# MSUB Mathematics Department

### M 273 Multivariable Calculus

Course Description

4 credits
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.

Learning Outcomes

• 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.

Course Documents