- LiveMath Notebook: 1.05.G5.the
- M5.3f: 1.05.G6: Driving the big Mack trucks
- LiveMath Notebook: 1.05.G6.the
- M5.3g: 1.05.G7: The space shuttle Challenger and its O-rings
- LiveMath Video: M5.3.g-LMVideo.mp4
- LiveMath Video: 1.05.G7-JV1a.mp4
- LiveMath Notebook: 1.05.G7.the
- M5.3h: 1.05.G8: Management analysis
- LiveMath Notebook: 1.05.G8.the
- M5.3i: 1.05.G9: Up then down for x^t/e^x
- LiveMath Notebook: 1.05.G9.the
- M5.3j: 1.05.G10: Other max-min problems
- LiveMath Video: M5.3.j-LMVideo.mp4
- LiveMath Video: 1.05.G10-Hint1.mp4
- LiveMath Notebook: 1.05.G10.the
- M5.3k: 1.05.G11: At what age is the Bernese Mountain Dog growing the fastest?
- LiveMath Notebook: 1.05.G11.the
- M5.4: 1.05 - Literacy
- M5.4a: 1.05.LiteracySheet
- LiveMath Notebook: 1.05.Literacy.the
- M6: 1.06: DiffEq
- M6.1: 1.06 - Basics
- M6.1a: 1.06.B1: The most important of all differential equations: y'(x) = r*y(x)
- LiveMath Video: 1.06.B1.mp4
- LiveMath Notebook: 1.06.B1.the
- M6.1b: 1.06.B2: The logistic differential equation
- LiveMath Video: 1.06.B2.mp4
- LiveMath Notebook: 1.06.B2.the
- M6.1c: 1.06.B3: Logistic growth is controlled growth
- LiveMath Video: 1.06.B3.mp4
- LiveMath Notebook: 1.06.B3.the
- M6.1d: 1.06.B4: The differential equation y'(x) = r*y(x) + b
- LiveMath Video: 1.06.B4.mp4
- LiveMath Notebook: 1.06.B4.the
- M6.2: 1.06 - Tutorials
- M6.2a: 1.06.T1: Radioactive decay and carbon dating
- LiveMath Notebook: 1.06.T1.the
- M6.2b: 1.06.T2: Socking money away
- LiveMath Notebook: 1.06.T2.the
- M6.2c: 1.06.T3: Wal-Mart: Exponential or logistic growth?
- LiveMath Notebook: 1.06.T3.the
- M6.2d: 1.06.T4: Pollution elimination
- LiveMath Notebook: 1.06.T4.the
- M6.3: 1.06 - Give It a Try
- M6.3a: 1.06.G1: Quick calculations
- LiveMath Notebook: 1.06.G1.the
- M6.3b: 1.06.G2: Data analysis
- LiveMath Notebook: 1.06.G2.the
- M6.3c: 1.06.G3: Logistic growth versus exponential growth
- LiveMath Notebook: 1.06.G3.the
- M6.3d: 1.06.G4: Why do they turn out this way?
- LiveMath Notebook: 1.06.G4.the
- M6.3e: 1.06.G5: Other differential equations
- LiveMath Notebook: 1.06.G5.the
- M6.3f: 1.06.G6: Managing your money
- LiveMath Notebook: MM6.3.f.the
- M6.3g: 1.06.G7: Which animals grow faster after their birth than they are growing at the time of their birth?
- LiveMath Notebook: 1.06.G7.the
- M6.3h: 1.06.G8: Newton's law of cooling: How a differential equation can help you enjoy your favorite cooled beverage
- LiveMath Notebook: 1.06.G8.the
- M6.3i: 1.06.G9: Pressure altimeters
- LiveMath Notebook: 1.06.G9.the
- M6.4: 1.06 - Literacy
- M6.4a: 1.06.LiteracySheet
- LiveMath Notebook: 1.06.Literacy.the
- M7: 1.07: Races
- M7.1: 1.07 - Basics
- M7.1a: 1.07.B1: The Race Track Principle
- LiveMath Notebook: 1.07.B1.the
- M7.1b: 1.07.B2: The Race Track Principle and differential equations
- LiveMath Notebook: 1.07.B2.the
- M7.1c: 1.07.B3: The Race Track Principle and Euler's method of faking the plot of the solution of a differential equation
- LiveMath Notebook: 1.07.B3.the
- M7.1d: 1.07.B4: Tangent lines and the Race Track Principle
- LiveMath Notebook: 1.07.B4.the
- M7.2: 1.07 - Tutorials
- M7.2a: 1.07.T1: Using Euler's method to fake the plot of f(x) given f ' (x) and one value of f(x)
- LiveMath Notebook: 1.07.T1.the
- M7.2b: 1.07.T2: Using the Race Track Principle to help to estimate roundoff error
- LiveMath Notebook: 1.07.T2.the
- M7.2c: 1.07.T3: If f''(x) is always positive then tangent lines run below the curve
- LiveMath Notebook: 1.07.T3.the
- M7.3: 1.07 - Give It a Try
- M7.3a: 1.07.G1: Versions of the Race Track Principle
- LiveMath Notebook: 1.07.G1.the
- M7.3b: 1.07.G2: Running Euler's faker
- LiveMath Notebook: 1.07.G2.the
- M7.3c: 1.07.G3: The Race Track Principle and differential equations
- LiveMath Notebook: 1.07.G3.the
- M7.3d: 1.07.G4: The error function Erf(x)
- LiveMath Notebook: 1.07.G4.the
- M7.3e: 1.07.G5: Round off
- LiveMath Notebook: 1.07.G5.the
- M7.3f: 1.07.G6: Calculating accurate values of ln(x)
- LiveMath Notebook: 1.07.G6.the
- M7.3g: 1.07.G7: Calculating accurate values of e^x
- LiveMath Notebook: 1.07.G7.the
- M7.3h: 1.07.G8: Euler's faker and the second derivative
- LiveMath Notebook: 1.07.G8.the
- M7.3i: 1.07.G9: Inequalities
- LiveMath Notebook: 1.07.G9.the
- M7.3j: 1.07.G10: The Law of the Mean
- LiveMath Notebook: 1.07.G10.the
- M7.3k: 1.07.G11: If f''(x) is never positive then tangent lines run above the curve; At points of inflection, the tangent line crosses the curve
- LiveMath Notebook: 1.07.G11.the
- M7.4: 1.07 - Literacy
- M7.4a: 1.07.LiteracySheet
- LiveMath Notebook: 1.07.Literacy.the
- M8: 1.08: DiffEq2
- M8.1: 1.08 - Basics
- M8.1a: 1.08.B1: Euler's faker and LiveMath's Runge-Kutta faker
- LiveMath Notebook: 1.08.B1.the
- M8.1b: 1.08.B2: Simultaneous differential equations: The predator-prey model
- LiveMath Notebook: 1.08.B2.the
- M8.2: 1.08 - Tutorials
- M8.2a: 1.08.T1: Using a differential equation to analyze Bubba's toot
- LiveMath Notebook: 1.08.T1.the
- M8.2b: 1.08.T2: Analysis of the predator-prey model
- LiveMath Notebook: 1.08.T2.the
- M8.3: 1.08 - Give It a Try
- M8.3a: 1.08.G1: Variable interest rates
- LiveMath Notebook: 1.08.G1.the
- M8.3b: 1.08.G2: Drinking and driving
- LiveMath Notebook: 1.08.G2.the
- M8.3c: 1.08.G3: Further analysis of the predator-prey model
- LiveMath Notebook: 1.08.G3.the
- M8.3d: 1.08.G4: The drug equation
- LiveMath Notebook: 1.08.G4.the
- M8.3e: 1.08.G5: War games
- LiveMath Notebook: 1.08.G5.the
- M8.3f: 1.08.G6: Logistic harvesting
- LiveMath Notebook: 1.08.G6.the
- M8.3g: 1.08.G7: The logistic predator-prey model
- LiveMath Notebook: 1.08.G7.the
- M8.3h: 1.08.G8: Epidemics
- LiveMath Notebook: 1.08.G8.the
- M8.3i: 1.08.G9: Hints of chaos
- LiveMath Notebook: 1.08.G9.the
- M8.4: 1.08 - Literacy
- M8.4a: 1.08.LiteracySheet
- LiveMath Notebook: 1.08.Literacy.the
- M9: 1.09: ParamPlot
- M9.1: 1.09 - Basics
- M9.1a: 1.09.B1: Parametric plots in two dimensions: Circular parameters
- LiveMath Video: 1.09.B1.mp4
- LiveMath Notebook: 1.09.B1.the
- M9.1b: 1.09.B2: Parametric plots of curves in three dimensions
- LiveMath Video: 1.09.B2.mp4
- LiveMath Notebook: 1.09.B2.the
- M9.1c: 1.09.B3: Parametric plots of surfaces in three dimensions
- LiveMath Video: 1.09.B3.mp4
- LiveMath Notebook: 1.09.B3.the
- M9.1d: 1.09.B4: Derivatives for curves given parametrically: The cycloid
- LiveMath Video: 1.09.B4.mp4
- LiveMath Notebook: 1.09.B4.the
- M9.2: 1.09 - Tutorials
- M9.2a: 1.09.T1: Parametric plotting for projectile motion
- LiveMath Video: 1.09.T1.mp4
- LiveMath Notebook: 1.09.T1.the
- M9.2b: 1.09.T2: Parametric plotting for designing a cam
- LiveMath Video: 1.09.T2.mp4
- LiveMath Notebook: 1.09.T2.the
- M9.2c: 1.09.T3: Parametric plotting of the predator-prey model
- LiveMath Video: 1.09.T3.mp4
- LiveMath Notebook: 1.09.T3.the
- M9.2d: 1.09.T4: Quick calculations
- LiveMath Video: 1.09.T4.mp4
- LiveMath Notebook: 1.09.T4.the
- M9.3: 1.09 - Give It a Try
- M9.3a: 1.09.G1: Quick calculations
- LiveMath Notebook: 1.09.G1.the
- M9.3b: 1.09.G2: Parametric plotting of circles and ellipses in two dimensions
- LiveMath Notebook: 1.09.G2.the
- M9.3c: 1.09.G3: Elliptical orbits of planets and asteroids
- LiveMath Notebook: 1.09.G3.the
- M9.3d: 1.09.G4: Parametric plotting of circles, tubes and horns in three dimensions
- LiveMath Notebook: 1.09.G4.the
- M9.3e: 1.09.G5: Surfaces you can make by rotating curves
- LiveMath Notebook: 1.09.G5.the
- M9.3f: 1.09.G6: Projectile marksmanship
- LiveMath Notebook: 1.09.G6.the
- M9.3g: 1.09.G7: More cams
- LiveMath Notebook: 1.09.G7.the
- M9.3h: 1.09.G8: Parametric plotting of a predator-prey model in which the prey don't reproduce and the predators don't die
- LiveMath Notebook: 1.09.G8.the
- M9.3i: 1.09.G9: Politics and the environment
- LiveMath Notebook: 1.09.G9.the
- M9.3j: 1.09.G10: Epidemics
- LiveMath Notebook: 1.09.G10.the
- M9.3k: 1.09.G11: Collision?
