MATH208C: Multivariable Calculus

Credits 4 Lab/Practicum/Clinical Hours 0 Lecture Hours 4
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A study of vectors, vector products, vector algebra, and vector-valued functions; motion in space; partial differentiation, gradient, divergence, curl, chain rule, tangent planes, extrema, and Lagrange multipliers; multiple, line, and surface integrals; divergence, and Green’s and Stokes’ theorems. A graphing calculator is required.


Students must pass all prerequisite courses with a grade of C or higher.
Learning Outcomes
  • State, interpret, and apply the definitions, theorems, and properties involving the algebra and differential and integral calculus of multivariable vector-valued functions, including Green’s, Stokes', and divergence theorem.
  • Solve problems involving vector algebra and vector products.
  • Solve problems involving limits, derivatives, and integrals of multivariable vector-valued functions including those invoking the use of Green’s, Stokes’, and divergence theorem.
  • Approximate the value of a function using the tangent plane approximation.
  • Graph cylinders, quadric surfaces, multivariable functions and their level curves, and vector-valued functions.
  • Apply vector products to calculate curvature and torsion.
  • Solve extremization problems using the second derivative test and the Lagrange multiplier technique.