MATH 205 - Multivariable Calculus

Number of Credits: 4
Multivariable Calculus continues MATH 136 with vectors and analytic geometry in three dimensions, partial derivatives, multiple integrals, line and surface integrals, and vector field theory. Students will be required to use a significant mathematical software such as Mathematica, Maple, or MATLAB throughout the course. See Mathematics Division web site for details (Fall) Five hours lecture. Four Credits. Four billable hours.

Pre-requisite(s): MATH 136 with a minimum grade of C or better.
Course Objectives: Upon successful completion of this course, students will be able to:

Perform vector operations with dot and cross products. (GE2, GE3,PG2,PG3)
Graph lines and surfaces in 3-dimensional space. (GE2,GE3, PG2,PG3)
Compute derivatives and integrals for vector functions. (GE2, PG3)
Analyze torsion and curvature. (GE2,GE3,PG2,PG3)
Compute partial derivatives for multi-variable functions. (GE2,GE3,PG2,PG3)
Compute directional derivatives and gradients. (GE2,GE3,PG2, PG3)
Apply maximization techniques to multi-variable functions. (GE2,GE3,PG2,PG3)
Compute multiple integrals. (GE2,GE3,PG2,PG3)
Apply multiple integration to physical problems. (GE2,GE3, PG2,PG3)
Derive and apply Green’s and Stoke’s Theorems. (GE2,GE3,PG2, PG3)
Apply vector analysis to potential and conservation of energy problems. (GE2,GE3,PG2,PG3)
Set-up and solve application problems using technology, such as graphing calculators and mathematical software. (GE1,GE2,GE3,GE4,PG1,PG2,PG3,PG4)