A Course of Modern Analysis by E. T. Whittaker, G. N. Watson
A Course of Modern Analysis - Table of Contents
Part I – THE PROBESSES 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, * Taylor’s theorem, Laurent’s theorem, Liouville’s theorem
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 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. Legendre Functions
16. The Confluent Hypergeometric Function
17. Bessel Functions
18. The Equations of Mathematical Physics
19. Mathieu Functions
20. Elliptic Functions: General Theorems and the Weierstrassian Functions
21. The Theta Functions
22. The Jacobian Elliptic Functions
23. Ellipsoidal Harmonics and Lamé’s Equation
What You Will Learn in A Course of Modern Analysis
"A Course of Modern Analysis" by E. T. Whittaker and G. N. Watson is a classic text in "mathematical analysis" and "complex functions". It provides a rigorous yet accessible approach to advanced analysis, making it a cornerstone for students and researchers alike. The book carefully introduces foundational concepts such as "infinite series", convergence, and analytic functions, laying the groundwork for deeper study in applied and theoretical mathematics.
The text explores a wide range of topics, including differentiation and integration in the complex plane, "special functions" like gamma, Bessel, and hypergeometric functions, as well as Fourier series and asymptotic expansions. Whittaker and Watson combine clear explanations with numerous examples, helping readers understand both the theory and practical applications of these powerful mathematical tools.
Renowned for its clarity, precision, and breadth, "A Course of Modern Analysis" remains an essential reference in mathematics, physics, and engineering. Its systematic treatment of "complex analysis" and real-variable methods has influenced generations of mathematicians, providing insights that bridge classical and modern approaches. Today, it continues to serve as a fundamental resource for mastering advanced analytic techniques.
Book Details & Specifications
Title:
A Course of Modern Analysis by E. T. Whittaker, G. N. Watson
Publisher:
University Press
Year:
1920
Pages:
602
Type:
PDF
Language:
English
ISBN-10 #:
1316518930
ISBN-13 #:
978-1316518939
License:
Public Domain Work
Amazon:
Amazon
About the Author: Sir, Edmund Taylor Whittaker
The author Sir, Edmund Taylor Whittaker
(1873–1956) was a prominent British mathematician known for his work in "mathematical analysis" and applied mathematics. Educated at Cambridge, he made significant contributions to "complex functions", special functions, and mathematical physics, combining rigor with clarity to make advanced topics accessible to students and researchers. "G. N. Watson" (1886–1965) was a leading mathematician who expanded and revised Whittaker’s work, focusing on "special functions" and modern analytic methods. Together, their collaboration produced "A Course of Modern Analysis", a classic text that bridges classical theory with contemporary approaches, remaining a foundational reference in mathematics, physics, and engineering.
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