A course of modern analysis : an introduction to the general theory of infinite processes and of analytic functions with an account of the principal transcendental functions

This classic work has been a unique resource for thousands of mathematicians, scientists and engineers since its first appearance in 1902. Never out of print, its continuing value lies in its thorough and exhaustive treatment of special functions of mathematical physics and the analysis of differential equations from which they emerge. The book also is of historical value as it was the first book in English to introduce the then modern methods of complex analysis. This fifth edition preserves the style and content of the original, but it has been supplemented with more recent results and references where appropriate. All the formulas have been checked and many corrections made. A complete bibliographical search has been conducted to present the references in modern form for ease of use. A new foreword by Professor S.J. Patterson sketches the circumstances of the book's genesis and explains the reasons for its longevity. A welcome addition to any mathematician's bookshelf, this will allow a whole new generation to experience the beauty contained in this text. 00. 9781316518939 01.0_pp_i_iv_Frontmatter 02.0_pp_v_xvi_Contents 03.0_pp_xvii_xx_Foreword 04.0_pp_xxi_xxii_Preface_to_the_Fifth_Edition 05.0_pp_xxiii_xxiii_Preface_to_the_Fourth_Edition 06.0_pp_xxiv_xxiv_Preface_to_the_Third_Edition 07.0_pp_xxv_xxv_Preface_to_the_Second_Edition 08.0_pp_xxvi_xxvi_Preface_to_the_First_Edition 09.0_pp_xxvii_lii_Introduction 10.0_pp_1_2_The_Process_of_Analysis 11.0_pp_3_9_Complex_Numbers 12.0_pp_10_39_The_Theory_of_Convergence 13.0_pp_40_57_Continuous_Functions_and_Uniform_Convergence 14.0_pp_58_80_The_Theory_of_Riemann_Integration 15.0_pp_81_109_The_Fundamental_Properties_of_Analytic_Functions_Taylors_Laurents_and_Liouvilles_Theorems 16.0_pp_110_124_The_Theory_of_Residues_Application_to_the_Evaluation_of_Definite_Integrals 17.0_pp_125_152_The_Expansion_of_Functions_in_Infinite_Series 18.0_pp_153_162_Asymptotic_Expansions_and_Summable_Series 19.0_pp_163_200_Fourier_Series_and_Trigonometric_Series 20.0_pp_201_218_Linear_Differential_Equations 21.0_pp_219_240_Integral_Equations 22.0_pp_241_242_The_Transcendental_Functions 23.0_pp_243_275_The_Gamma-Function 24.0_pp_276_292_The_Zeta-Function_of_Riemann 25.0_pp_293_315_The_Hypergeometric_Function 26.0_pp_316_354_Legendre_Functions 27.0_pp_355_372_The_Confluent_Hypergeometric_Function 28.0_pp_373_406_Bessel_Functions 29.0_pp_407_425_The_Equations_of_Mathematical_Physics 30.0_pp_426_450_Mathieu_Functions 31.0_pp_451_485_Elliptic_Functions_General_Theorems_and_the_Weierstrassian_Functions 32.0_pp_486_516_The_Theta-Functions 33.0_pp_517_566_The_Jacobian_Elliptic_Functions 34.0_pp_567_610_Ellipsoidal_Harmonics_and_Lames_Equation 35.0_pp_611_624_The_Elementary_Transcendental_Functions 36.0_pp_625_647_References 37.0_pp_648_651_Author_index 38.0_pp_652_668_Subject_index "The book is divided into two distinct parts. Part I. The Processes of Analysis discusses topics that have become standard in beginning courses. Of course the emphasis is in concrete examples and regrettably, this is different nowadays. Moreover the quality and level of the problems presented in this part is higher than what appears in more modern texts. During the second part of the last century, the tendency in introductory Analysis texts was to emphasize the topological aspects of the material"-- Provided by publisher Continuously in print since its appearance in 1902, Whittaker and Watson is one of those rare books known simply by its authorship. This fifth edition preserves the style and content of the fourth, supplementing it with more recent results. The exhaustive bibliography has been revised to be much more usable.