MATH 255 Vector Calculus • 5 Cr.
Course topics include multiple integration, line and surface integrals and the theorems of Green, Gauss and Stokes with applications. Related topics such as conservative vector fields, change of variables in special coordinate systems, the higher-dimensional Taylor's Theorem and constrained optimization will be considered. Prerequisite: Multivariable Calculus (MATH& 254).
After completing this class, students should be able to:Students taking this course will increase their understanding of the basic theory of functions of several variables, using vectors throughout. They should be able to: 1. Demonstrate they understand the basic integration and differentiation theory for functions of several variables. 2. Perform calculations relating to double and triple integrals in cartesian, polar, cylindrical and spherical coordinates. 3. Demonstrate the ability to visualize vector fields in various dimensions. 4. Explain the basic theory of line and surface integrals and the theorems of Green, Stokes and Gauss. 5. Perform basic calculations relating to line and surface integrals and apply the theorems of Green, Stokes and Gauss. 6. Demonstrate understanding of basic applications of these additional topics.