MATH 2219 - Multivariable Calculus
5 Credits
Extends concepts of single-variable calculus to calculus of several variables. The topics include vectors in three-dimensional space, quadric surfaces, limits in two and three dimensions, partial derivatives, gradients, extreme value problems, multiple integration and applications, space curves, curvature, The Frenet frame, divergence, curl, line integrals, conservative vector fields and potential functions, surface and volume integrals, Green’s, Stokes’ and the Divergence Theorems. Knowledge of computer algebra system is expected. Use of technology will be embedded throughout the course.
Pre-Requisites MATH 1134
Major Content Areas
Line integrals and surface 5% Space curves and motion in space 15% Polar, cylindrical, and spherical coordinates 10% Stokes’ Theorem & Divergence Theorem 10% Vector fields and operations on them 5% Limits and continuity of functions of several variables 5% Partial derivatives and gradients 10% Applications of partial derivatives 5% Double and triple integrals 15% Three dimensional analytic geometry 15%
Learning Outcomes
Compare and contrast the generalizations of the Fundamental Theorem of Calculus listed above. Fine derivatives of vector-valued functions and use those derivatives to describe an object’s motion. Use line integrals to calculate work done by a force field in moving an object along a curve. Compute gradients and directional derivatives and apply them to finding tangent spaces and normal lines. State and apply the Fundamental Theorem of Line Integrals, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem. Use partial derivatives and/or Lagrange multipliers to locate extreme values and saddles points of a function of several variables. Evaluate iterated integrals using rectangular, cylindrical, and spherical coordinate systems. Use triple integrals to solve3 problems such as calculating volume, center of mass, moments of inertia, and the expected value of a continuous random variable. Recognize vector fields. Compute and interpret curl, divergence, and flux. Explain the concepts of limits and continuity for real-valued functions of two or more variables.
Minnesota Transfer Curriculum (MNTC) Goals
02 - Critical Thinking 04 - Mathematical/Logical Reasoning
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