Dec 02, 2023  
2023-2024 Academic Catalog 
2023-2024 Academic Catalog
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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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