Calculus III

Course Objectives:

1. Calculate various operations or functions for vectors, including addition, cross product (in 3-space), dot product, length;
2. Work with space curves and calculate velocity, tangent vector, acceleration, arc length, curvature, binormal, torque, and other properties and functions of curves, and to find parameterizations of curves in terms of arc length;
3. Calculate points of discontinuity, partial derivatives, total derivatives, directional derivatives, local extrema, tangent planes, normals, gradients, for multivariable functions and surfaces, and classify local extrema using information stored in the Hessian matrix
4. Use Lagrange multipliers to solve constrained optimization problems;
5. Use double and triple integrals in rectangular, spherical, polar, and cylindrical co-ordinates to calculate volume, mass, centroids, moments of inertia, surface area;
6. Perform change of variables in multiple integrals using Jacobian matrices;
7. Use line integrals to calculate work in a vector field and other related applications, use path-independence and potential functions (where appropriate) to calculate line integrals, use Green’s theorem to evaluate line integrals; Work with curl, divergence, calculate surface integrals and flux.