Multivariable Calculus

Multivariable calculus is the study of functions of multiple variables, with the understanding that these functions can be thought of as vectors. In particular, it encompasses the study of partial derivatives, multiple integrals, and vector calculus.

Partial derivatives allow for the determination of how a function changes when one of its variables is changed, while holding the other variables constant. This is especially useful in optimization problems, where the aim is to find the maximum or minimum value of a function.

Multiple integrals extend the concept of a single integral to functions of multiple variables. Essentially, this allows for the calculation of the area or volume under a curve. Vector calculus is the study of how vectors interact with one another, including the analysis of vector fields. This is particularly useful in physics, where the behavior of objects in a given field can be predicted.