Multivariable and Vector Calculus

Learning outcomes

What learners can expect

1. Compute and interpret partial derivatives, gradients, total differentials, tangent planes, Hessians, and local extrema.
2. Solve constrained optimization problems with geometric and Lagrange-multiplier reasoning, including regularity checks.
3. Set up/evaluate double and triple integrals and transform coordinates with correct Jacobians.
4. Compute divergence, curl, line integrals, conservative potentials, and path-independence conditions.
5. Parameterize surfaces, compute area and oriented flux, and manage orientation consistently.
6. Apply and independently verify Green's, Stokes', and divergence theorems with correct hypotheses and geometry.