A Tasty Combination: Multivariable Calculus and Differential Forms

TL;DR

This paper introduces differential forms as a unifying framework for multivariable calculus, enhancing understanding of differentiation and integration in higher dimensions, and connecting to de Rham Cohomology.

Contribution

It presents differential forms as a comprehensive approach to multivariable calculus, linking classical calculus concepts with modern geometric and topological methods.

Findings

Differential forms unify differentiation and integration in multiple variables.

The approach connects multivariable calculus to de Rham Cohomology.

Provides a new perspective on calculus through geometric and topological tools.

Abstract

Differential Calculus is a staple of the college mathematics major's diet. Eventually one becomes tired of the same routine, and wishes for a more diverse meal. The college math major may seek to generalize applications of the derivative that involve functions of more than one variable, and thus enjoy a course on Multivariate Calculus. We serve this article as a culinary guide to differentiating and integrating functions of more than one variable -- using differential forms which are the basis for de Rham Cohomology.