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Mathematics 431

MATH 430:431

Catalog Entry

MATH 430:431. Advanced Calculus
Three hours lecture (3:3).

Prerequisites: MATH 252

A systematic modern approach to the differential and integral calculus of one and several variables, including standard theorems and analytical techniques of mathematical analysis.


Detailed Description of Content of Course

The course will cover the following topics:

1. The construction of the real numbers from the rational numbers
2. The topology of the real numbers
3. Sequences
4. Limits
5. Bolzano-Weierstress Theorem
6. Continuous functions
7. Maximum and minimum
8. Intermediate values
9. Uniform Continuity
10. Functions of bounded variation
11. Differentiation
12. Mean value theorem
13. Taylor's theorem
14. Integration
15. Sequences and series of functions
16. Functions of several variables (differentiation and integration)
17. Line and surface integrals


Detailed Description of Conduct of Course

This is a lecture based course. Students will develop an understanding of the material by working exercises. Some instructors may require students to make presentations.


Goals and Objectives of the Course

This course is primarily for mathematics majors. Its goals and objectives are:

1. to develop an understanding of the structure of the real number system,
2. to develop an understanding of the theory of calculus,
3. to improve the student's skills in the mathematical methods, including the logical and orderly presentation of proofs.


Assessment Measures

Assessment measures include a final examination and may include any of the following:
in-class tests, quizzes, exercises, in-class presentations and research papers.


Other Course Information

The instructor may require that the students use a computer in exercises designed to enhance the understanding of theoretical material.


Review and Approval

Sept. 2001 Review Stephen Corwin, Chair