M 273 Multivariable Calculus
Prerequisite: M 172 and either M 110 or EGEN 105
Covers vector-valued functions, functions of two and three variables, partial differentiation, as well as multiple, line, and surface integrals; includes a variety of applications.
- Explain three-dimensional coordinate systems, dot and cross products, equations of lines and planes, cylinders and quadric surfaces;
- Explain vector-valued functions and space curves, their derivatives, arc length and curvature, and motion in space;
- Explain limits, continuity and partial derivatives of functions of several variables;
- Explain tangent planes to surfaces and linear approximations;
- Explain the chain rule, directional derivative and gradient vector, extreme values and Lagrange Multipliers;
- Explain double and triple integrals over general regions, and their applications;
- Explain triple integrals in cylindrical and spherical coordinates;
- Explain vector fields, line integrals and the Fundamental Theorem of Line Integrals;
- Define Green's Theorem;
- Explain curl and divergence of vector fields;
- Explain surface integrals, Stokes Theorem, and the Divergence Theorem.
Be prepared to take a wide variety of upper-division mathematics courses.