ADVANCED CALCULUS II

MA 451

Catalogue Description

Elements of partial differentiation, implicit function theorems, inverse function theorem, line integrals, Green’s Theorem, transformation of double integrals, uniform continuity, theory of integration, uniform convergence, and infinite series are studied in this course. 3 credits. Prerequisite: MATH 450 Advanced Calculus I or equivalent.

Goals

A. To present advanced topics of Calculus including Functions of Several Variables.

B. To demonstrate applications of Calculus to a variety of disciplines.

Procedures

A. Lecture/Discussion

B. Readings and assigned problems

Course Content

A. Integral Calculus of Functions of Several Variables

B. Improper Integrals

C. Vector Integral Calculus

D. Line and Surface Integrals

E. Theorems of Green, Gauss and Stokes

F. Functions and Sequences

G. Infinite Series of Constants

Evaluation Methods

1. Adherence to the Attendance Policy

2. Preparation of Homework Assignments

3. Class Participation

4. Comprehensive Mid-term and Final Examination

Bibliography

Required Text: Buck, R. Creighton, Advanced Calculus, 3rd Ed., McGraw Hill Publishing, International Series in Pure and Applied Mathematics, 1968.

Kaplan, Wilfred, Advanced Calculus, Addison-Wesley, 1991.

Olmstead, John H., Advanced Calculus, Prentice Hall, 1961.

Spiegel, Murray R., Schaum's Outline Series in Math, McGraw Hill Publishing, 1968.

Taylor, Angus E. and Mann, W. Robert, Advanced Calculus, John Wiley & Sons, 1983.