- LiveMath Notebook: 1.09.G11.the
- M9.4: 1.09 - Literacy
- M9.4a: 1.09.LiteracySheet
- LiveMath Notebook: M9.4.a.the
- M10: 1.10: Limits and Continuity
- M10.1: 1.10 - Basics
- M10.1a: 1.10.B1: It's Broken
- LiveMath Video: M10.1.a-LMVideo.mp4
- LiveMath Notebook: M10.1.a.the
- LiveMath Video: 1.00.B1-LMVideo.mp4
- M10.1b: 1.10.B2: "At" vs. "Approaching"
- LiveMath Notebook: M10.1.b.the
- LiveMath Video: M10.1.b-LMVideo.mp4
- LiveMath Video: 1.00.B2-LMVideo.mp4
- M10.1c: 1.10.B3: Limits
- LiveMath Notebook: 1.00.B3.the
- LiveMath Video: M10.1.c-LMVideo.mp4
- LiveMath Video: 1.00.B3-LMVideo.mp4
- M10.1d: 1.10.B4: Continuity
- LiveMath Video: M10.1.d-LMVideo.mp4
- LiveMath Video: 1.00.B4-LiveMath.mp4
- LiveMath Notebook: 1.00.B4.the
- M10.2: 1.10 - Tutorials
- M10.2a: 1.10.T1: Limits
- LiveMath Video: 1.00.T1-LMVideo.mp4
- LiveMath Notebook: 1.00.T1.the
- M10.2b: 1.10.T2: Limit Rules
- LiveMath Video: 1.00.T2-LMVideo.mp4
- LiveMath Notebook: 1.00.T2.the
- M10.2c: 1.10.T3: Continuity
- LiveMath Video: 1.00.T3-LMVideo.mp4
- LiveMath Notebook: 1.00.T3.the
- M10.3: 1.10 - Give It a Try
- M10.3a: 1.10.G1: Limits
- LiveMath Notebook: 1.00.G1.the
- M10.3b: 1.10.G2: More Limits
- LiveMath Notebook: 1.00.G2.the
- M10.3c: 1.10.G3: Continuity
- LiveMath Notebook: 1.00.G3.the
Accumulation. That's what the integral really means. Too often the concept of the integral is tied up into the Riemann Sum construction, with students not really learning the more fundamental concept of accumulationM, whose theme is returned to again and again in the development of integration theory. The Fundamental Theorem of Calculus is explored via looking at integral functions - functions created using the integral object, and then looking at derivatives of the integral functions. Something you can only study via the usage of high powered technology like LiveMath (or Mathematica). In the middle of this curriculum we study Green's Theorem and the relationship between double integrals and path integrals - a topic usually reserved for vector calculus a year forward in the traditional curriculum. With a tool like LiveMath, what then becomes the student of antidifferentiation? There are some hand techniques for mathematical literacy, but then we move into using these technological tools, understanding what techniques they are applying to "crack the integral", and even use advanced techniques like complex integrals and Euler's formula to attack trigonometric integrals. ![]()
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>>>Show Table of Contents (With Demo Sections & Content)
- N0: 2.01: Measure Area
- N0.1: 2.01 - Basics
- N0.2: 2.01 - Tutorials
- N0.2a: 2.01.T1: Calculation of integrals for area measurements
- LiveMath Video: N0.2.a-LMVideo.mp4
- LiveMath Video: 2.01.T1.mp4
- LiveMath Notebook: 2.01.T1.the
- N0.2b: 2.01.T2: Areas suggested by data lists
- LiveMath Video: N0.2.b-LMVideo.mp4
- LiveMath Video: 2.01.T2.mp4
- LiveMath Notebook: 2.01.T2.the
- N0.2c: 2.01.T3: Nonsense integrals
- LiveMath Video: N0.2.c-LMVideo.mp4
- LiveMath Video: 2.01.T3.mp4
- LiveMath Notebook: 2.01.T3.the
- N0.3: 2.01 - Give It a Try
- N0.3a: 2.01.G1: Plotting and Calculating: Symmetry
- N0.3b: 2.01.G2: More Plotting and Integrating
- N0.3c: 2.01.G3: Calculating Some Integrals
- N0.3d: 2.01.G4: Experiments geared toward breaking the code of the integral
- LiveMath Notebook: 2.01.G4.the
- N0.3e: 2.01.G5: Using numerical integration
- LiveMath Notebook: 2.01.G5.the
- N0.3f: 2.01.G6: The Flavor of Calculate
- LiveMath Notebook: 2.01.G6.the
- N0.3g: 2.01.G7: Estimating the area of a piece of ground
- LiveMath Notebook: 2.01.G7.the
- N0.3h: 2.01.G8: Integration of data lists
- LiveMath Notebook: 2.01.G8.the
- N0.3i: 2.01.G9: Integrating, plotting, measuring and guessing
- LiveMath Notebook: 2.01.G9.the
- N0.4: 2.01 - Literacy
- N0.4a: Literacy Sheet
- LiveMath Notebook: NN0.4.a.the
- N1: 2.02: Fundamental Formula
- N1.1: 2.02 - Basics
- N1.1a: 2.02.B1: The Fundamental Theorem, Part 1
- N1.1b: 2.02.B2: The Fundamental Theorem, Part 2
- LiveMath Video: N1.1.b-LMVideo.mp4
- LiveMath Video: 2.02.B2.mp4
- LiveMath Notebook: 2.02.B2.the
- N1.1c: 2.02.B3: Measurements of distance and velocity via the fundamental formula
- LiveMath Video: N1.1.c-LMVideo.mp4
- LiveMath Video: 2.02.B3.mp4
- LiveMath Notebook: 2.02.B3.the
- N1.1d: 2.02.B4: Infinite Integrals and the Fundamental Formula
- LiveMath Video: N1.1.d-LMVideo.mp4
- LiveMath Video: 2.02.B4.mp4
- LiveMath Notebook: 2.02.B4.the
- N1.1e: 2.02.B5: The integral of the sum is the sum of the integrals
- LiveMath Video: N1.1.e-LMVideo.mp4
- LiveMath Video: 2.02.B5.mp4
- LiveMath Notebook: 2.02.B5.the
- N1.1f: 2.02.B6: Integrating Backward
- LiveMath Video: N1.1.f-LMVideo.mp4
- LiveMath Video: 2.02.B6.mp4
- LiveMath Notebook: 2.02.B6.the
- N1.1g: 1.07.B3: Euler's Fakers
- N1.2: 2.02 - Tutorials
- N1.2a: 2.02.T1: Getting the feel of the fundamental formula by using it to calculate integrals
- LiveMath Video: N1.2.a-LMVideo.mp4
- LiveMath Video: 2.02.T1.mp4
- LiveMath Notebook: 2.02.T1.the
- N1.2b: 2.02.T2: Velocity, acceleration and the fundamental formula
- LiveMath Notebook: 2.02.T2.the
- N1.2c: 2.02.T3: Some measurements based on the fundamental formula
- LiveMath Notebook: 2.02.T3.the
- N1.2d: 2.02.T4: Area between curves
- LiveMath Notebook: 2.02.T4.the
- N1.2e: 2.02.T5: Approximate calculation of Infinite Integrals
- LiveMath Notebook: N1.2.e.the
- N1.2f: 2.02.T6: The fundamental formula and its relation to differential equations
- LiveMath Notebook: 2.02.T6.the
- N1.2g: 2.02.T7: The "Indefinite Integral"
- LiveMath Notebook: 2.02.T7.the
- N1.2h: 1.07.T1: Euler's Fakers 1
- LiveMath Notebook: N1.2.h.the
- N1.2i: 1.07.G2: Euler's Fakers 2
- LiveMath Notebook: N1.2.i.the
- N1.2j: 1.07.G8: Euler's Fakers 3
- LiveMath Notebook: N1.2.j.the
- N1.3: 2.02 - Give It a Try
- N1.3a: 2.02.G1: Calculating integrals by solving differential equations
- N1.3b: 2.02.G2: How does LiveMath calculate an integral?
