M 273M - Multivariable Calculus

Credit(s): 5

Prerequisite(s): a grade of “C” or better in M 172 or Math Department consent.
This is the third semester of a three semester sequence in calculus, intended for students majoring in engineering, mathematics, chemistry, or physics. It includes vectors, vector-valued functions, partial derivatives, multiple integrals, and integration in vector fields. (Fall Semester)

Course Learning Outcomes: Upon completion of the course, students will be able to

Use mathematical techniques to problem solve.
Explain three-dimensional coordinate systems, dot and cross products, equations of lines and planes, cylinders and quadratic 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.