Multivariable Calculus

Full course description

Multivariable calculus develops calculus into more than one variable. Multivariable calculus can help to better understand techniques and algorithms used to analyze multidimensional data or optimization techniques used to train neural networks. In this course, we introduce power series and Taylor approximation/polynomials, as well as Taylor’s theorem to approximate functions. We use vector calculus combined with calculus/analysis, and we introduce path functions, and how to calculate lengths of paths or to integrate along a path. We discuss extensions of the chain rule and product rule to higher dimensions, and the corresponding extensions of derivative and tangent lines/planes.  We also cover part of optimization problems, and we introduce multiple integrals to compute areas and volumes, among others. Finally, we look at several types of differential equations.