.

0 (hodnocen0 x )

BK

Third edition

Cambridge (UK) : Cambridge University Press, 2006

x, 534 stran : ilustrace ; 25 cm

ISBN 978-0-521-67973-2 (brožováno)

001636153

Mathematical Methods for Physics and Engineering, Third Edition, is the latest edition of a highly acclaimed undergraduate textbook that teaches all the mathematics likely to be needed for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the ‘special functions’ of physical science, cover an extended range of practical applications of complex variables and give an introduction to quantum operators. // This Solutions Manual accompanies the third edition of Mathematical Methods for Physics and Engineering. It contains complete worked solutions to over 400 of the exercises in the main textbook, namely the odd-numbered ones, which in the main textaře provided with only hints and outline answers. For each exercise, the original question is reproduced and then followed by a fully worked solution. For those original exercises that make internal reference to the text, the questions have been reworded, usually by including additional information, so that the questions can stand alone. // • The solutions are intended to be instructional as well as utilitarian and so some solutions are even fuller than might be expected of a model answer. // • The original questions are reproduced in full and so, although it is not its prime purpose, this manual could be used independently by those wishing to learn mathematical methods

by following worked examples. // The even-numbered exercises in the main text have no hints, answers or worked solutions and are intended for unaided homework problems; full solutions to these are available to instructors on a password-protected website, www.cambridge.org/9780521679718. Teachers wishing to have access to the website should contact solutions(a)cambridge.org for registration details. // Cover designed by Zoe Naylor // Cambridge // UNIVERSITY PRESS www.cambridge.org // 679732 // 9780521679732 // Contents // Preface vii // 1 Preliminary algebra 1 // 2 Preliminary calculus 17 // 3 Complex numbers and hyperbolic functions 39 // 4 Series and limits 55 // 5 Partial differentiation 71 // 6 Multiple integrals 90 // 7 Vector algebra 104 // 8 , Matrices and vector spaces 119 // 9 Normal modes 145 // 10 Vector calculus 156 // 11 Line, surface and volume integrals 176 // v // 12 // 13 // 14 // 15 // 16 // 17 // 18 // 19 // 20 // 21 // 22 // 23 // 24 // 25 // 26 // 27 // 28 // 29 // 193 // 211 // 228 // 246 // 269 // 283 // 296 // 313 // 319 // 335 // 353 // 374 // 386 // 400 // 420 // 440 // 461 // 480 // CONTENTS // Fourier series Integral transforms First-order ODEs Higher-order ODEs Series solutions of ODEs Eigenfunction methods for ODEs Special functions Quantum operators // PDEs: general and particular solutions // PDEs: separation of variables // Calculus of variations // Integral equations // Complex variables // Applications of complex variables // Tensors // Numerical

methods Group theory Representation theory // vi // CONTENTS // 30 Probability 494 // 31 Statistics // 519