实例介绍
【实例简介】
Mathematical Methods for Physicists (7th Ed).pdf
ⅵ ATHEMATICAL METHODS FOR PHYSICISTS A Comprehensive guide SEVENTH EDITION George B. Arfken Miami university Oxford. OH Hans j. weber University of virginia Charlottesville. VA frank e. harris University of Utah, Salt Lake City, UT nd University of florida, gainesville, Fl AMSTERDAM· BOSTON· HEIDELBERO· LONDON NEW YORK· OXFORD· PARIS· SAN DIEGO SAN FRANCISCO· SINGAPORE· SYDNEY· TOKYO ELSEVIER Academic Press is an imprint of elsevier Academic Press is an imprint of elsevier 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 IGB, UK o 2013 Elsevier Inc. All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission and further information about the Publisher's permissions policies and our arrangements with organizations such as the copyright Clearance Center and the Copyright Licensing Agency, can be found at our website www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein) Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information methods compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing-in-Publication Data a catalogue record for this book is available from the British library ISBN:978-0-12-384654-9 For information on all Academic Press publications visitourwebsitewww.elsevierdirect.com Typeset by: diacriTech, India Printed in the united states of america 121314987654321 Working together to grow libraries in developing countries www.elsevier.comwww.bookaid.orgwww.sabre.org ELSEVIER BOOK AID Internationa Sabre foundation CONTENTS PREFACE MATHEMATICAL PRELIMINARIES 1.1 Infinite Series.......... 1.2. Series of Functions 1.3 Binomial theorem 1.4 40 1.5 Operations of Series Expansions of Functions……… 1.6. Some Important serles… 45 1.7 Vectors ∴46 1.8. Complex Numbers and Functions 1.9 Derivatives and extrema 1.10.Eva/ uation of integrals…… 65 111. Dirac delta functions 75 Additional Readings................. 2. DETERMINANTS AND MATRICES 2.1 Determinants 2.2 Matrices… 5 Additional Readings......... 121 3. VECTOR ANALYSIS ∴123 3.1 Review of Basics Properties................. 3.2 Vector in3- D Spaces…,…,…, 126 Coordinate transformations 133 3.4 Rotations in界 139 3.5 Differential Vector Operators... 3.6 Differenti/ Vector Operators: Further Properties.…….….…..….. 153 3.7 Vector Integrations 159 3.8 Integral Theorems 音量最 164 3.9 Potential Theory. 170 3. 10 Curvilinear coordinate Additiong/ Readings… 203 4. TENSOR AND DIFFERENTIAL FORMS 205 4.1 7 ensor ang/ysis… ,205 4.2 Pseudotensors. Dual tensors 215 4.3 Tensor in general coordinates 218 4.4 Jacobians 227 4.5 Differentia/ Forms…… 232 4.6 Differentiating Forms……… 238 4.7 Integrating Forms…….,…,… 243 Additional Readings 249 5 VECTOR SPACES 251 5.1 ector in Function spaces 251 5.2 Gram- Schmidt Orthogonalization 5.3 Operators 275 5.4 Self-Adjoint operato 5.5 5.6 Transformations of operators 5.7 Invariants 5.8 Summary- Vector Space Notations 296 Additiona/ Readings 297 6. EIGENVALUE PROBLEMS 29 6.1 Eigenvalue equations 299 6.2Matrⅸ Eigenvalue prob/ems… 301 6.3 Hermitian Eigenvalue problems 310 6.4 hermitian Matrix Diagonalization 311 6.5 Normal matrices 319 Additiona/ Readings 328 7. ORDINARY DIFFERENTIAL EQUATIONS 329 