

Course ID:  MATH 2270. 4 hours. 
Course Title:  Calculus III for Science and Mathematics 
Course Description:  Calculus of functions of two and three variables: Parametric
curves and applications to planetary motion. Derivatives, the
gradient, Lagrange multipliers. Multiple integration, area,
volume, and physical applications, polar, cylindrical, and
spherical coordinates. Line and surface integrals, Green's,
Stokes's, and Divergence theorems, with applications to physics. 
Oasis Title:  Calc III Science and Math 
Duplicate Credit:  Not open to students with credit in MATH 2270H, MATH 2500, MATH 2500E 
Prerequisite:  MATH 2260 or MATH 2310H or MATH 2410 or MATH 2410H 
Semester Course Offered:  Offered fall, spring and summer semester every year. 
Grading System:  AF (Traditional) 

Course Objectives:  Students should be able to calculate partial derivatives,
directional derivatives and gradients. Students should be able
to solve maximum and minimum problems using Lagrange
multipliers. They should learn to calculate area, volume,
center of mass, and moment of inertia using multiple integrals.
They are expected to understand integrals along curves and
surfaces, culminating in various generalizations of the
Fundamental Theorem of Calculus. Students should be able to
apply the tools learned in this course to areas such as
planetary motion, gravitation, data fitting, Gauss's Law, and
fluid dynamics. 
Topical Outline:  1. Review of vector algebra.
2. Parametric curves; Kepler's laws.
3. Partial differentiation: directional derivatives, gradients,
tangent planes, chain rule, maximum/minimum problems, and
Lagrange multipliers.
4. Multiple integration: double and triple integrals, change of
order of integration, applications to computations of areas,
volumes, center of mass and moments of inertia. Polar,
cylindrical, and spherical coordinates.
5. Line integrals, work, pathindependence, and Green's Theorem.
6. Surface integrals and flux. Curl, divergence, Stokes's and
Divergence Theorems and their applications. 