MA 2233 Calculus III

MA 2233 Calculus III

Course Goals: To help students to develop skills and knowledge for standard concepts in multivariate calculus and vector algebra.

Course Objectives:

  1. Extend single variable calculus concepts to higher dimensions (e.g. partial derivatives, gradients, integrals, etc.).
  2. Introduce vector notation and algebra.
  3. Explore visualizations in space.
  4. Introduce parameterizations of curves and surfaces.
  5. Introduce particle motion concepts (e.g. velocity and acceleration)
  6. Introduce arc length and curvature.
  7. Introduce multivariate optimization.
  8. Introduce non-rectangular coordinate systems.
  9. Introduce generalizations of the fundamental theorem of calculus (e.g. Green’s theorem).

Student Learning Outcomes: Students will be able to:

  1. Cite basic definitions.
  2. Evaluate vector operations.
  3. Use Maple to visualize higher dimensional graphs.
  4. Compute standard quantities (e.g. arc length, curvature, unit tangent vector, etc.)
  5. Change coordinates (e.g., polar, cylindrical, etc.)
  6. Compute differential and integral operations (partial derivatives, gradients, double integrals, etc.)
  7. Find critical points, relative and absolute extrema, etc.
  8. Compute standard types of integrals (curve integrals, area integrals, surface integrals, etc.)
  9. Compute integrals using standard theorems (e.g. with potential functions, Green’s theorem, etc.)