- LiveMath Notebook: 2.02.G2.the
- N1.3c: 2.02.G3: Velocity and acceleration
- LiveMath Notebook: 2.02.G3.the
- N1.3d: 2.02.G4: Functions defined by integrals
- LiveMath Notebook: 2.02.G4.the
- N1.3e: 2.02.G5: Fundamental ideas
- LiveMath Notebook: N1.3.e.the
- N1.3f: 2.02.G6: Some measurements coming from the fundamental formula
- LiveMath Notebook: N1.3.f.the
- N1.3g: 2.02.G7: Exact and approximate calculations of Infinite Integrals
- LiveMath Notebook: N1.3.g.the
- N1.3h: 2.02.G8: Waterloo Tiles
- LiveMath Notebook: 2.02.G8.the
- N1.3i: 2.02.G9: Bad Integrals
- LiveMath Notebook: 2.02.G9.the
- N1.4: 2.02 - Literacy
- N1.4a: 2.02.LiteracySheet
- LiveMath Notebook: NN1.4.a.the
- N2: 2.03: Measurements
- N2.1: 2.03 - Basics
- N2.1a: 2.03.B1: Measurements based on slicing and accumulating: Area and volume
- LiveMath Video: N2.1.a-LMVideo.mp4
- LiveMath Video: 2.03.B1.mp4
- LiveMath Notebook: 2.03.B1.the
- N2.1b: 2.03.B2: Measurements based on slicing and accumulating: Density and mass
- LiveMath Video: N2.1.b-LMVideo.mp4
- LiveMath Video: 2.03.B2.mp4
- LiveMath Notebook: 2.03.B2.the
- N2.1c: 2.03.B3: Measurements based on approximating and acculumating: Arc Length
- LiveMath Video: N2.1.c-LMVideo.mp4
- LiveMath Video: 2.03.B3.mp4
- LiveMath Notebook: 2.03.B3.the
- N2.1d: 2.03.B4: Measurements based on the fundamental formula: Accumulated growth
- LiveMath Video: N2.1.d-LMVideo.mp4
- LiveMath Video: 2.03.B4.mp4
- LiveMath Notebook: 2.03.B4.the
- N2.2: 2.03 - Tutorials
- N2.2a: 2.03.T1: Volumes of solids
- N2.2b: 2.03.T2: Linear dimension: Volume and area
- LiveMath Video: N2.2.b-LMVideo.mp4
- LiveMath Video: 2.03.T2.mp4
- LiveMath Notebook: 2.03.T2.the
- N2.3: 2.03 - Give It a Try
- N2.3a: 2.03.G1: Using the Tools: Measurements of accumulation
- LiveMath Notebook: 2.03.G1.the
- N2.3b: 2.03.G2: Using the Tools: Measurements of length, volume, and mass
- LiveMath Notebook: 2.03.G2.the
- N2.3c: 2.03.G3: Slicing for area measurements
- LiveMath Notebook: 2.03.G3.the
- N2.3d: 2.03.G4: Volume measurements for some tubes and horns
- LiveMath Notebook: 2.03.G4.the
- N2.3e: 2.03.G5: Work
- LiveMath Notebook: 2.03.G5.the
- N2.3f: 2.03.G6: Champagne glasses with a logarithmic flare
- LiveMath Notebook: 2.03.G6.the
- N2.3g: 2.03.G7: The derivative of arc length
- LiveMath Notebook: 2.03.G7.the
- N2.3h: 2.03.G8: Present value of a profit-making scheme
- LiveMath Notebook: 2.03.G8.the
- N2.3i: 2.03.G9: Linear dimension
- LiveMath Notebook: 2.03.G9.the
- N2.3j: 2.03.G10: Catfish harvesting
- LiveMath Notebook: 2.03.G10.the
- N2.4: 2.03 - Literacy
- N2.4a: 2.04.LiteracySheet
- LiveMath Notebook: 2.03.Literacy.the
- N3: 2.04: Transforming Integrals
- N3.1: 2.04 - Basics
- N3.1a: 2.04.B1: Breaking more of the code of the integral: Transforming integrals
- LiveMath Video: N3.1.a-LMVideo.mp4
- LiveMath Video: 2.04.B1.mp4
- LiveMath Notebook: 2.04.B1.the
- N3.1b: 2.04.B2: Measuring area under curves given parametrically
- LiveMath Notebook: 2.04.B2.the
- N3.1c: 2.04.B3: Bell-shaped curves and Gauss's normal law
- LiveMath Notebook: 2.04.B3.the
- N3.2: 2.04 - Tutorials
- N3.2a: 2.04.T1: Transforming integrals
- LiveMath Notebook: 2.04.T1.the
- N3.2b: 2.04.T2: Transforming integrals to help understand LiveMath output
- LiveMath Notebook: 2.04.T2.the
- N3.2c: 2.04.T3: Measuring area inside closed curves
- LiveMath Notebook: 2.04.T3.the
- N3.2d: 2.04.T4: Polar plots and area measurements
- LiveMath Notebook: 2.04.T4.the
- N3.2e: 2.04.T5: Gauss's normal law
- LiveMath Notebook: 2.04.T5.the
- N3.3: 2.04 - Give It a Try
- N3.3a: 2.04.G1: Transforming integrals
- LiveMath Notebook: 2.04.G1.the
- N3.3b: 2.04.G2: Transforming integrals to explain LiveMath output
- LiveMath Notebook: 2.04.G2.the
- N3.3c: 2.04.G3: Area measurements
- LiveMath Notebook: 2.04.G3.the
- N3.3d: 2.04.G4: Volume measurements
- LiveMath Notebook: 2.04.G4.the
- N3.3e: 2.04.G5: Gauss's normal law all around us
- LiveMath Notebook: 2.04.G5.the
- N3.3f: 2.04.G6: Using transformations to analyze normally distributed measurements
- LiveMath Notebook: 2.04.G6.the
- N3.3g: 2.04.G7: Transforming integrals to explain measurements of area, length and volume
- LiveMath Notebook: 2.04.G7.the
- N3.3h: 2.04.G8: A transformation bails out a materials science student
- LiveMath Notebook: 2.04.G8.the
- N3.3i: 2.04.G9: Gauss's normal law and grading on the curve
- LiveMath Notebook: 2.04.G9.the
- N3.3j: 2.04.G10: Polar plots: Rotating and measuring
- LiveMath Notebook: 2.04.G10.the
- N3.3k: 2.04.G11: Counterclockwise or clockwise?
- LiveMath Notebook: 2.04.G11.the
- N3.3l: 2.04.G12: Work and velocity
- LiveMath Notebook: 2.04.G12.the
- N3.4: 2.04 - Literacy
- N3.4a: 2.04.LiteracySheet
- LiveMath Notebook: 2.04.Literacy.the
- N4: 2.05: 2D Integrals
- N4.1: 2.05 - Basics
- N4.1a: 2.05.B1: 2D integrals for Volume Measurements
- LiveMath Video: N4.1.a-LMVideo.mp4
- LiveMath Video: 2.05.B1.mp4
- LiveMath Notebook: 2.05.B1.the
- N4.1b: 2.05.B2: Double Integrals for Non-Positive Integrand
- LiveMath Video: N4.1.b-LMVideo.mp4
- LiveMath Video: 2.05.B2.mp4
- LiveMath Notebook: 2.05.B2.the
- N4.1c: 2.05.B3: Double Integrals over Non-Rectangular Regions
- LiveMath Video: N4.1.c-LMVideo.mp4
- LiveMath Video: 2.05.B3.mp4
- LiveMath Notebook: 2.05.B3.the
- N4.1d: 2.05.B4: The Gauss-Green formula helps you calculate Double Integrals
- LiveMath Video: N4.1.d-LMVideo.mp4
- LiveMath Video: 2.05.B4.mp4
- LiveMath Notebook: 2.05.B4.the
- N4.1e: 2.05.B5: An indication of some of the ideas behind the Gauss-Green formula
- LiveMath Notebook: 2.05.B5.the
- N4.2: 2.05 - Tutorials
- N4.2a: 2.05.T1: Using a 2D integral to measure area
- N4.2b: 2.05.T2: Volume measurements with 2D integrals
- LiveMath Video: N4.2.b-LMVideo.mp4
- LiveMath Video: 2.05.T2.mp4
- LiveMath Notebook: 2.05.T2.the
- N4.2c: 2.05.T3: Calculation strategies for minimum effort on your part
- LiveMath Video: N4.2.c-LMVideo.mp4
- LiveMath Video: 2.05.T3.mp4
- LiveMath Notebook: 2.05.T3.the
- N4.2d: 2.05.T4: Gauss-Green when you have a clockwise parameterization
- LiveMath Video: N4.2.d-LMVideo.mp4
- LiveMath Video: 2.05.T4.mp4
- LiveMath Notebook: 2.05.T4.the
- N4.2e: 2.05.T5: Gauss's normal law in 2D and using it to plan bombing runs
- LiveMath Notebook: 2.05.T5.the
- N4.3: 2.05 - Give It a Try
- N4.3a: 2.05.G1: Volume measurements
