Handbook

Understand and apply multivariable calculus to problems in the mathematical and physical sciences;

Find and classify the extrema of functions of several variables;

Compute Taylor series for functions of several variables;

Compute line, surface and volume integrals in Cartesian, cylindrical and polar coordinates;

Apply the integral theorems of Green, Gauss and Stokes;

Use computer algebra packages to solve mathematical problems;

Present a mathematical argument in written form;

Understand and apply the formal definition of a limit to functions of several variables;

Prove various identities between grad, div and curl;

Develop and present rigorous mathematical proofs.

Demonstrate an understanding of the notions of torsion and curvature and be able to compute them;

Apply stereographic projection and its properties;

Articulate the difference between pointwise and uniform convergence for functions of one variable;

Use the properties of analytic functions to prove fundamental results.