Continuation of MAT 231. Vectors, geometry, differentiation, and integration in Euclidean n-space. Line and surface integrals. Theorems of Green, Gauss, and Stokes.
Prerequisites
MAT 231 with a grade of “C” or higher
Student Learning Outcomes
- Define and operate with vectors in Euclidean 2- and 3-space.
- Define lines and curves in space.
- Apply vector-valued functions.
- Calculate the length of curves, curvature, and normal vectors.
- Write equations of planes, quadratic surfaces, and level curves.
- Evaluate limits and continuity of vector-value functions.
- Calculate partial derivatives.
- Determine directional derivatives and the gradient.
- Write equations of tangent planes and linear approximations.
- Determine absolute and relative extrema to surfaces.
- Evaluate multiple integrals.
- Draw vector fields and line integrals.
- Apply Green’s Theorem, curl, and divergence.
- Use surface integrals in applications.
- Apply Stoke’s Theorem and Divergence Theorem.
- Use MatLab to draw curves in two and three space.