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9780521588072

A Course of Modern Analysis

by
  • ISBN13:

    9780521588072

  • ISBN10:

    0521588073

  • Edition: 4th
  • Format: Paperback
  • Copyright: 1996-09-13
  • Publisher: Cambridge University Press

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Summary

This classic text is known to and used by thousands of mathematicians and students of mathematics throughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principal transcendental functions.

Table of Contents

PART I. THE PROCESSES OF ANALYSIS 3(232)
I Complex Numbers
3(8)
II The Theory of Convergence
11(30)
III Continuous Functions and Uniform Convergence
41(20)
IV The Theory of Riemann Integration
61(21>)
V The fundamental properties of Analytic Functions; Taylor's, Laurent's, and Liouville's Theorems
82(29)
VI The Theory of Residues; application to the evaluation of Definite Integrals
111(14)
VII The expansion of functions in Infinite Series
125(25)
VIII Asymptotic Expansions and Summable Series
150(10)
IX Fourier Series and Trigonometrical Series
160(34)
X Linear Differential Equations
194(17)
XI Integral Equations
211(24)
PART II. THE TRANSCENDENTAL FUNCTIONS 235(344)
XII The Gamma Function
235(30)
XIII The Zeta Function of Riemann
265(16)
XIV The Hypergeometric Function
281(21)
XV Legendre Functions
302(35)
XVI The Confluent Hypergeometric Function
337(18)
XVII Bessel Functions
355(31)
XVIII The Equations of Mathematical Physics
386(18)
XIX Mathieu Functions
404(25)
XX Elliptic Functions. General theorems and the Weierstrassian Functions
429(33)
XXI The Theta Functions
462(29)
XXII The Jacobian Elliptic Functions
491(45)
XXIII Ellipsoidal Harmonics and Lame's Equation
536(43)
APPENDIX 579(12)
LIST OF AUTHORS QUOTED 591(4)
GENERAL INDEX 595

Supplemental Materials

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