A Course of Modern Analysis

Still in print more than a century after its 1902 publication, this historic text by two great mathematicians has inspired generations of students and scholars. The original treatment consists of two parts, The Processes of Analysis and The Transcendental Functions; a final chapter, Ellipsoidal Harmonies and Lamé's Equations, was added in 1920.
The first part covers complex numbers, the theories of convergence and Riemann integration, the expansion of functions in infinite series, Fourier and trigonometrical series, and linear differential and integral equations, among other subjects. Part two explores the gamma function, Legendre and Bessel functions, equations of mathematical physics, Mathieu and theta functions, and other topics. A Course of Modern Analysis is suitable for advanced undergraduates and graduate students of mathematics as well as historians of mathematics.

Edmund Taylor Whittaker (1873–1956) studied mathematics at Trinity College, Cambridge. He became Professor of Mathematics at the University of Edinburgh in 1911 and taught there for the rest of his career, specializing in applied mathematics, mathematical physics, and special functions.
George Neale Watson (1886–1965) also studied at Trinity College, Cambridge. From 1914 to 1918 he was a lecturer at University College, London, and in 1918 became Professor of Mathematics at the University of Birmingham.

Part I The Process of Analysis
Chapters
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: Taylor's, Laurent's and Liouville's Theorems 
6. The Theory of Residues; application to the evaluation of Definite Integrals
7. The Expansion of Functions in Infinite Series
8. Asymptotic Expansions and Summable Series
9. Fourier Series and Trigonomentrical Series
10. Linear Differential Equations
11. Integral Equations

Part II The Transcendental Functions
12. The Gamma Function
13. The Zeta Functions of Riemann
14. The Hypergeometric Function
15 Legendre Functions
16. The Confluent Hypergeometic Function
17. Bessel Functions
18. The equations of Mathematical Physics
19. Mathieu Functions
20. Elliptic Functions: General Theorems and the Weirstrassian Functions
21. The Theta Functions
22. The Jacobian Elliptic Functions
23 Ellipsoidal Harmonics and Lame's Equation
Appendix
List of Authors Quoted
General Index