Undergraduate Analysis /
This is a logically self-contained introduction to analysis, suitable for students who have had two years of calculus. The book centers around those properties that have to do with uniform convergence and uniform limits in the context of differentiation and integration. Topics discussed include the...
| Main Author: | |
|---|---|
| Corporate Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1997.
|
| Edition: | Second edition. |
| Series: | Undergraduate texts in mathematics.
|
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
Table of Contents:
- Review of Calculus: Sets and Mappings. Real Numbers. Limits and Continuous Functions. Differentiation. Elementary Functions. The Elementary Real Integral
- Convergence: Normed Vector Spaces. Limits. Compactness. Series. The Integral in One Variable
- Applications of the Integral: Fourier Series. Improper Integrals. The Fourier Integral
- Calculus in Vector Spaces: Function on n-Space. The Winding Number and Global Potential Functions. Derivatives in Vector Spaces. Inverse Mapping Theorem. Ordinary Differential Equations
- Multiple Integration: Multiple Integrals. Differential Forms
- Appendix
- Index.