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A Course of Modern Analysis

Table of Contents

Part I. The Processes of Analysis
1. Complex numbers
2. The theory of convergence
3. Continuous functions and uniform convergence
4. The theory of Riemann integration
5. The fundamental properties of analytic functions
6. The theory of residues
7. The expansion of functions in infinite series
8. Asymptotic expansions and summable series
9. Fourier series and trigonometrical series
10. Linear differential equations
11. Integral equations

Part II. The Transcendental Functions
12. The gamma function
13. The zeta function of Riemann
14. The hypergeometric function
15. The Legendre function
16. The confluent hypergeometric functions
17. Bessel functions
18. The equations of mathematical physics
19. Mathieu functions
20. Elliptic functions
21. The theta functions
22. Jacobian elliptic functions
23. Ellipsoidal harmonics and Lamé's equation

Appendix: The Elementary Transcendental Functions

List of Authors Quoted

General Index

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