ABSTRACT
Multivariable calculus is essentially an extension of the calculus with one variable in which the system now depends on many variables. In engineering, multivariable calculus can be used to model higher dimensional system behavior, that is, stress may depend on the x, y, and z positions. Most of the concepts introduced in the one-variable calculus discussions can be extended to multivariable calculus starting with the ideas of partial derivatives. The higher-order partial derivatives lead onto the multivariable chain rule and ideas of a general directional derivative with applications to tangent planes. Higher-order integration of double and triple integrals using different coordinate systems is considered as well as how the concepts are used in real-world applications. There are many physical applications of double and triple integration, most of which depend on the idea of splitting a region into smaller pieces and summing over all the pieces.
