Methods of Theoretical Physics part1
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English Pages 1059
Table of contents :
PREFACE......Page 4
Contents ......Page 8
CHAPTER 1 Types of Fields......Page 22
1.1 Scalar Fields ......Page 25
1.2 Vector Fields ......Page 29
1.3 Curvilinear Coordinates......Page 42
1.4 The Differential Operator V......Page 52
1.5 Vector and Tensor Formalism......Page 65
1.6 Dyadics and Other Vector Operators ......Page 75
1.7 The Lorentz Transformation, Four^ectors, Spinors......Page 114
Problems ......Page 128
Table of Useful Vector and Dyadic Equations......Page 135
Table of Properties of Curvilinear Coordinates ......Page 136
Bibliography ......Page 138
CHAPTER 2 Equations Governing Fields ......Page 140
2.1 The Flexible String......Page 141
2.2 Waves in an Elastic Medium ......Page 163
2.3 Motion of Fluids ......Page 172
2.4 Diffusion and Other Percolative Fluid Motion ......Page 192
2.5 The Electromagnetic Field ......Page 221
2.6 Quantum Mechanics ......Page 243
Problems ......Page 288
Standard Forms for Some of the Partial Differential Equations of Theoretical Physics ......Page 292
Bibliography ......Page 294
CHAPTER 3 Fields and the Variational Principle ......Page 296
3.1 The Variational Integral and the Euler Equations......Page 297
3.2 Hamilton s Principle and Classical Dynamics......Page 301
3.3 Scalar Fields ......Page 322
3.4 Vector Fields ......Page 339
Problems ......Page 358
Tabulation of Variational Method ......Page 362
Bibliography ......Page 368
CHAPTER 4 Functions of a Complex Variable ......Page 369
4.1 Complex Numbers and Variables ......Page 370
4.2 Analytic Functions ......Page 377
4.3 Derivatives of Analytic Functions, Taylor and Laurent Series......Page 395
4.4 Multivalued Functions ......Page 419
4.5 Calculus of Residues; Gamma and Flliptic Functions......Page 429
4.6 Asymptotic Series: Method of Steepest Descent ......Page 455
4.7 Conformal Mapping ......Page 464
4.8 Fourier Integrals ......Page 474
Problems ......Page 492
Tabulation of Properties of Functions of Complex Variable ......Page 501
Tables of Special Functions of General Use ......Page 507
Bibliography ......Page 511
CHAPTER 5 Ordinary Differential Equations ......Page 513
5.1 Separable Coordinates ......Page 515
5.2 General Properties, Series Solutions ......Page 544
5.3 Integral Representations ......Page 598
Problems ......Page 667
Table of Separable Coordinates in Three Dimensions......Page 676
Second-order Differential Equations and Their Solutions......Page 688
Bibliography ......Page 695
6.1 Types of Equations and of Boundary Conditions ......Page 697
6.2 Difference Equations and Boundary Conditions ......Page 713
6.3 Eigenfunctions and Their Use ......Page 730
Problems ......Page 799
Table of Useful Eigenfunctions and Their Properries......Page 802
Eigenfunctions by the Factorization Method ......Page 809
Bibliography ......Page 811
CHAPTER 7 Green's Functions......Page 812
7.1 Source Points and Boundary Points ......Page 814
7.2 Green s Functions for Steady Waves ......Page 824
7.3 Green s Functioh for the Scalar Wave Equation ......Page 855
7.4 Green s Function for Diffusion ......Page 878
7.5 Green's Function in Abstract Vector Form ......Page 890
Problems ......Page 907
Table of Green's Functions ......Page 911
Bibliography ......Page 915
8.1 Integral Equations of Physics, Their Classification ......Page 917
8.2 General Properties of Integral Equations ......Page 928
8.3 Solution of Fredholm Equations of the First Kind......Page 946
8.4 Solution of Integral Equations of the Second Kind ......Page 970
8.5 Fourier Transforms and Integral Equations ......Page 981
Tables of Integral Equations and Their Solutions......Page 1013
Bibliography ......Page 1017
Index......Page 1020
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