Introduction to Multivariable Calculus for Undergraduates

Multivariable calculus is often seen is an entirely new kind of calculus, but in reality, it's an application of single variable calculus to 3-dimensional space. Topics covered include vectors and surfaces, partial derivatives, double and triple integrals in various coordinate systems, and applications of both derivatives and integrals in 3D. This course covers all of the essential topics to multivariable calculus, but not advanced topics that some undergraduate courses don't cover such as Green's Theorem, Stoke's Theorem, Divergence Theorem, surface integrals, or vector integrals. This course will get you exactly what you need for your freshman or sophomore level multivariable course, and will be a great review for an upper level vector calculus course!

I find too often that students don’t know why they are learning something or how it relates to future classes or career. Some professors are too focused on getting the material over to you and giving you the test. Sound familiar? I will teach you how to think like an engineer, which means being able to break down complicated problems into simple pieces that you already know how to do! I recognize that students value simplicity and logic over complicated derivations and memorized processes. I will teach you the simplest way that has helped my students become successful for the past 5 years.

By the end of the course, you will know how to approach fundamental problems in each of the major topics and explain why they are relevant in engineering. The course is designed to also be used as a reference when you are taking the full version of the course as well, so don’t be afraid if you don’t pick everything up the first time you see it! My hope is that you have the “ah-ha that’s why Scott approached it that way” moment when you take the real course.