MATH 430:431: Advanced Calculus
Prerequisites: MATH 271, amd MATH 300. MATH 430 is a prerequisite for MATH 431.
Credit Hours: (3:3)
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: Some selected contents will be explored with appropriate technological tools.
1. Construction of the real numbers from the rational numbers
2. Topology of the real numbers
3. Limits of Sequences
4. Monotone Convergence Theorem, Fixed Point Theorem, and Newton's Method
5. Limits and Partial Limits
6. Bolzano-Weierstress Theorem
7. Limits and continuity of functions
8. Maximum and minimum
9. Intermediate value Theorem
10. Uniform Continuity
11. Differentiation
12. Mean Value and Cauchy Mean Value Theorems
13. Taylor's theorem
14. Integration
15. Sequences and series of functions, including uniform convergence and Fourier series.
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
February 20, 2017
Sept. 2001 Review Stephen Corwin, Chair