7.1 Introduction 329 7.2 First- Order Equations 331 7.3 ODEs with Constant Coefficients ∴342 Second-Order Linear odes 343 7.5 Series solutions- Frobenius method 346 7.6 Other solutions 358 homogeneous Linear ODE5…...,… 375 7.8 Nonlinear Differential Equations 377 Additiong/ Readings… .380 8. STURM-LIOUVILLE THEORY 381 8.1 Introduction 38 8.2 ermitian Operators 8.3 ODE Eigenvalue Problems ∴389 8.4 Variation methods 395 8.5 Summary, Eigenvalue problems 398 Additiona/ Readings 399 9. PARTIAL DIFFERENTIAL EQUATIONS 9.1 Introduction 9.2 First- Order Equations 403 9.3 Second-Order Equations.... 量量音 409 9.4 Separation of variables... 414 9.5 Laplace and Poisson Equations….…… 9.6 Wave equations ∴435 9.7 Heat -Flow, or Diffution PDE ∴437 9.8 Summary. Additional Readings 445 10. GREEN FUNCTIONS 447 10.1 One-Dimensiona problems 448 10.2 Problems in two and three dimensions 459 Additiong/ Readings….,.,… 467 11. CoMPLEX VARIABLE THEORY 469 11.1 Complex Variables and Functions.... 470 11.2 Cauchy-Riemann Conditions 471 11.3 Cauchy's Integral Theorem 477 11.4 Cauchy' s Integral Formula 86 11.5 Laurent Expansion 492 11.6 Singularities 497 11.7 Calculus of reside 509 11.8 Evaluation of definite integrals 522 11.9 Evaluation of Sums 544 11.10 Miscellaneous Topics……,…, .547 Additiona/ Readings................ 50 12. FURTHER TOPICS IN ANALYSIS 551 12.1 Orthogonal Polynomials 551 12.2 Bernoulli numbers… 560 12.3 Euler-Maclaurin Integration Formula ∴567 12.4 Dirichlet series 571 12.5 Infinite Products 574 12.6 Asymptotic Series 577 12.7 Method of steepest Descents 585 128DipertionReations....... 591 Additional Readings...................... 598 13. GAMMA FUNCTION ∴599 13.1 Definitions, Properties 599 13.2 Digamma and Polygamma Functions 610 13. 3 The beta function 量量音 617 13. 4 Stirlings series 622 3.5 Riemann zeta function 626 13. 6 Other ralated function 633 Additiona/ Readings 641 14. BESSEL FUNCTIONS 音音 14.1 Bessel Functions of the First kind, Jv(x) 643 4.2 Orthogonality…… 14.3 Neumann Functions, Besse/ Functions of the Second kind 667 14.4 Hankel functions 674 14.5 Modified Bessel Functions, /v(x)and K (x) 14.6 Asymptotic Expansions 688 14.7 Spherical Bessel Functions Additiona/ Readings 713 15. LEGENDRE FUNCTIONS 715 15.1 Legendre polynomials 716 152 Orthogonality… 724 15.3 Physical Interpretation of generating Function 736 15.4 Associated Legendre equation 741 15.5 Spherical harmonics 756 15.6 Legendre functions of the Second Kind 766 Additiong/ Readings… 771 16. ANGULAR MOMENTUM 773 16.1 Angular Momentum Operators.…… 774 16.2 Angular Momentum Coupling 16.3 Spherical Tensors... 796 16.4 Vector Spherical Harmonics .809 Additional Readings 814 17. GROUP TI 815 17.1 troduction to Group 815 17.2 Representation of groups 821 17.3 Symmetry and Physic 826 17.4 Discrete groups 830 17.5 Direct products 837 17.6 Simmetric Grou 840 17.7 Continous Groups 845 17.8 Lorentz Group…….…….….…..……… 862 17.9 Lorentz Covariance of Maxwell's equantions 866 17.10 Space groups Additiona/ Readings 870 18. MORE SPECIAL FUNCTIONS .871 18.1 Hermite functions wwwwwwwwwwwwwwwwwww 871 18.2 Applications of hermite functio 878 18.3 Laguerre Functions....... 