MATH 3300 - Calculus III

• Athens: Every fall and spring
• Regional Campuses: Regional Campuses Course Offerings

• Students will be able to perform and apply vector operations, including the dot and cross product of vectors, in the plane and space.
• Students will be able to graph and find equations of lines, planes, cylinders and quadratic surfaces.
• Students will be able to differentiate and integrate vector-valued functions.
• Students will be able to interpret position vectors that are a function of time as velocity and acceleration.
• Students will be able to evaluate limits and determine the continuity and differentiability of functions of several variables.
• Students will be able to describe graphs, level curves and level surfaces of functions of several variables.
• Students will be able to find partial derivatives, directional derivatives, and gradients and use them to solve applied problems.
• Students will be able to find equations of tangent planes and normal lines to surfaces that are given implicitly or parametrically.
• Students will be able to use the chain rule for functions of several variables (including implicit differentiation).
• Students will be able to find critical points using first partials and interpret them as relative extrema/saddle points using the second partials test.
• Students will be able to find absolute extrema on a closed region.
• Students will be able to solve to optimization problems for functions of several variables.
• Students will be able to use Lagrange multipliers to solve constrained optimization problems.
• Students will be able to evaluate multiple integrals in appropriate coordinate systems such as rectangular, polar, cylindrical and spherical coordinates.
• Students will be able to apply integration techniques to solve problems involving volume, surface area, density, moments and centroids.
• Students will be able to use Jacobians to change variables in multiple integrals.
• Students will be able to use evaluate line and surface integrals.
• Students will be able to identify when a line integral is independent of path and use the Fundamental Theorem of Line Integrals to solve applied problems.
• Students will be able to identify conservative and inverse square fields.
• Students will be able to find the curl and divergence of a vector field.
• Students will be able to solve applied problems by finding the work done on an object moving in a vector field.
• Students will be able to solve applied problems by finding the flux of a field through a surface.
• Students will be able to solve problems using Green’s Theorem, the Divergence Theorem and Stokes’s Theorem.