COURSE NUMBER AND TITLE: MATH 2013 Calculus and Analytic Geometry III

CREDIT HOURS: 4

CATALOG DESCRIPTION: A study of calculus on multivariate functions. Topics include vectors, vector-valued functions, functions of several variables, parametric equations, partial differentiation, multiple integration with applications, line integrals, and Green’s theorem.

PREREQUISITE(S): Math 2012 (grade of C or better) or advanced placement.

SUGGESTED TEXT(S):
Calculus, by Salas, Hille, Etgen
Calculus, by Rogawski

COURSE OUTLINE:

1. Vector Calculus
   • Vectors
   • Dot Products; Cross Products
   • Vector Parametrization of Lines and Planes
   • Vector Functions
   • Differentiation Formulas
   • Curvilinear Motion; Curvature; Vector Calculus in Mechanics
2. Functions of Several Variables
   • Partial Derivatives
   • Open Sets and Closed Sets
3. Gradients; Extreme Values; Differentials
   • Differentiability and the Gradient; Directional Derivatives
   • Applications
4. Double and Triple Integrals
   • Double Integrals in Polar Coordinates
   • Some Applications of Double Integration
   • Triple Integrals in Cylindrical Coordinates
   • Jacobians; Changing Variables in Multiple Integration
5. Line Integrals and Surface Integrals
   • The Fundamental Theorem for Line Integrals
   • Line Integrals with respect to Arc Length
   • Green’s Theorem
   • Surface Integrals
   • The Divergence Theorem
   • Stokes’ Theorem