- LiveMath Notebook: 2.05.G1.the
- N4.3b: 2.05.G2: Calculating double integrals
- LiveMath Notebook: 2.05.G2.the
- N4.3c: 2.05.G3: Area and volume measurements via the Gauss-Green formula
- LiveMath Video: NN4.3.c-LMVideo.mp4
- LiveMath Video: N4.3.c-LMVideo.mp4
- LiveMath Video: 2.05.G3-Hint.mp4
- LiveMath Notebook: 2.05.G3.the
- N4.3d: 2.05.G4: Plot3D versus ParametricPlot3D
- LiveMath Notebook: 2.05.G4.the
- N4.3e: 2.05.G5: Big league plotting and measuring
- LiveMath Notebook: 2.05.G5.the
- N4.3f: 2.05.G6: Average value and centroids
- LiveMath Notebook: 2.05.G6.the
- N4.3g: 2.05.G7: Bombing runs
- LiveMath Notebook: 2.05.G7.the
- N4.4: 2.05 - Literacy
- N4.4a: 2.05.LiteracySheet
- LiveMath Notebook: 2.05.Literacy.the
- N5: 2.06: More Tools
- N5.1: 2.06 - Basics
- N5.1a: 2.06.B1: Separating the variables and integrating to get formulas for solutions of some differential equations
- LiveMath Video: N5.1.a-LMVideo.mp4
- LiveMath Video: 2.06.B1.mp4
- LiveMath Notebook: 2.06.B1.the
- N5.1b: 2.06.B2: Integration by parts
- LiveMath Video: N5.1.b-LMVideo.mp4
- LiveMath Video: 2.06.B2.mp4
- LiveMath Notebook: 2.06.B2.the
- N5.1c: 2.06.B3: Complex numbers, Euler's formula, and Logarithm of a Negative Number
- LiveMath Video: N5.1.c-LMVideo.mp4
- LiveMath Video: 2.06.B3.mp4
- LiveMath Notebook: 2.06.B3.the
- N5.1d: 2.06.B4: Using Complex Exponentials
- LiveMath Video: N5.1.d-LMVideo.mp4
- LiveMath Video: 2.06.B4.mp4
- LiveMath Notebook: 2.06.B4.the
- N5.1e: 2.06.B5: The technique of calculating integrals by taking derivatives
- LiveMath Video: N5.1.e-LMVideo.mp4
- LiveMath Video: 2.06.B5.mp4
- LiveMath Notebook: 2.06.B5.the
- N5.2: 2.06 - Tutorials
- N5.2a: 2.06.T1: Formulas for the solutions of certain differential equations by separating and integrating
- LiveMath Notebook: 2.06.T1.the
- N5.2b: 2.06.T2: Using integration by parts to do integration by iteration
- LiveMath Video: N5.2.b-LMVideo.mp4
- LiveMath Video: 2.06.T2-Help1.mp4
- LiveMath Notebook: 2.06.T2.the
- N5.2c: 2.06.T3: Using the complex exponential to help understand LiveMath output
- LiveMath Notebook: N5.2.c.the
- N5.2d: 2.06.T4: Which technique to go with
- LiveMath Notebook: 2.06.T4.the
- N5.3: 2.06 - Give It a Try
- N5.3a: 2.06.G1: Separating and integrating
- LiveMath Video: N5.3.a-LMVideo.mp4
- LiveMath Video: 2.06.G1-Help1.mp4
- LiveMath Notebook: 2.06.G1.the
- N5.3b: 2.06.G2: Integration by parts
- LiveMath Notebook: 2.06.G2.the
- N5.3c: 2.06.G3: Chemical reaction model and the spread of infection model
- LiveMath Notebook: 2.06.G3.the
- N5.3d: 2.06.G4: Tables of integrals via iteration
- LiveMath Notebook: 2.06.G4.the
- N5.3e: 2.06.G5: Meet sinh(x) and cosh(x)
- LiveMath Notebook: 2.06.G5.the
- N5.3f: 2.06.G6: The gamma function
- LiveMath Notebook: 2.06.G6.the
- N5.3g: 2.06.G7: The algebra of [the complex] exponentials is much easier than that of sines and cosines
- LiveMath Notebook: 2.06.G7.the
- N5.3h: 2.06.G8: Error propagation via iteration: Against you and for you
- LiveMath Notebook: 2.06.G8.the
- N5.3i: 2.06.G9: Using the techniques
- LiveMath Notebook: 2.06.G9.the
- N5.4: 2.06 - Literacy
- N5.4a: 2.06.LiteracySheet
- LiveMath Notebook: 2.06.Literacy.the
- N6: 2.07: Pattern Procedures
- N6.1: 2.07 - Basics
- N6.1a: 2.07.B1: Partial fractions for quotients of polynomials
- LiveMath Notebook: 2.07.B1.the
- N6.1b: 2.07.B2: Trigonometric Integrals
- LiveMath Notebook: 2.07.B2.the
- N6.1c: 2.07.B3: Trig substitution and hyperbolic substitution
- LiveMath Notebook: 2.07.B3.the
- N6.1d: 2.07.B4: Ad hoc substitution
- LiveMath Notebook: 2.07.B4.the
- N6.2: 2.07 - Tutorials
- N6.2a: 2.07.T1: Traditional pat procedures: A frank discussion
- LiveMath Notebook: 2.07.T1.the
- N6.2b: 2.07.T2: Integrals to try the pat procedures on
- LiveMath Notebook: N6.2.b.the
- N6.3: 2.07 - Give It a Try
- N6.3a: 2.07.G1-G3: Traditional Pat Integrations, Part 1
- LiveMath Notebook: 2.07.G1-G3.the
- N6.3b: 2.07.G4-G6: Traditional Pat Integrations, Part 2
- LiveMath Notebook: 2.07.G4-G6.the
- N6.3c: 2.07.G7-G9: Traditional Pat Integrations, Part 3
- LiveMath Notebook: 2.07.G7-G9.the
- N6.3d: 2.07.G10-G12: Traditional Pat Integrations, Part 4
- LiveMath Notebook: 2.07.G10-G12.the
- N6.4: 2.07 - Literacy
- N6.4a: 2.07.LiteracySheet
- LiveMath Notebook: 2.07.Literacy.the
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Approximation. Just like decimals may approximate any real number, polynomial functions may approximate any real (well-behaved, differentiable) function. The (often dreary) traditional approach to sequences and series is replaced by a lively and useful approached based upon splines to approximate general functions. This leads naturally to Taylor's Theorem, and finding the relationship between degrees of points of contact, derivatives, and shape of curves, all leading to the ability to integrate functions once you have a polynomial approximation, and then winding back to sequences and convergence, upending the traditional order of topics. This spline approach in the curriculum converts the last portion of first year calculus into a wonderful finale, quite different than the expected "p-test, this converges, this doesn't" bucket of confusion that most students experience in Calculus III. |
>>>Show Table of Contents (With Demo Sections & Content)
- O1: 3.01 - Splines
- O1.1: 3.01-Basics
- O1.2: 3.01-Tutorials
- O1.2a: 3.01.T1: Splining functions and polynomials
- LiveMath Notebook: OO1.2.a.the
- O1.2b: 3.01.T2: Landing an airplane
- O1.2c: 3.01.T3: Does LiveMath's Tabulate function give you a smooth spline?
- LiveMath Notebook: OO1.2.c.the
- O1.3: 3.01-Give It a Try
- O1.3a: 3.01.G1: Explain the plots
- LiveMath Notebook: OO1.3.a.the
- O1.3b: 3.01.G2: Splining functions and polynomials
- LiveMath Notebook: OO1.3.b.the
- O1.3c: 3.01.G3: Splines in road design
- LiveMath Notebook: OO1.3.c.the
- O1.3d: 3.01.G4: Order of contact for derivatives and integrals
- LiveMath Notebook: OO1.3.d.the
- O1.3e: 3.01.G5: Changing the variable to improve the order of contact at a
- LiveMath Notebook: OO1.3.e.the
- O1.3f: 3.01.G6: The natural cubic spline
- LiveMath Notebook: OO1.3.f.the
- O1.4: 3.01-Literacy
- O1.4a: 3.01.LiteracySheet
- LiveMath Notebook: OO1.4.a.the
- O2: 3.02 - Expansions
- O2.1: 3.02-Basics
- O2.1a: 3.02.B1: The expansion of a function f(x) in powers of x
