# 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: Dec 9, 2019*

Review by: Louisa A.

Courses Completed: Calculus I

Review: My microeconomics class required college-level calculus as a prerequisite, and I didn't want to wait until next year to take the class. So, I took DC's Calculus I class over the summer, so I could register for econ when I got back to school this fall. I actually think I got more help taking the class online than I would have in the huge lecture classes here. Prof. Curtis was really clear in explaining concepts and talking me through the topics that I was having trouble with. It took me about 10 weeks to finish the class, which didn't seem too long and didn't feel rushed. My friends who are in calculus now, trying to finish the prereq, are pretty jealous!

*Date Posted: Jul 25, 2020*

Review by: Michael Linton

Student Email: mdl264@cornell.edu

Courses Completed: Calculus I

Review: Amazing professor, extremely helpful and graded assignments quickly. To any Cornellians out there, this is the Calculus Course to take in Summer to fulfill your reqs! I would definitely take more Calculus Classes this way in the future!

Transferred Credits to: Cornell University

## 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