MATH2219 — Multivariable Calculus
MATH 2219 - Multivariable Calculus 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. 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
Prerequisites: MATH1134