- LiveMath Notebook: OO2.1.a.the
- O2.1b: 3.02.B2: The expansions every literate calculus person knows
- LiveMath Notebook: OO2.1.b.the
- O2.1c: 3.02.B3: Expansions for approximation
- LiveMath Notebook: OO2.1.c.the
- O2.2: 3.02-Tutorials
- O2.2a: 3.02.T1: Expansions by substitution
- LiveMath Notebook: OO2.2.a.the
- O2.2b: 3.02.T2: Expansions by differentiation
- LiveMath Notebook: OO2.2.b.the
- O2.2c: 3.02.T3: Expansions by integration
- LiveMath Notebook: OO2.2.c.the
- O2.3: 3.02-Give It a Try
- O2.3a: 3.02.G1: A festival of expansions and approximations
- LiveMath Notebook: OO2.3.a.the
- O2.3b: 3.02.G2: Writing down expansions
- LiveMath Notebook: OO2.3.b.the
- O2.3c: 3.02.G3: Trick questions
- LiveMath Notebook: OO2.3.c.the
- O2.3d: 3.02.G4: Serious approximations
- LiveMath Notebook: OO2.3.d.the
- O2.3e: 3.02.G5: Circles
- LiveMath Notebook: OO2.3.e.the
- O2.3f: 3.02.G6: Turning the tables
- LiveMath Notebook: OO2.3.f.the
- O2.3g: 3.02.G7: Turning the tables
- LiveMath Notebook: OO2.3.g.the
- O2.4: 3.02-Literacy
- O2.4a: 3.02.LiteracySheet
- LiveMath Notebook: OO2.4.a.the
- O3: 3.03 - Use Expansions
- O3.1: 3.03-Basics
- O3.1a: 3.03.B1: Expansions in powers of (x - b) and approximations based on them
- O3.1b: 3.03.B2: Tangent lines and Newton's method
- LiveMath Notebook: OO3.1.b.the
- O3.1c: 3.03.B3: The LiveMath Taylor Series Instruction (and Watching For Errors)
- LiveMath Notebook: OO3.1.c.the
- O3.1d: 3.03.B4: Using expansions to help to calculate limits
- O3.1e: 3.03.B5: Expansions and the complex exponential function
- LiveMath Notebook: OO3.1.e.the
- O3.2: 3.03-Tutorials
- O3.2a: 3.03.T1: Using expansions to calculate limits
- LiveMath Notebook: OO3.2.a.the
- O3.2b: 3.03.T2: Square roots by Newton's method
- LiveMath Notebook: OO3.2.b.the
- O3.2c: 3.03.T3: Using the complex exponential to generate trigonometric identities
- LiveMath Notebook: OO3.2.c.the
- O3.2d: 3.03.T4: Using expansions to get precise estimates of integrals
- LiveMath Notebook: OO3.2.d.the
- O3.3: 3.03-Give It a Try
- O3.3a: 3.03.G1: Approximation of functions by means of their expansions in powers of (x - b)
- LiveMath Video: O3.3.a-LMVideo.mp4
- LiveMath Notebook: OO3.3.a.the
- LiveMath Video: 3.03.G1Help-H264.mp4
- O3.3b: 3.03.G2: Calculating some limits
- LiveMath Notebook: OO3.3.b.the
- O3.3c: 3.03.G3: Centering the expansion
- LiveMath Notebook: OO3.3.c.the
- O3.3d: 3.03.G4: Root Finding and Newton's method
- LiveMath Notebook: OO3.3.d.the
- O3.3e: 3.03.G5: Using expansions to get precise estimates of integrals
- LiveMath Notebook: OO3.3.e.the
- O3.3f: 3.03.G6: Expansions and the controversy between spherical mirrors and parabolic mirrors
- O3.3g: 3.03.G7: Getting the expansion of tan(x) by division
- LiveMath Notebook: OO3.3.g.the
- O3.3h: 3.03.G8: Generating identities for sin(m x)
- LiveMath Notebook: OO3.3.h.the
- O3.3i: 3.03.G9: Behavior close to 0
- LiveMath Notebook: OO3.3.i.the
- O3.3j: 3.03.G10: Behavior away from 0
- LiveMath Notebook: OO3.3.j.the
- O3.3k: 3.03.G11: Error at the endpoints
- LiveMath Notebook: OO3.3.k.the
- O3.4: 3.03-Literacy
- O3.4a: 3.03.LiteracySheet
- LiveMath Notebook: OO3.4.a.the
- O4: 3.04 - Taylor's Formula
- O4.1: 3.04-Basics
- O4.1a: 3.04.B1: Taylor's formula for the expansion of f(x) in powers of (x - b)
- LiveMath Notebook: OO4.1.a.the
- O4.1b: 3.04.B2: Four approximations based on Taylor's formula and how they can be used to estimate integrals
- LiveMath Notebook: OO4.1.b.the
- O4.2: 3.04-Tutorials
- O4.2a: 3.04.T1: Taylor's formula in reverse
- LiveMath Notebook: OO4.2.a.the
- O4.2b: 3.04.T2: Limits
- LiveMath Notebook: OO4.2.b.the
- LiveMath Video: O4.2.b-LMVideo.mp4
- LiveMath Video: 3.04.T2.mp4
- O4.2c: 3.04.T3: Approximations and fake plots of solutions of some differential equations
- LiveMath Notebook: OO4.2.c.the
- O4.3: 3.04-Give It a Try
- O4.3a: 3.04.G1: Taylor's formula in reverse
- LiveMath Notebook: OO4.3.a.the
- O4.3b: 3.04.G2: Limits, Taylor's formula and L'Hospital's rule
- O4.3c: 3.04.G3: Taylor's formula and expansions of derivatives
- LiveMath Notebook: OO4.3.c.the
- O4.3d: 3.04.G4: G.4) Pulling the expansions of 1/(1-x), sin(x), cos(x), and e^x in powers of (x-b) out of your back pocket
- LiveMath Notebook: OO4.3.d.the
- O4.3e: 3.04.G5: Rectangles, trapezoids, midpoints and parabolas
- LiveMath Notebook: OO4.3.e.the
- O4.3f: 3.04.G6: The midpoint and Runge-Kutta approximations versus expansions
- LiveMath Notebook: OO4.3.f.the
- O4.3g: 3.04.G7: Midpoint versus trapezoidal approximation
- LiveMath Notebook: OO4.3.g.the
- O4.3h: 3.04.G8: Approximations and fake plots of solutions of differential equations
- LiveMath Notebook: OO4.3.h.the
- O4.3i: 3.04.G9: The kissing parabola
- LiveMath Notebook: OO4.3.i.the
- O4.4: 3.04-Literacy
- O4.4a: 3.04.LiteracySheet
- LiveMath Notebook: OO4.4.a.the
- O5: 3.05 - Convergence
- O5.1: 3.05-Basics
- O5.1a: 3.05.B1: Barriers and complex numbers
- O5.1b: 3.05.B2: Why you don't run into barriers when you approximate e^x, sin(x), and cos(x)
- LiveMath Notebook: OO5.1.b.the
- O5.1c: 3.05.B3: Why some functions like x^(9/2) don't have expansions in powers of x
- LiveMath Notebook: OO5.1.c.the
- O5.1d: 3.05.B4: Barriers and convergence intervals
- LiveMath Notebook: OO5.1.d.the
- O5.2: 3.05-Tutorials
- O5.2a: 3.05.T1: Convergence intervals
- LiveMath Notebook: OO5.2.a.the
- O5.2b: 3.05.T2: The convergence intervals for f(x), f ' (x) and Integral(f(t)) are all the same
- LiveMath Notebook: OO5.2.b.the
- O5.2c: 3.05.T3: 1/(1 - x) = 1+x+x^2+x^3 + ... + x^k + ... for -1
- LiveMath Notebook: OO5.2.c.the
- O5.2d: 3.05.T4: Infinite sums of numbers
- LiveMath Notebook: OO5.2.d.the
- O5.2e: 3.05.T5: Using the expansion of 1/(1 - x) for drug dosing
- O5.3: 3.05-Give It a Try
- O5.3a: 3.05.G1: Convergence intervals
- LiveMath Notebook: OO5.3.a.the
- O5.3b: 3.05.G2: Convergence intervals and plots
- LiveMath Notebook: OO5.3.b.the
- O5.3c: 3.05.G3: Sharing ink
- LiveMath Notebook: OO5.3.c.the
- O5.3d: 3.05.G4: Infinite sums of numbers
- LiveMath Notebook: OO5.3.d.the
- O5.3e: 3.05.G5: Barriers resulting from splines
- LiveMath Notebook: OO5.3.e.the
- O5.3f: 3.05.G6: Dosing
- LiveMath Notebook: OO5.3.f.the
- O5.3g: 3.05.G7: Some more uses of the expansion 1/(1-x) = 1+x+(x)^(2)+(x)^(3)+(x)^(4) + ...
