The course covers multivariable calculus, including multiple integration, partial differentiation, optimization, and vector calculus. Additional topics include line and surface integrals, parametric curves, vectors, geometry, and differentiation and integration in Euclidean n-space. The course emphasizes the application of divergence, curl, Green's Theorem, Stokes' Theorem, and the Divergence Theorem to vector fields.
Prerequisites
MAT 231 with a grade of “C” or higher
1. Apply vectors in three-dimensional space to solve mathematical problems.
2. Define lines and curves in space.
3. Apply vector-valued functions.
4. Utilize equations of planes and surfaces to address mathematical problems.
5. Apply cylindrical and spherical coordinate systems to solve mathematical problems.
6. Calculate partial derivatives of multivariable functions.
7. Compute extremes of functions of two variables.
8. Calculate differentials, directional derivatives, gradients, and equations of tangent planes.
9. Evaluate multiple integrals over various regions.
10. Apply multiple integrals to solve real-world and applied problems.
11. Define and recognize vector fields in mathematical contexts.
12. Evaluate line integrals and surface integrals.
13. Apply divergence, curl, Green's Theorem, Stokes' Theorem, and the Divergence Theorem to vector fields.