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内容提要:
Developed from a highly successful series of lectures given at Yale University, this volume has a reputation as one of the best texts in its field. A thorough treatment of the fundamental elements, concepts,and theorems pertaining to the function of a complex variable, it offers a complete study, suitable for advanced mathematics students,physicists, and advanced engineers.
Students of applied mathematics will particularly value the full exposi-tion of the theory of linear differential equations, especially in regard to the functions of Legendre, Laplace, Bessel, and Lame. Three chapters are devoted to elliptic functions, explaining both their intrinsic value and their role as splendid applications of function theory. Rigorous and detailed in its treatment, this text features carefully selected and com-pletely worked-out problems that illustrate each topic. 目录:
CHAPTER I ARITHMETICAL OPERATIONS
ARTICLES CHAPTER II REAL TERM SERIES POSITIVE TERM SERIES CHAPTER III SERIES WITH COMPLEX TERMS ARTICLES POWER SERIES CHAPTER IV THE ELEMENTARY FUNCTIONS EXPONENTIAL FUNCTION CIRCULAR FUNCTIONS ARTICLES OTHER FUNCTIONS CHAPTER V RELA VARIABLES INTEGRATION CHAPTER VI DEFFERENTIATION AND INTEGRATION ARTICLES INTEGRATION FUNCTIONS DEFINED BY SERIES CHAPTER VII ANALYTIC FUNCTIONS CHAPTER VIII INFINITE PRODUCTS ARTICLES CHAPTER IX B AND F FUNCTIONS,ASYMPTOTIC EXPANSIONS ASYMPTOTIC EXPANSIONS CHAPTER X FUNCTIONS OF WEIERSTRASS ARTICLES CHAPTER XI FUNCTICON AND JACOBI CHAPTER XII THETA FUNCTIONS CHATPER XIII LINEAR DEFFERENTIAL EQUATIONS CHAPTER XIV FUNCTIONS OF LEGENDRE AND LAPLACE LAPLACE'S FUNCTIONS ARTICTES CHAPTER XV BESSEL AND LAME FUNCTIONS NOTE |