- LiveMath Notebook: OO5.3.g.the
- O5.3h: 3.05.G8: More adventures of the lab pest Calculus Cal
- LiveMath Notebook: OO5.3.h.the
- O5.3i: 3.05.G9: sqrt(x) and ln(x)
- LiveMath Notebook: OO5.3.i.the
- O5.3j: 3.05.G10: Impossibilities and outrages
- LiveMath Notebook: OO5.3.j.the
- O5.3k: 3.05.G11: Infinite sums, decimals, and expansions
- LiveMath Notebook: OO5.3.k.the
- O5.3l: 3.05.G12: Point fit with polynomials, expansions, and convergence intervals
- LiveMath Notebook: OO5.3.l.the
- O5.4: 3.05-Literacy
- O5.4a: 3.05.LiteracySheet
- LiveMath Notebook: OO5.4.a.the
- O6: 3.06 - Power Series
- O6.1: 3.06-Basics
- O6.1a: 3.06.B1: Functions defined by power series
- LiveMath Notebook: OO6.1.a.the
- O6.1b: 3.06.B2: Functions defined by power series via differential equations
- LiveMath Notebook: OO6.1.b.the
- O6.1c: 3.06.B3: Convergence intervals for functions defined by power series via differential equations
- LiveMath Notebook: OO6.1.c.the
- O6.1d: 3.06.B4: Convergence intervals for general power series
- LiveMath Video: O6.1.d-LMVideo.mp4
- LiveMath Notebook: OO6.1.d.the
- LiveMath Video: 3.06.B4-LMVideo.mp4
- O6.2: 3.06-Tutorials
- O6.2a: 3.06.T1: Trying to plot functions defined by power series
- LiveMath Notebook: OO6.2.a.the
- O6.2b: 3.06.T2: Functions defined by power series via differential equations
- LiveMath Notebook: OO6.2.b.the
- O6.2c: 3.06.T3: Using the Power Series Convergence Principle: The Ratio Test
- LiveMath Video: O6.2.c-LMVideo.mp4
- LiveMath Notebook: OO6.2.c.the
- LiveMath Video: 3.06.T3-LMVideo.mp4
- O6.2d: 3.06.T4: Infinite sums of numbers
- LiveMath Notebook: OO6.2.d.the
- O6.3: 3.06-Give It a Try
- O6.3a: 3.06.G1: Trying to plot functions defined by power series
- LiveMath Notebook: OO6.3.a.the
- O6.3b: 3.06.G2: Taylor's formula and power series
- LiveMath Notebook: OO6.3.b.the
- O6.3c: 3.06.G3: A differential equations medley
- LiveMath Notebook: OO6.3.c.the
- O6.3d: 3.06.G4: Convergence intervals for power series coming from differential equations
- LiveMath Notebook: OO6.3.d.the
- O6.3e: 3.06.G5: Guaranteed convergence intervals for power series
- LiveMath Notebook: OO6.3.e.the
- O6.3f: 3.06.G6: The simple Airy function
- LiveMath Notebook: OO6.3.f.the
- O6.3g: 3.06.G7: Infinite sums of numbers
- LiveMath Notebook: OO6.3.g.the
- O6.3h: 3.06.G8: A couple of bricks short of a load
- LiveMath Notebook: OO6.3.h.the
- O6.3i: 3.06.G9: e^x, sin(x), and cos(x) from the advanced viewpoint
- LiveMath Notebook: OO6.3.i.the
- O6.3j: 3.06.G10: Ratios and roots
- LiveMath Notebook: OO6.3.j.the
- O6.4: 3.06-Literacy
- O6.4a: 3.06.LiteracySheet
- LiveMath Notebook: OO6.4.a.the
The utilization of LiveMath comes alive in the multivariable calculus curriculum, bringing the power of easy-to-create 3D graphs of curves and surfaces in LiveMath to a fresh and innovative exploration of the topics of Vector Calculus. The theme of accumulation features prominently, as it did in C&LM II, this time with the accumulation of vector fields dot producted with differential vectors, sometimes tangential, sometimes orthogonal, providing a unique development of path integrals. The course progresses to the theorems of Green, Stokes, and Gauss, which are all just variations of the Fundament Theorem of Multivariable Calculus. Of all of the C&LM texts, this Vector Calculus&LiveMath is felt by many to be the best of the best. ![]()
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>>>Show Table of Contents (With Demo Sections & Content)
- V1: VC.01 - Vectors
- V1.1: VC.01 - Basics
- V1.1a: VC.01.B1: Vectors: How you move them, how you add them, how you subtract them, and how you multiply them by numbers
- LiveMath Video: V1.1.a-LMVideo.mp4
- LiveMath Video: VC.01.B1.mp4
- LiveMath Notebook: V1.1.a.the
- V1.1b: VC.01.B2: Tangent vectors, velocity vectors, and tangent lines
- V1.1c: VC.01.B3: Length of a vector, dot product, and distance between two points
- LiveMath Video: V1.1.c-LMVideo.mp4
- LiveMath Video: VC.01.B3.mp4
- LiveMath Notebook: V1.1.c.the
- V1.1d: VC.01.B4: The push of one vector in the direction of another, and the formula: X * Y = |x| |y| cos(b) where b is the angle between X and Y}
- LiveMath Video: V1.1.d-LMVideo.mp4
- LiveMath Video: VC.01.B4.mp4
- LiveMath Notebook: V1.1.d.the
- V1.1e: VC.01.B5: X*Y = 0 means X is perpendicular to Y
- LiveMath Video: V1.1.e-LMVideo.mp4
- LiveMath Video: VC.01.B5.mp4
- LiveMath Notebook: V1.1.e.the
- V1.2: VC.01 - Tutorials
- V1.2a: VC.01.T1: Velocity and acceleration
- LiveMath Video: V1.2.a-LMVideo.mp4
- LiveMath Video: VC.01.T1.mp4
- LiveMath Notebook: V1.2.a.the
- V1.2b: VC.01.T2: Using the normal vector to bounce light beams off two-dimensional curves
- LiveMath Video: V1.2.b-LMVideo.mp4
- LiveMath Video: VC.01.T2.mp4
- LiveMath Notebook: V1.2.b.the
- V1.2c: VC.01.T3: Lines
- LiveMath Video: V1.2.c-LMVideo.mp4
- LiveMath Video: VC.01.T3.mp4
- LiveMath Notebook: V1.2.c.the
- V1.2d: VC.01.T4: Pursuits
- LiveMath Video: V1.2.d-LMVideo.mp4
- LiveMath Video: VC.01.T4.mp4
- LiveMath Notebook: VC.01.T4.the
- V1.2e: VC.01.T5: Spying along the tangent
- LiveMath Video: V1.2.e-LMVideo.mp4
- LiveMath Video: VC.01.T5.mp4
- LiveMath Notebook: V1.2.e.the
- V1.3: VC.01 - Give It a Try
- V1.3a: VC.01.G1: Vector and line fundamentals
- LiveMath Notebook: V1.3.a.the
- V1.3b: VC.01.G2: Measurements
- LiveMath Notebook: V1.3.b.the
- V1.3c: VC.01.G3: With or against?
- LiveMath Notebook: V1.3.c.the
- V1.3d: VC.01.G4: Velocity and acceleration
- LiveMath Notebook: V1.3.d.the
- V1.3e: VC.01.G5: The coordinate axes and coordinate planes in three dimensions
- LiveMath Notebook: V1.3.e.the
- V1.3f: VC.01.G6: Serious plotting: Parametric planets
- V1.3g: VC.01.G7: Lines
- LiveMath Notebook: V1.3.g.the
- V1.3h: VC.01.G8: Lasers
- LiveMath Notebook: V1.3.h.the
- V1.3i: VC.01.G9: Parabolic reflectors, spherical reflectors, and elliptical reflectors
- LiveMath Notebook: V1.3.i.the
- V1.3j: VC.01.G10: Pursuits by a robotic cowhand
- LiveMath Notebook: V1.3.j.the
- V1.3k: VC.01.G11: Stealth technology
- LiveMath Notebook: V1.3.k.the
- V1.4: VC.01 - Literacy
- V1.4a: VC.01.LiteracySheet
- LiveMath Notebook: V1.4.a.the
- V2: VC.02 - Perpendicularity
- V2.1: VC.02 - Basics
- V2.1a: VC.02.B1: The cross product X*Y of two 3D vectors is perpendicular to both X and Y
- LiveMath Video: V2.1.a-LMVideo.mp4
- LiveMath Video: VC.02.B1.mp4
- LiveMath Notebook: V2.1.a.the
- V2.1b: VC.02.B2: Planes in 3D
- V2.1c: VC.02.B3: Normal vectors for curved surfaces in 3D
- V2.2: VC.02 - Tutorials
- V2.2a: VC.02.T1: True scale plots via the options TrueProportions and StretchToFit
- LiveMath Notebook: V2.2.a.the
- V2.2b: VC.02.T2: Flatness and plotting
- LiveMath Notebook: V2.2.b.the
- V2.2c: VC.02.T3: Unit vectors and perpendicularity: Plotting curves on planes and a new, easy way of calculating the cross product.
- LiveMath Notebook: V2.2.c.the
- V2.2d: VC.02.T4: Unit vectors and perpendicularity:Main unit normals, binormals, tubes, horns, and corrugations
- LiveMath Notebook: V2.2.d.the
- V2.3: VC.02 - Give It a Try
- V2.3a: VC.02.G1: Plane fundamentals
- LiveMath Notebook: V2.3.a.the
- V2.3b: VC.02.G2: Plotting on planes
- LiveMath Notebook: V2.3.b.the
- V2.3c: VC.02.G3: Serious 3D plots: Tubes and ribbons
- LiveMath Notebook: V2.3.c.the
- V2.3d: VC.02.G4: Experiments with linearizations
- LiveMath Notebook: V2.3.d.the
- V2.3e: VC.02.G5: Badger borings
- LiveMath Notebook: V2.3.e.the
- V2.3f: VC.02.G6: Using the product rule to break acceleration vectors into normal and tangential components
- LiveMath Notebook: V2.3.f.the
- V2.3g: VC.02.G7: Using the normal vector to bounce light beams off surfaces
- LiveMath Notebook: V2.3.g.the
- V2.3h: VC.02.G8: Kissing circles and curvature
- LiveMath Notebook: V2.3.h.the
- V2.3i: VC.02.G9: Measurements with the cross product
- LiveMath Notebook: V2.3.i.the
- V2.3j: VC.02.G10: Thumbs up or thumbs down
- LiveMath Notebook: VC.02.G10.the
- V2.4: VC.02 - Literacy
- V2.4a: VC.02.LiteracySheet
- LiveMath Notebook: V2.4.a.the
- V3: VC.03 - Gradient
- V3.1: VC.03 - Basics
- V3.1a: VC.03.B1: The gradient and the chain rule
- V3.1b: VC.03.B2: Level curves, level surfaces and the gradient as normal vector
- V3.1c: VC.03.B3: The gradient points in the direction of greatest initial increase
- LiveMath Video: V3.1.c-LMVideo.mp4
- LiveMath Video: VC.03.B3.mp4
- LiveMath Notebook: V3.1.c.the
- V3.1d: VC.03.B4: Using linearizations to help to explain the chain rule
- LiveMath Video: V3.1.d-LMVideo.mp4
- LiveMath Video: VC.03.B4.mp4
- LiveMath Notebook: V3.1.d.the
- V3.2: VC.03 - Tutorials
- V3.2a: VC.03.T1: The total differential
- LiveMath Notebook: V3.2.a.the
- LiveMath Video: V3.2.a-LMVideo.mp4
- LiveMath Video: VC.03.T1.mp4
- V3.2b: VC.03.T2: What's the chain rule good for?
