MATH 223 - Calculus and Analytic Geometry III

4 Credits: (4 lecture)

Course Description
This course is a continuation of Calculus and Analytic Geometry II. It includes a study of plane and solid analytical geometry and vectors, partial differentiation, multiple integrals, and vector analysis. 

Note Spring semester only.

Prerequisite MATH 222.

A. Show the significance of the vector and utilize the vector to perform the basic vector operations of addition and multiplication by a scalar.

B. Find the dot product and the vector product of two vectors.

C. Perform the differentiation and integration of vectors.

D. utilize solid analytic geometry including the concepts of planes and lines

E. Solve the function of two or more variables for the partial derivative.

F. Utilize the partial derivative to find the directional derivative, gradient, tangent plane, and normal lines.

G. Extend the partial derivative concept to find higher order partial derivatives.

H. Use multiple integrals.

I. Utilize the concept of multiple integrals to examine cylindrical and spherical coordinates.

J. Perform line integrals.

K. Apply Green’s Theorem, Stoke’s Theorem, and the Divergence Theorem.

Content
A. Vectors in the plane

B. Vectors in space

C. Lines and planes in space

D. Vector valued functions

E. Partial differentiation

F. Multiple integration

G. Cylindrical and spherical coordinates

H. Vector analysis

I. Line integrals

J. Green’s Theorem

K. Stoke’s Theorem

L. The Divergence Theorem

Student Evaluation
Daily assignments in problem solving and the operations, periodic quizzes, and midterm and final examinations.