Mathematical Methods for Physicists, Fourth Edition

This new and completely revised **Fourth Edition** provides thorough coverage of the important mathematics needed for upper-division and graduate study in physics and engineering. Following more than 28 years of successful class-testing, **Mathematical Methods for Physicists** is considered the standard text on the subject. A new chapter on nonlinear methods and chaos is included, as are revisions of the differential equations and complex variables chapters. The entire book has been made even more accessible, with special attention given to clarity, completeness, and physical motivation. It is an excellent reference apart from its course use. This revised Fourth Edition includes: Modernized terminology Group theoretic methods brought together and expanded in a new chapter An entirely new chapter on nonlinear mathematical physics Significant revisions of the differential equations and complex variables chapters Many new or improved exercises Forty new or improved figures An update of computational techniques for today's contemporary tools, such as microcomputers, __Numerical Recipes,__ and __Mathematica(r),__ among others Content: Front Matter , Page iii Copyright , Page iv Dedication , Page v PREFACE , Pages xv-xvi INTRODUCTION , Pages xvii-xviii 1 - VECTOR ANALYSIS , Pages 1-98 2 - VECTOR ANALYSIS IN CURVED COORDINATES AND TENSORS , Pages 99-155 3 - DETERMINANTS AND MATRICES , Pages 156-222 4 - GROUP THEORY , Pages 223-283 5 - INFINITE SERIES , Pages 284-362 6 - FUNCTIONS OF A COMPLEX VARIABLE I: Analytic Properties Mapping , Pages 363-409 7 - FUNCTIONS OF A COMPLEX VARIABLE II: Calculus of Residues , Pages 410-455 8 - DIFFERENTIAL EQUATIONS , Pages 456-536 9 - STURM—LIOUVILLE THEORY—ORTHOGONAL FUNCTIONS , Pages 537-590 10 - THE GAMMA FUNCTION (FACTORIAL FUNCTION) , Pages 591-626 11 - BESSEL FUNCTIONS , Pages 627-692 12 - LEGENDRE FUNCTIONS , Pages 693-765 13 - SPECIAL FUNCTIONS , Pages 766-807 14 - FOURIER SERIES , Pages 808-845 15 - INTEGRAL TRANSFORMS , Pages 846-919 16 - INTEGRAL EQUATIONS , Pages 920-951 17 - CALCULUS OF VARIATIONS , Pages 952-991 18 - NONLINEAR METHODS AND CHAOS , Pages 992-1004 APPENDIX 1 - Real Zeros of a Function , Pages 1005-1008 APPENDIX 2 - Gaussian Quadrature , Pages 1009-1015 GENERAL REFERENCES , Page 1016 INDEX , Pages 1017-1029 This edition provides coverage of the mathematics needed for upper-division and graduate study in physics and engineering, as well as serving as a reference work for professional scientists and graduate students. It includes a new chapter on nonlinear methods and chaos.