# Vector Calculus and Linear Algebra for Advanced High School Students

Many rockstar 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 advanced students may finish Calculus I (AB) and Calculus II (BC) during their junior year of high school. For these students, enrolling in Linear Algebra, and perhaps Multivariable Calculus and Differential Equations, 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 Calculus 3 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 12, 2020*

Review by: Anonymous

Courses Completed: Calculus I

Review: This course is amazing! I took it as a requirement for admission to an MBA program, and couldn't have been happier with the quality and rigor of the course. I previously took calculus two times (at a public high school and then a large public university commonly cited as a "public ivy"), this course was by far the best and *finally* made the concepts click. Previously I had no idea what was going on because terrible PhD students were teaching the course and saying stuff like "a derivative is the slope of a tangent line" - ??? but what does that mean ???, but the instructors in the Shorter University course explain everything in ways where it FINALLY made sense (e.g., "imagine a roller coaster hitting the top of a hill, there's a moment where it shifts momentum and you're not accelerating or decelerating, that's what a 0 rate of change is - that's when the derivative would be zero"). They explain everything in multiple ways and relate it to other concepts. It all made perfect sense when I finally had a good instructor. Really recommend this class

Transferred Credits to: The Wharton School, UPenn

*Date Posted: Jun 6, 2020*

Review by: Douglas Z.

Courses Completed: Multivariable Calculus, Differential Equations, Linear Algebra, Probability Theory

Review: I loved these courses. So in depth and comprehensive. The mix of software and math curriculum was tremendously helpful to my future studies and career in engineering. I highly recommend these courses if you are bored of textbook courses.

Transferred Credits to: University of Massachusetts, Amherst

*Date Posted: Mar 17, 2020*

Review by: Rebecca M.

Courses Completed: Calculus II, Multivariable Calculus

Review: Fantastic courses! I barely made it through Cal 1, and halfway through Cal 2 I found this program. I took Cal 2 and then Multivariable and I just loved it! SOOOOOOO much better than a classroom+textbook class. I highly recommend!

Transferred Credits to: Tulane University

## Distance Calculus - Curriculum Exploration

### VC.06 - Sources

- V6: VC.06 - Sources:
- V6.1: VC.06 - Sources - Basics
- V6.1.a: VC.06.B1: Using a 2D integral to measure flow across closed curves
- V6.1.b: VC.06.B2: Sources, sinks, and the divergence of a vector field
- V6.1.c: VC.06.B3: Flow-across-the-curve measurements in the presence of singularities
- V6.2: VC.06 - Sources - Tutorials
- V6.2.a: VC.06.T1: The pleasure of calculating path integrals when mixed partials equation = 0
- V6.2.b: VC.06.T2: Using a 2D integral to measure flow along closed curves
- V6.2.c: VC.06.T3: Rotation (swirl) of a vector field
- V6.2.d: VC.06.T4: Summary of main ideas.
- V6.3: VC.06 - Sources - Give It a Try
- V6.3.a: VC.06.G1: Sources, sinks and swirls
- V6.3.b: VC.06.G2: Singularity sources, sinks and swirls
- V6.3.c: VC.06.G3: Agree or disagree
- V6.3.d: VC.06.G4: Flow calculations in the presence of singularities
- V6.3.e: VC.06.G5: 2D electric fields, dipole fields, and Gauss's law in physics
- V6.3.f: VC.06.G6: The Laplacian and steady-state heat
- V6.3.g: VC.06.G7: Calculating path integrals in the presence of singularities
- V6.3.h: VC.06.G8: Water and electricity
- V6.3.i: VC.06.G9: Is parallel flow always irrotational?
- V6.3.j: VC.06.G10: Spin fields
- V6.4: VC.06 - Sources - Literacy