- LiveMath Video: V3.2.b-LMVideo.mp4
- LiveMath Video: VC.03.T2.mp4
- LiveMath Notebook: V3.2.b.the
- V3.2c: VC.03.T3: The gradient and maximization and minimization
- V3.2d: VC.03.T4: Eye-balling a function for max-min
- LiveMath Video: V3.2.d-LMVideo.mp4
- LiveMath Video: VC.03.T4.mp4
- LiveMath Notebook: V3.2.d.the
- V3.2e: VC.03.T5: Data fit
- LiveMath Video: V3.2.e-LMVideo.mp4
- LiveMath Video: VC.03.T5.mp4
- LiveMath Notebook: V3.2.e.the
- V3.2f: VC.03.T6: Lagrange's method for constrained maximization and minimization
- LiveMath Video: V3.2.f-LMVideo.mp4
- LiveMath Video: VC.03.T6.mp4
- LiveMath Notebook: V3.2.f.the
- V3.3: VC.03 - Give It a Try
- V3.3a: VC.03.G1: The gradient points in the direction of greatest initial increase
- LiveMath Video: V3.3.a-LMVideo.mp4
- LiveMath Video: VC.03.G1a.mp4
- LiveMath Notebook: V3.3.a.the
- V3.3b: VC.03.G2: The gradient is perpendicular to the level curves and surfaces
- LiveMath Video: V3.3.b-LMVideo.mp4
- LiveMath Video: VC.03.G2a.mp4
- LiveMath Notebook: V3.3.b.the
- V3.3c: VC.03.G3: The heat seeker
- LiveMath Notebook: V3.3.c.the
- V3.3d: VC.03.G4: Doing 'em by hand
- LiveMath Video: V3.3.d-LMVideo.mp4
- LiveMath Video: VC.03.G4-1a.mp4
- LiveMath Notebook: V3.3.d.the
- V3.3e: VC.03.G5: The highest crests and the deepest dips
- LiveMath Notebook: V3.3.e.the
- V3.3f: VC.03.G6: Closest points, gradients and Lagrange's method
- LiveMath Video: V3.3.f-LMVideo.mp4
- LiveMath Notebook: V3.3.f.the
- LiveMath Video: VC.03.G6-Help.mp4
- V3.3g: VC.03.G7: The Cobb-Douglas manufacturing model for industrial engineering
- LiveMath Notebook: V3.3.g.the
- V3.3h: VC.03.G8: Data Fit in two variables: Plucking a guitar string
- LiveMath Notebook: V3.3.h.the
- V3.3i: VC.03.G9: Linearizations and total differentials
- LiveMath Notebook: V3.3.i.the
- V3.3j: VC.03.G10: Keeping track of constituent costs
- LiveMath Notebook: V3.3.j.the
- V3.3k: VC.03.G11: The great pretender
- LiveMath Notebook: V3.3.k.the
- V3.3l: VC.01.G1-A: Another Help Movie
- LiveMath Video: V3.3.l-LMVideo.mp4
- LiveMath Video: VC.03.G1-2a.mp4
- V3.3m: VC.01.G1-B: Another Help Movie
- LiveMath Video: V3.3.m-LMVideo.mp4
- LiveMath Video: VC.03.G1-c.mp4
- V3.3n: VC.01.G1-C: Yet Another Help Movie
- LiveMath Video: V3.3.n-LMVideo.mp4
- LiveMath Video: VC.03.G1-4a.mp4
- V3.3o: VC.03.G2.c Hint
- LiveMath Notebook: V3.3.o.the
- V3.4: VC.03 - Literacy
- V3.4a: VC.03.LiteracySheet
- LiveMath Notebook: V3.4.a.the
- V4: VC.04 - Trajectories
- V4.1: VC.04 - Basics
- V4.1a: VC.04.B1: Vector fields and their trajectories
- V4.1b: VC.04.B2: Flow of vector fields along curves; flow of vector fields across curves: Visual inspection
- LiveMath Video: V4.1.b-LMVideo.mp4
- LiveMath Video: VC.04.B2.mp4
- LiveMath Notebook: V4.1.b.the
- V4.1c: VC.04.B3: Flow of vector fields along curves; flow of vector fields across curves
- LiveMath Notebook: V4.1.c.the
- V4.2: VC.04 - Tutorials
- V4.2a: VC.04.T1: Flow across and flow along: Visual inspection
- LiveMath Notebook: V4.2.a.the
- V4.2b: VC.04.T2: Differential equations and and their associated vector fields
- LiveMath Notebook: V4.2.b.the
- V4.2c: VC.04.T3: Flow across and along a curve and the sign of the dot product
- LiveMath Notebook: V4.2.c.the
- V4.2d: VC.04.T4: The 2D electric field
- LiveMath Notebook: V4.2.d.the
- V4.2e: VC.04.T5: Troubleshooting plots of vector fields
- LiveMath Notebook: V4.2.e.the
- V4.3: VC.04 - Give It a Try
- V4.3a: VC.04.G1: Looking for sinks (drains)
- LiveMath Notebook: V4.3.a.the
- V4.3b: VC.04.G2: Flow along and flow across
- LiveMath Notebook: V4.3.b.the
- V4.3c: VC.04.G3: Normals, tangents and dot plots
- LiveMath Notebook: V4.3.c.the
- V4.3d: VC.04.G4: The most important vector field of them all: The gradient field
- LiveMath Notebook: V4.3.d.the
- V4.3e: VC.04.G5: Differential equations and their associated vector fields
- LiveMath Notebook: V4.3.e.the
- V4.3f: VC.04.G6: Trajectories: Can they cross?
- LiveMath Notebook: V4.3.f.the
- V4.3g: VC.04.G7: Drifting along with a tumbleweed
- LiveMath Notebook: V4.3.g.the
- V4.3h: VC.04.G8: Logistic harvesting revisited
- LiveMath Notebook: V4.3.h.the
- V4.3i: VC.04.G9: Water flow with spigots and drains
- LiveMath Notebook: V4.3.i.the
- V4.3j: VC.04.G10: 2D Electrical fields
- LiveMath Notebook: V4.3.j.the
- V4.3k: VC.04.G11: Gradient fields for max-min, Hamiltonian fields for level curves, and implicitly defined functions
- LiveMath Notebook: V4.3.k.the
- V4.4: VC.04 - Literacy
- V4.4a: VC.04.LiteracySheet
- LiveMath Notebook: V4.4.a.the
- V5: VC.05 - 2D Measurements
- V5.1: VC.05 - 2D Measurements - Basics
- V5.1a: VC.05.B1: Measuring flow across a curve with the integral
- V5.1b: VC.05.B2: Measuring flow along a curve with the integral
- LiveMath Video: V5.1.b-LMVideo.mp4
- LiveMath Notebook: V5.1.b.the
- LiveMath Video: VC.05.B2.mp4
- V5.1c: VC.05.B3: Measurements by path integrals
- LiveMath Video: V5.1.c-LMVideo.mp4
- LiveMath Notebook: V5.1.c.the
- LiveMath Video: VC.05.B3.mp4
- V5.1d: VC.05.B4: Directed curves; path integral; path independence, and graident fields
- LiveMath Video: V5.1.d-LMVideo.mp4
- LiveMath Notebook: V5.1.d.the
- LiveMath Video: VC.05.B4.mp4
- V5.2: VC.05 - 2D Measurements - Tutorials
- V5.2a: VC.05.T1: Backward and forward
- LiveMath Notebook: V5.2.a.the
- V5.2b: VC.05.T2: Screwing up
- LiveMath Notebook: V5.2.b.the
- V5.2c: VC.05.T3: Recognizing gradient fields: The gradient test
- LiveMath Notebook: V5.2.c.the
- V5.2d: VC.05.T4: Line integrals
- LiveMath Notebook: V5.2.d.the
- V5.2e: VC.05.T5: Summary of main ideas
- LiveMath Notebook: V5.2.e.the
- V5.3: VC.05 - 2D Measurements - Give It a Try
- V5.3a: VC.05.G1: Flow along and flow across
- V5.3b: VC.05.G2: Path integrals: Backward and forward
- LiveMath Notebook: V5.3.b.the
- V5.3c: VC.05.G3: Calculations and interpretations
- LiveMath Notebook: V5.3.c.the
- V5.3d: VC.05.G4: Water
- LiveMath Notebook: V5.3.d.the
- V5.3e: VC.05.G5: Sources and sinks
- LiveMath Notebook: V5.3.e.the
- V5.3f: VC.05.G6: Gradient fields are where the mathematical action is
- LiveMath Notebook: V5.3.f.the
- V5.3g: VC.05.G7: Work and how the physicists measure it
- LiveMath Notebook: V5.3.g.the
- V5.3h: VC.05.G8: Spin fields
- LiveMath Notebook: V5.3.h.the
- V5.3i: VC.05.G9: "Calculus Cal" screws up again
- LiveMath Notebook: V5.3.i.the
- V5.3j: VC.05.G10
- LiveMath Notebook: V5.3.j.the
- V5.4: VC.05 - 2D Measurements - Literacy
- V5.4a: VC.05.LiteracySheet
- LiveMath Notebook: V5.4.a.the
- V6: VC.06 - Sources
- V6.1: VC.06 - Sources - Basics
- V6.1a: VC.06.B1: Using a 2D integral to measure flow across closed curves
- LiveMath Notebook: V6.1.a.the
- LiveMath Video: V6.1.a-LMVideo.mp4
- V6.1b: VC.06.B2: Sources, sinks, and the divergence of a vector field
- LiveMath Video: V6.1.b-LMVideo.mp4
- LiveMath Notebook: V6.1.b.the
- V6.1c: VC.06.B3: Flow-across-the-curve measurements in the presence of singularities
- V6.2: VC.06 - Sources - Tutorials
- V6.2a: VC.06.T1: The pleasure of calculating path integrals when mixed partials equation = 0
- LiveMath Notebook: V6.2.a.the
- LiveMath Video: V6.2.a-LMVideo.mp4
- V6.2b: VC.06.T2: Using a 2D integral to measure flow along closed curves
- LiveMath Notebook: V6.2.b.the
- V6.2c: VC.06.T3: Rotation (swirl) of a vector field
- LiveMath Notebook: V6.2.c.the
- V6.2d: VC.06.T4: Summary of main ideas.
