COURSE SYLLABUS

COURSE SYLLABUS

Course Number: MATH2630

Course Title: CALCULUS III

Credit Hours: 4

Prerequisites: MATH1620

Corequisite:

Bulletin Description:

CALCULUS III (4). Pr., MATH1620. Multivariate calculus: vector-valued functions, partial derivatives, multiple integration, vector calculus.

Students may receive credit for only one of MATH2630, MATH2637, MATH2730.

Objectives:

To develop student mathematical and analytic skills. To present the fundamental concepts of multivariate calculus and to develop student understanding and skills in the topic necessary for its applications in the sciences and engineering.

Course Content:

Three Dimensional Analytic Geometry and Vectors. [6 days]

Vector-Valued Functions and Space Curves, Motion in Space, Cylindrical and Spherical Coordinates.

Partial Derivatives. [18 days]

Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Differentials, The Chain Rule, Directional Derivatives and the Gradient Vector, Maxima, Minima, and Saddle Points, Lagrange Multipliers.

Multiple Integrals. [14 days]

Double Integrals over Rectangles, Iterated Integrals, Integrals over General Regions, Triple Integrals, Integrals in Cylindrical and spherical Coordinates and Change of Variable in Multiple Integrals.

Vector Calculus. [14 days]

Vector Fields, Line Integrals, Green's Theorem in the Plane, Curl and Divergence, parametric Surfaces, Surface Integrals, Stokes' Theorem and the Divergence Theorem.