18.4 Chebyshev Poly 89 18.5 Hypergeometric Functions 911 186 Confluent Hypergeometric Functions...….….….,….…………………………917 18.7 Dilogarithi 923 188E∥ iptic Integ 927 Additiong/ Readings… ∴932 19. FOURIER SERIES ∴935 19. 1 General Properties 935 19.2 Application of Fourier Series 949 19. 3 Gibbs phenomenon 957 Additiona/ Readings 962 20. INTEGRAL TRANSFORMS 963 20.1 ntroduction………… 963 20.2 Fourier Transforms 966 20.3 Properties of fourier Transforms........... 980 20.4 Fourier convolution theorem 985 20.5 Signal- Proccesing Applications 997 20.6 Discrete Fourier Transforms 1002 20.7 Laplace Transforms..…… 1008 20.8 Properties of laplace Tr 1016 20. 9 Laplace Convolution Transforms 1034 20.10 Inverse laplace Transforms... 1038 Additiona/ Readings 1045 21.丨 NTEGRAL EQUATIONS 1047 21.1 Introduction 1047 21.2 Some Specia/ Methods 1053 21.3 Neumann series 1064 21.4 Hilbert -Schmidt Theory Additional Readings 1079 22. CALCULUS OF VARIATIONS 1081 22.1 Euler Equation 1081 22.2 More general variations 1096 22.3 Constrained Minima/Maxima...............................1107 22. 4 Variation with constraints 1111 Additiona/ Readings…...,,… 1124 23. PROBABILITY AND STATISTICS 1125 23.1 Probability;: Definitions, Simple properties.....….………,1126 23.2 Random variables 1134 23. 3 Binomia/ Distribution 1148 23.4 Poisson distribution 23.5 Gauss Noma/ distribution 1155 23.6 Transformation of random variables 1159 23.7 Statistics 1165 Additiong/ Readings…..,.,.,… 1179 INDEX 1181 【实例截图】
【核心代码】
Mathematical Methods for Physicists (7th Ed).pdf
ⅵ ATHEMATICAL METHODS FOR PHYSICISTS A Comprehensive guide SEVENTH EDITION George B. Arfken Miami university Oxford. OH Hans j. weber University of virginia Charlottesville. VA frank e. harris University of Utah, Salt Lake City, UT nd University of florida, gainesville, Fl AMSTERDAM· BOSTON· HEIDELBERO· LONDON NEW YORK· OXFORD· PARIS· SAN DIEGO SAN FRANCISCO· SINGAPORE· SYDNEY· TOKYO ELSEVIER Academic Press is an imprint of elsevier Academic Press is an imprint of elsevier 225 Wyman Street, Waltham, MA 02451, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 IGB, UK o 2013 Elsevier Inc. All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Details on how to seek permission and further information about the Publisher's permissions policies and our arrangements with organizations such as the copyright Clearance Center and the Copyright Licensing Agency, can be found at our website www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein) Notices Knowledge and best practice in this field are constantly changing. As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information methods compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein Library of Congress Cataloging-in-Publication Data Application submitted British Library Cataloguing-in-Publication Data a catalogue record for this book is available from the British library ISBN:978-0-12-384654-9 For information on all Academic Press publications visitourwebsitewww.elsevierdirect.com Typeset by: diacriTech, India Printed in the united states of america 121314987654321 Working together to grow libraries in developing countries www.elsevier.comwww.bookaid.orgwww.sabre.org ELSEVIER BOOK AID Internationa Sabre foundation CONTENTS PREFACE MATHEMATICAL PRELIMINARIES 1.1 Infinite Series.......... 