Course Goals: To help students to develop skills and knowledge for standard concepts in multivariate calculus and vector algebra.
- Extend single variable calculus concepts to higher dimensions (e.g. partial derivatives, gradients, integrals, etc.).
- Introduce vector notation and algebra.
- Explore visualizations in space.
- Introduce parametrizations of curves and surfaces.
- Introduce particle motion concepts (e.g. velocity and acceleration)
- Introduce arclength and curvature.
- Introduce multivariate optimization.
- Introduce non-rectangular coordinate systems.
- Introduce generalizations of the fundamental theorem of calculus (e.g. Green’s theorem).
Student Learning Outcomes: Students will be able to:
- Cite basic definitions.
- Evaluate vector operations.
- Use Maple to visualize higher dimensional graphs.
- Compute standard quantities (e.g. arclength, curvature, unit tangent vector, etc.)
- Change coordinates (e.g., polar, cylindrical, etc.)
- Compute differential and integral operations (partial derivatives, gradients, double integrals, etc.)
- Find critical points, relative and absolute extrema, etc.
- Compute standard types of integrals (curve integrals, area integrals, surface integrals, etc.)
- Compute integrals using standard theorems (e.g. with potential functions, Green’s theorem, etc.)