# Differential Equations, Multivariable Calculus and Linear Algebra for Advanced High School Students

Many excellent high school students will finish Calculus AB (Calculus I) and Calculus BC (Calculus II) during their junior or senior year of high school, and look to take more mathematics courses during high school. Yet, in most high schools, Calculus II is the highest course offered.Some very awesome students may finish Calculus I (AB) and Calculus II (BC) during their junior year of high school. For these accelerated students, enrolling in Differential Equations, Linear Algebra, and perhaps Multivariable Calculus, via Distance Calculus @ Roger Williams University is an excellent way to FINISH your lower division mathematics courses even before you step foot onto your new college/university campus the following Fall semester!

If you finish these AP Calculus courses during your senior year, then one option to get ahead with your academic plan is to complete the next few courses: Linear Algebra, Calculus 3 (Calculus III) - Multivariable Calculus, and perhaps even Differential Equations and/or Calculus-Based Statistics (Probability Theory) - during your senior year or during the summer before you start your new undergraduate university. Earning real collegiate academic credits for Linear Algebra and then transferring those credits to your new undergraduate college/university is an excellent way to start your new school with some advanced mathematics credits under your belt.

Here is a video about our Linear Algebra course via Distance Calculus @ Roger Williams University:

## Multivariable Calculus & High School

## Linear Algebra Course

## After AP Calculus for High School Students

## Distance Calculus - Student Reviews

*Date Posted: Jan 19, 2020*

Review by: William Williams

Student Email: wf.williamster@gmail.com

Courses Completed: Linear Algebra, Probability Theory

Review: I have difficulty learning calculus based math, akin to dyslexia when examining the symbolic forms, equations, definitions, and problems. Mathematica based calculus courses allowed me to continue with my studies because of the option of seeing the math expressed as a programming language for which I have no difficulty in interpreting visually and the immediate feedback of graphical representations of functions, equations, or data makes a huge impact on understanding. Mathematica based calculus courses should be the default method of teaching Calculus everywhere.

Transferred Credits to: Thomas Edison State College

*Date Posted: May 3, 2018*

Review by: James Holland

Courses Completed: Calculus I, Calculus II

Review: I needed to finish the Business Calculus course very very very fast before my MBA degree at Wharton started. With the AWESOME help of Diane, I finished the course in about 3 weeks, allowing me to start Wharton on time. Thanks Diane!

Transferred Credits to: Wharton School of Business, University of Pennsylvania

*Date Posted: Feb 19, 2020*

Review by: Rebecca Johnson

Courses Completed: Applied Calculus

Review: I took the Business Calculus course from Distance Calculus in 2013. I was admitted to my MBA program, but then they told me I needed to take Calculus before starting the program. I finished the Business Calculus course in about 3 weeks in August before my program started. Not the most fun thing to do over the summer, but at least I got it done. Thanks Diane and Distance Calculus team!

Transferred Credits to: Kellogg MBA Program

## Distance Calculus - Curriculum Exploration

### VC.03 - Gradient

- V3: VC.03 - Gradient:
- V3.1: VC.03 - Basics
- V3.1.a: VC.03.B1: The gradient and the chain rule
- V3.1.b: VC.03.B2: Level curves, level surfaces and the gradient as normal vector
- V3.1.c: VC.03.B3: The gradient points in the direction of greatest initial increase
- V3.1.d: VC.03.B4: Using linearizations to help to explain the chain rule
- V3.2: VC.03 - Tutorials
- V3.2.a: VC.03.T1: The total differential
- V3.2.b: VC.03.T2: What's the chain rule good for?
- V3.2.c: VC.03.T3: The gradient and maximization and minimization
- V3.2.d: VC.03.T4: Eye-balling a function for max-min
- V3.2.e: VC.03.T5: Data fit
- V3.2.f: VC.03.T6: Lagrange's method for constrained maximization and minimization
- V3.3: VC.03 - Give It a Try
- V3.3.a: VC.03.G1: The gradient points in the direction of greatest initial increase
- V3.3.b: VC.03.G2: The gradient is perpendicular to the level curves and surfaces
- V3.3.c: VC.03.G3: The heat seeker
- V3.3.d: VC.03.G4: Doing 'em by hand
- V3.3.e: VC.03.G5: The highest crests and the deepest dips
- V3.3.f: VC.03.G6: Closest points, gradients and Lagrange's method
- V3.3.g: VC.03.G7: The Cobb-Douglas manufacturing model for industrial engineering
- V3.3.h: VC.03.G8: Data Fit in two variables: Plucking a guitar string
- V3.3.i: VC.03.G9: Linearizations and total differentials
- V3.3.j: VC.03.G10: Keeping track of constituent costs
- V3.3.k: VC.03.G11: The great pretender
- V3.3.l: VC.01.G1-A: Another Help Movie
- V3.3.m: VC.01.G1-B: Another Help Movie
- V3.3.n: VC.01.G1-C: Yet Another Help Movie
- V3.3.o: VC.03.G2.c Hint
- V3.4: VC.03 - Literacy
- V3.5: VC.03 - Revisited
- V3.5.a: VC.03.B1 - Revisited
- V3.5.b: VC.03.B2 - Revisited
- V3.5.c: VC.03.B3 - Revisited
- V3.5.d: VC.03.T1 - Revisited
- V3.5.e: VC.03.T2 - Revisited
- V3.5.f: VC.03.T3 - Revisited
- V3.5.g: VC.03.T4 - Revisited
- V3.5.h: VC.03.T6 - Revisited
- V3.5.i: VC.03.G1.b.i - Revisited
- V3.5.j: VC.03.G1.d.i - Revisited
- V3.5.k: VC.03.G1.d.ii - Revisited
- V3.5.l: VC.03.G2.c - Revisited