1.2. Series of Functions 1.3 Binomial theorem 1.4 40 1.5 Operations of Series Expansions of Functions……… 1.6. Some Important serles… 45 1.7 Vectors ∴46 1.8. Complex Numbers and Functions 1.9 Derivatives and extrema 1.10.Eva/ uation of integrals…… 65 111. Dirac delta functions 75 Additional Readings................. 2. DETERMINANTS AND MATRICES 2.1 Determinants 2.2 Matrices… 5 Additional Readings......... 121 3. VECTOR ANALYSIS ∴123 3.1 Review of Basics Properties................. 3.2 Vector in3- D Spaces…,…,…, 126 Coordinate transformations 133 3.4 Rotations in界 139 3.5 Differential Vector Operators... 3.6 Differenti/ Vector Operators: Further Properties.…….….…..….. 153 3.7 Vector Integrations 159 3.8 Integral Theorems 音量最 164 3.9 Potential Theory. 170 3. 10 Curvilinear coordinate Additiong/ Readings… 203 4. TENSOR AND DIFFERENTIAL FORMS 205 4.1 7 ensor ang/ysis… ,205 4.2 Pseudotensors. Dual tensors 215 4.3 Tensor in general coordinates 218 4.4 Jacobians 227 4.5 Differentia/ Forms…… 232 4.6 Differentiating Forms……… 238 4.7 Integrating Forms…….,…,… 243 Additional Readings 249 5 VECTOR SPACES 251 5.1 ector in Function spaces 251 5.2 Gram- Schmidt Orthogonalization 5.3 Operators 275 5.4 Self-Adjoint operato 5.5 5.6 Transformations of operators 5.7 Invariants 5.8 Summary- Vector Space Notations 296 Additiona/ Readings 297 6. EIGENVALUE PROBLEMS 29 6.1 Eigenvalue equations 299 6.2Matrⅸ Eigenvalue prob/ems… 301 6.3 Hermitian Eigenvalue problems 310 6.4 hermitian Matrix Diagonalization 311 6.5 Normal matrices 319 Additiona/ Readings 328 7. ORDINARY DIFFERENTIAL EQUATIONS 329 7.1 Introduction 329 7.2 First- Order Equations 331 7.3 ODEs with Constant Coefficients ∴342 Second-Order Linear odes 343 7.5 Series solutions- Frobenius method 346 7.6 Other solutions 358 homogeneous Linear ODE5…...,… 375 7.8 Nonlinear Differential Equations 377 Additiong/ Readings… .380 8. STURM-LIOUVILLE THEORY 381 8.1 Introduction 38 8.2 ermitian Operators 8.3 ODE Eigenvalue Problems ∴389 8.4 Variation methods 395 8.5 Summary, Eigenvalue problems 398 Additiona/ Readings 399 9. PARTIAL DIFFERENTIAL EQUATIONS 9.1 Introduction 9.2 First- Order Equations 403 9.3 Second-Order Equations.... 量量音 409 9.4 Separation of variables... 414 9.5 Laplace and Poisson Equations….…… 9.6 Wave equations ∴435 9.7 Heat -Flow, or Diffution PDE ∴437 9.8 Summary. Additional Readings 445 10. GREEN FUNCTIONS 447 10.1 One-Dimensiona problems 448 10.2 Problems in two and three dimensions 459 Additiong/ Readings….,.,… 467 11. CoMPLEX VARIABLE THEORY 469 11.1 Complex Variables and Functions.... 470 11.2 Cauchy-Riemann Conditions 471 11.3 Cauchy's Integral Theorem 477 11.4 Cauchy' s Integral Formula 86 11.5 Laurent Expansion 492 11.6 Singularities 497 11.7 Calculus of reside 509 11.8 Evaluation of definite integrals 522 11.9 Evaluation of Sums 544 11.10 Miscellaneous Topics……,…, .547 Additiona/ Readings................ 50 12. FURTHER TOPICS IN ANALYSIS 551 12.1 Orthogonal Polynomials 551 12.2 Bernoulli numbers… 560 12.3 Euler-Maclaurin Integration Formula ∴567 12.4 Dirichlet series 571 12.5 Infinite Products 574 12.6 Asymptotic Series 577 12.7 Method of steepest Descents 585 128DipertionReations....... 