- LiveMath Notebook: V6.2.d.the
- V6.3: VC.06 - Sources - Give It a Try
- V6.3a: VC.06.G1: Sources, sinks and swirls
- LiveMath Notebook: V6.3.a.the
- V6.3b: VC.06.G2: Singularity sources, sinks and swirls
- LiveMath Notebook: V6.3.b.the
- V6.3c: VC.06.G3: Agree or disagree
- LiveMath Notebook: V6.3.c.the
- V6.3d: VC.06.G4: Flow calculations in the presence of singularities
- LiveMath Notebook: V6.3.d.the
- V6.3e: VC.06.G5: 2D electric fields, dipole fields, and Gauss's law in physics
- LiveMath Notebook: V6.3.e.the
- V6.3f: VC.06.G6: The Laplacian and steady-state heat
- LiveMath Notebook: V6.3.f.the
- V6.3g: VC.06.G7: Calculating path integrals in the presence of singularities
- LiveMath Notebook: V6.3.g.the
- V6.3h: VC.06.G8: Water and electricity
- LiveMath Notebook: V6.3.h.the
- V6.3i: VC.06.G9: Is parallel flow always irrotational?
- LiveMath Notebook: V6.3.i.the
- V6.3j: VC.06.G10: Spin fields
- LiveMath Notebook: V6.3.j.the
- V6.4: VC.06 - Sources - Literacy
- V6.4a: VC.06.LiteracySheet
- LiveMath Notebook: VC.06.Literacy.the
- V7: VC.07 - Transforming 2D Integrals
- V7.1: VC.07 - Transforming 2D Integrals - Basics
- V7.1a: VC.07.B1
- LiveMath Video: V7.1.a-LMVideo.mp4
- LiveMath Video: VC.07.B1-LMVideo.mp4
- LiveMath Notebook: V7.1.a.the
- V7.1b: VC.07.B2
- LiveMath Notebook: V7.1.b.the
- V7.1c: VC.07.B3
- LiveMath Video: V7.1.c-LMVideo.mp4
- LiveMath Notebook: V7.1.c.the
- V7.2: VC.07 - Transforming 2D Integrals - Tutorials
- V7.2a: VC.07.T1
- LiveMath Notebook: V7.2.a.the
- V7.2b: VC.07.T2
- LiveMath Notebook: V7.2.b.the
- V7.2c: VC.07.T3
- LiveMath Notebook: V7.2.c.the
- V7.2d: VC.07.T4
- LiveMath Notebook: V7.2.d.the
- V7.3: VC.07 - Transforming 2D Integrals - Give It a Try
- V7.3a: VC.07.G1
- LiveMath Notebook: V7.3.a.the
- V7.3b: VC.07.G2
- LiveMath Notebook: V7.3.b.the
- V7.3c: VC.07.G3
- LiveMath Notebook: V7.3.c.the
- V7.3d: VC.07.G4
- LiveMath Notebook: V7.3.d.the
- V7.3e: VC.07.G5
- LiveMath Notebook: V7.3.e.the
- V7.3f: VC.07.G6
- LiveMath Notebook: V7.3.f.the
- V7.3g: VC.07.G7
- LiveMath Notebook: V7.3.g.the
- V7.3h: VC.07.G8
- LiveMath Notebook: V7.3.h.the
- V7.3i: VC.07.G9
- LiveMath Notebook: V7.3.i.the
- V7.3j: VC.07.G10
- LiveMath Notebook: V7.3.j.the
- V7.3k: VC.07.G11
- LiveMath Notebook: V7.3.k.the
- V7.4: VC.07 - Transforming 2D Integrals - Literacy
- V7.4a: VC.07.LiteracySheet
- LiveMath Notebook: VC.07.Literacy.the
- V8: VC.08 - Transforming 3D Integrals
- V8.1: VC.08 - Transforming 3D Integrals - Basics
- V8.1a: VC.08.B1
- LiveMath Notebook: V8.1.a.the
- V8.1b: VC.08.B2
- LiveMath Notebook: V8.1.b.the
- V8.1c: VC.08.B3
- LiveMath Notebook: V8.1.c.the
- V8.1d: VC.08.B4
- LiveMath Notebook: V8.1.d.the
- V8.2: VC.08 - Transforming 3D Integrals - Tutorials
- V8.2a: VC.08.T1
- LiveMath Notebook: V8.2.a.the
- V8.2b: VC.08.T2
- LiveMath Notebook: V8.2.b.the
- V8.2c: VC.08.T3
- LiveMath Notebook: V8.2.c.the
- V8.2d: VC.08.T4
- LiveMath Notebook: V8.2.d.the
- V8.3: VC.08 - Transforming 3D Integrals - Give It a Try
- V8.3a: VC.08.G1
- LiveMath Notebook: V8.3.a.the
- V8.3b: VC.08.G2
- LiveMath Notebook: V8.3.b.the
- V8.3c: VC.08.G3
- LiveMath Notebook: V8.3.c.the
- V8.3d: VC.08.G4
- LiveMath Notebook: V8.3.d.the
- V8.3e: VC.08.G5
- LiveMath Notebook: V8.3.e.the
- V8.3f: VC.08.G6
- LiveMath Notebook: V8.3.f.the
- V8.3g: VC.08.G7
- LiveMath Video: V8.3.g-LMVideo.mp4
- LiveMath Video: VC.08.G7-Help1.mp4
- LiveMath Notebook: V8.3.g.the
- V8.3h: VC.08.G8
- LiveMath Notebook: V8.3.h.the
- V8.3i: VC.08.G9
- LiveMath Notebook: V8.3.i.the
- V8.4: VC.08 - Transforming 3D Integrals - Literacy
- V8.4a: VC.08.Literacy
- LiveMath Notebook: V8.4.a.the
- V8.4b: VC.08.LS.2 Help
- LiveMath Video: V8.4.b-LMVideo.mp4
- LiveMath Notebook: V8.4.b.the
- LiveMath Video: VC.08.LS2.m4v
- V9: VC.09 - Spherical
- V9.1: VC.09 - Spherical - Basics
- V9.1a: VC.09.B1
- LiveMath Notebook: V9.1.a.the
- V9.1b: VC.09.B2
- LiveMath Notebook: V9.1.b.the
- V9.2: VC.09 - Spherical - Tutorials
- V9.2a: VC.09.T1
- LiveMath Notebook: V9.2.a.the
- V9.2b: VC.09.T2
- LiveMath Notebook: V9.2.b.the
- V9.2c: VC.09.T3
- LiveMath Notebook: V9.2.c.the
- V9.3: VC.09 - Spherical - Give It a Try
- V9.3a: VC.09.G1
- LiveMath Notebook: V9.3.a.the
- V9.3b: VC.09.G2
- LiveMath Notebook: V9.3.b.the
- V9.3c: VC.09.G3
- LiveMath Notebook: V9.3.c.the
- V9.3d: VC.09.G4
- LiveMath Notebook: V9.3.d.the
- V9.3e: VC.09.G5
- LiveMath Notebook: V9.3.e.the
- V9.3f: VC.09.G6
- LiveMath Notebook: V9.3.f.the
- V9.3g: VC.09.G7
- LiveMath Notebook: V9.3.g.the
- V9.3h: VC.09.G8
- LiveMath Notebook: V9.3.h.the
- V9.3i: VC.09.G9
- LiveMath Notebook: V9.3.i.the
- V9.3j: VC.09.G10
- LiveMath Notebook: V9.3.j.the
- V9.3k: VC.09.G11
- LiveMath Notebook: V9.3.k.the
- V9.4: VC.09 - Spherical - Literacy
- V9.4a: VC.09.LiteracySheet
- LiveMath Notebook: V9.4.a.the
- V10: VC.10 - 3D Measurements
- V10.1: VC.10 - 3D Measurements - Basics
- V10.1a: VC.10.B1
- LiveMath Notebook: V10.1.a.the
- V10.1b: VC.10.B2
- LiveMath Notebook: V10.1.b.the
- V10.1c: VC.10.B3
- LiveMath Notebook: V10.1.c.the
- V10.1d: VC.10.B4
- LiveMath Notebook: V10.1.d.the
- V10.1e: VC.10.B5
- LiveMath Notebook: V10.1.e.the
- V10.2: VC.10 - 3D Measurements - Tutorials
- V10.2a: VC.10.T1
- LiveMath Notebook: V10.2.a.the
- V10.2b: VC.10.T2
- LiveMath Notebook: V10.2.b.the
- V10.2c: VC.10.T3
- LiveMath Notebook: V10.2.c.the
- V10.2d: VC.10.T4
- LiveMath Notebook: V10.2.d.the
- V10.2e: VC.10.T5
- LiveMath Notebook: V10.2.e.the
- V10.3: VC.10 - 3D Measurements - Give It a Try
- V10.3a: VC.10.G1
- LiveMath Notebook: V10.3.a.the
- V10.3b: VC.10.G2
- LiveMath Notebook: V10.3.b.the
- V10.3c: VC.10.G3
- LiveMath Notebook: V10.3.c.the
- V10.3d: VC.10.G4
- LiveMath Notebook: V10.3.d.the
- V10.3e: VC.10.G5
- LiveMath Notebook: V10.3.e.the
- V10.3f: VC.10.G6
- LiveMath Notebook: V10.3.f.the
- V10.3g: VC.10.G7
- LiveMath Notebook: V10.3.g.the
- V10.3h: VC.10.G8
- LiveMath Notebook: V10.3.h.the
- V10.3i: VC.10.G9
- LiveMath Notebook: V10.3.i.the
- V10.3j: VC.10.G10
- LiveMath Notebook: V10.3.j.the
- V10.4: VC.10 - 3D Measurements - Literacy
- V10.4a: VC.10.LiteracySheet
- LiveMath Notebook: V10.4.a.the