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Sep 08, 2024
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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.
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