A Course of Modern Analysis

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Cambridge University Press, 13 sept. 1996 - 608 pages
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This classic text has entered and held the field as the standard book on the applications of analysis to the transcendental functions. The authors explain the methods of modern analysis in the first part of the book and then proceed to a detailed discussion of the transcendental function, unhampered by the necessity of continually proving new theorems for special applications. In this way the authors have succeeded in being rigorous without imposing on the reader the mass of detail that so often tends to make a rigorous demonstration tedious. Researchers and students will find this book as valuable as ever.
 

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Table des matières

Complex Numbers
3
The Theory of Convergence
11
Continuous Functions and Uniform Convergence
41
The Theory of Rieman Integration
61
The fundamental properties of Analytic Functions Taylors Laurents and Liouvilles Theorems
82
The Theory of Residues application to the evaluation of Definite Integrals
111
The expansion of functions in Infinite Series
125
Asymptotic Expansions and Summable Series
150
The Hypergeometric Function
281
Legendre Functions
302
The Confluent Hypergeometric Function
337
Bessel Functions
355
The Equations of Mathematical Physics
386
Mathieu Functions
404
Elliptic Functions General theorems and the Weierstrassian Functions
429
The Theta Functions
462

Fourier Series and Trigonometrical Series
160
Linear Differential Equations
194
Integral Equations
211
THE TRANSCENDENTAL FUNCTIONS
233
The Gamma Function
235
The Zeta Function of Rieman
265
The Jacobian Elliptic Functions
491
Ellipsoidal Harmonics and Lames Equation
536
APPENDIX
579
LIST OF AUTHORS QUOTED
591
GENERAL INDEX
595
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