591 Additional Readings...................... 598 13. GAMMA FUNCTION ∴599 13.1 Definitions, Properties 599 13.2 Digamma and Polygamma Functions 610 13. 3 The beta function 量量音 617 13. 4 Stirlings series 622 3.5 Riemann zeta function 626 13. 6 Other ralated function 633 Additiona/ Readings 641 14. BESSEL FUNCTIONS 音音 14.1 Bessel Functions of the First kind, Jv(x) 643 4.2 Orthogonality…… 14.3 Neumann Functions, Besse/ Functions of the Second kind 667 14.4 Hankel functions 674 14.5 Modified Bessel Functions, /v(x)and K (x) 14.6 Asymptotic Expansions 688 14.7 Spherical Bessel Functions Additiona/ Readings 713 15. LEGENDRE FUNCTIONS 715 15.1 Legendre polynomials 716 152 Orthogonality… 724 15.3 Physical Interpretation of generating Function 736 15.4 Associated Legendre equation 741 15.5 Spherical harmonics 756 15.6 Legendre functions of the Second Kind 766 Additiong/ Readings… 771 16. ANGULAR MOMENTUM 773 16.1 Angular Momentum Operators.…… 774 16.2 Angular Momentum Coupling 16.3 Spherical Tensors... 796 16.4 Vector Spherical Harmonics .809 Additional Readings 814 17. GROUP TI 815 17.1 troduction to Group 815 17.2 Representation of groups 821 17.3 Symmetry and Physic 826 17.4 Discrete groups 830 17.5 Direct products 837 17.6 Simmetric Grou 840 17.7 Continous Groups 845 17.8 Lorentz Group…….…….….…..……… 862 17.9 Lorentz Covariance of Maxwell's equantions 866 17.10 Space groups Additiona/ Readings 870 18. MORE SPECIAL FUNCTIONS .871 18.1 Hermite functions wwwwwwwwwwwwwwwwwww 871 18.2 Applications of hermite functio 878 18.3 Laguerre Functions....... 18.4 Chebyshev Poly 89 18.5 Hypergeometric Functions 911 186 Confluent Hypergeometric Functions...….….….,….…………………………917 18.7 Dilogarithi 923 188E∥ iptic Integ 927 Additiong/ Readings… ∴932 19. FOURIER SERIES ∴935 19. 1 General Properties 935 19.2 Application of Fourier Series 949 19. 3 Gibbs phenomenon 957 Additiona/ Readings 962 20. INTEGRAL TRANSFORMS 963 20.1 ntroduction………… 963 20.2 Fourier Transforms 966 20.3 Properties of fourier Transforms........... 980 20.4 Fourier convolution theorem 985 20.5 Signal- Proccesing Applications 997 20.6 Discrete Fourier Transforms 1002 20.7 Laplace Transforms..…… 1008 20.8 Properties of laplace Tr 1016 20. 9 Laplace Convolution Transforms 1034 20.10 Inverse laplace Transforms... 1038 Additiona/ Readings 1045 21.丨 NTEGRAL EQUATIONS 1047 21.1 Introduction 1047 21.2 Some Specia/ Methods 1053 21.3 Neumann series 1064 21.4 Hilbert -Schmidt Theory Additional Readings 1079 22. CALCULUS OF VARIATIONS 1081 22.1 Euler Equation 1081 22.2 More general variations 1096 22.3 Constrained Minima/Maxima...............................1107 22. 4 Variation with constraints 1111 Additiona/ Readings…...,,… 1124 23. PROBABILITY AND STATISTICS 1125 23.1 Probability;: Definitions, Simple properties.....….………,1126 23.2 Random variables 1134 23. 3 Binomia/ Distribution 1148 23.4 Poisson distribution 23.5 Gauss Noma/ distribution 1155 23.6 Transformation of random variables 1159 23.7 Statistics 1165 Additiong/ Readings…..,.,.,… 1179 INDEX 1181 【实例截图】
【核心代码】
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