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Solutions Manual to accompany Mathematical Methods for Physicists 6th edition 9780120598762

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Solutions Manual to accompany Mathematical Methods for Physicists 6th edition 9780120598762

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This best-selling title provides in one handy volume the essential mathematical tools and techniques used to solve problems in physics. It is a vital addition to the bookshelf of any serious student of physics or research professional in the field. The authors have put considerable effort into revamping this new edition.

* Updates the leading graduate-level text in mathematical physics
* Provides comprehensive coverage of the mathematics necessary for advanced study in physics and engineering
* Focuses on problem-solving skills and offers a vast array of exercises
* Clearly illustrates and proves mathematical relations

New in the Sixth Edition:
* Updated content throughout, based on users’ feedback
* More advanced sections, including differential forms and the elegant forms of Maxwell’s equations
* A new chapter on probability and statistics
* More elementary sections have been deleted

 

Table of Content:

  1. Chapter 1. Vector Analysis
  2. 1.1 Definitions, Elementary Approach
  3. 1.2 Rotation of the Coordinate Axes
  4. 1.3 Scalar or Dot Product
  5. 1.4 Vector or Cross Product
  6. 1.5 Triple Scalar Product, Triple Vector Product
  7. 1.6 Gradient, V
  8. 1.7 Divergence, V
  9. 1.8 Curl, V×
  10. 1.9 Successive Applications of V
  11. 1.10 Vector Integration
  12. 1.11 Gauss’ Theorem
  13. 1.12 Stokes’ Theorem
  14. 1.13 Potential Theory
  15. 1.14 Gauss’ Law, Poisson’s Equation
  16. 1.15 Dirac Delta Function
  17. 1.16 Helmholtz’s Theorem
  18. Additional Readings
  19. Chapter 2. Vector Analysis in Curved Coordinates and Tensors
  20. 2.1 Orthogonal Coordinates in R3
  21. 2.2 Differential Vector Operators
  22. 2.3 Special Coordinate Systems: Introduction
  23. 2.4 Circular Cylinder Coordinates
  24. 2.5 Spherical Polar Coordinates
  25. 2.6 Tensor Analysis
  26. 2.7 Contraction, Direct Product
  27. 2.8 Quotient Rule
  28. 2.9 Pseudotensors, Dual Tensors
  29. 2.10 General Tensors
  30. 2.11 Tensor Derivative Operators
  31. Additional Readings
  32. Chapter 3. Determinants and Matrices
  33. 3.1 Determinants
  34. 3.2 Matrices
  35. 3.3 Orthogonal Matrices
  36. 3.4 Hermitian Matrices, Unitary Matrices
  37. 3.5 Diagonalization of Matrices
  38. 3.6 Normal Matrices
  39. Additional Readings
  40. Chapter 4. Group Theory
  41. 4.1 Introduction to Group Theory
  42. 4.2 Generators of Continuous Groups
  43. 4.3 Orbital Angular Momentum
  44. 4.4 Angular Momentum Coupling
  45. 4.5 Homogeneous Lorentz Group
  46. 4.6 Lorentz Covariance of Maxwell’s Equations
  47. 4.7 Discrete Groups
  48. 4.8 Differential Forms
  49. Additional Readings
  50. Chapter 5. Infinite Series
  51. 5.1 Fundamental Concepts
  52. 5.2 Convergence Tests
  53. 5.3 Alternating Series
  54. 5.4 Algebra of Series
  55. 5.5 Series of Functions
  56. 5.6 Taylor’s Expansion
  57. 5.7 Power Series
  58. 5.8 Elliptic Integrals
  59. 5.9 Bernoulli Numbers, Euler–Maclaurin Formula
  60. 5.10 Asymptotic Series
  61. 5.11 Infinite Products
  62. Additional Readings
  63. Chapter 6. Functions of a Complex Variable I Analytic Properties, Mapping
  64. 6.1 Complex Algebra
  65. 6.2 Cauchy–Riemann Conditions
  66. 6.3 Cauchy’s Integral Theorem
  67. 6.4 Cauchy’s Integral Formula
  68. 6.5 Laurent Expansion
  69. 6.6 Singularities
  70. 6.7 Mapping
  71. 6.8 Conformal Mapping
  72. Additional Readings
  73. Chapter 7. Functions of a Complex Variable II
  74. 7.1 Calculus of Residues
  75. 7.2 Dispersion Relations
  76. 7.3 Method of Steepest Descents
  77. Additional Readings
  78. Chapter 8. The Gamma Function (Factorial Function)
  79. 8.1 Definitions, Simple Properties
  80. 8.2 Digamma and Polygamma Functions
  81. 8.3 Stirling’s Series
  82. 8.4 The Beta Function
  83. 8.5 Incomplete Gamma Function
  84. Additional Readings
  85. Chapter 9. Differential Equations
  86. 9.1 Partial Differential Equations
  87. 9.2 First-Order Differential Equations
  88. 9.3 Separation of Variables
  89. 9.4 Singular Points
  90. 9.5 Series Solutions—Frobenius’ Method
  91. 9.6 A Second Solution
  92. 9.7 Nonhomogeneous Equation—Green’s Function
  93. 9.8 Heat Flow, or Diffusion, PDE
  94. Additional Readings
  95. Chapter 10. Sturm–Liouville Theory—Orthogonal Functions
  96. 10.1 Self-Adjoint ODEs
  97. 10.2 Hermitian Operators
  98. 10.3 Gram–Schmidt Orthogonalization
  99. 10.4 Completeness of Eigenfunctions
  100. 10.5 Green’s Function—Eigenfunction Expansion
  101. Additional Readings
  102. Chapter 11. Bessel Functions
  103. 11.1 Bessel Functions of the First Kind, Jv(x)
  104. 11.2 Orthogonality
  105. 11.3 Neumann Functions
  106. 11.4 Hankel Functions
  107. 11.5 Modified Bessel Functions, Iv(x) and Kv(x)
  108. 11.6 Asymptotic Expansions
  109. 11.7 Spherical Bessel Functions
  110. Additional Readings
  111. Chapter 12. Legendre Functions
  112. 12.1 Generating Function
  113. 12.2 Recurrence Relations
  114. 12.3 Orthogonality
  115. 12.4 Alternate Definitions
  116. 12.5 Associated Legendre Functions
  117. 12.6 Spherical Harmonics
  118. 12.7 Orbital Angular Momentum Operators
  119. 12.8 Addition Theorem for Spherical Harmonics
  120. 12.9 Integrals of Three Y’s
  121. 12.10 Legendre Functions of the Second Kind
  122. 12.11 Vector Spherical Harmonics
  123. Additional Readings
  124. Chapter 13. More Special Functions
  125. 13.1 Hermite Functions
  126. 13.2 Laguerre Functions
  127. 13.3 Chebyshev Polynomials
  128. 13.4 Hypergeometric Functions
  129. 13.5 Confluent Hypergeometric Functions
  130. 13.6 Mathieu Functions
  131. Additional Readings
  132. Chapter 14. Fourier Series
  133. 14.1 General Properties
  134. 14.2 Advantages, Uses of Fourier Series
  135. 14.3 Applications of Fourier Series
  136. 14.4 Properties of Fourier Series
  137. 14.5 Gibbs Phenomenon
  138. 14.6 Discrete Fourier Transform
  139. 14.7 Fourier Expansions of Mathieu Functions
  140. Additional Readings
  141. Chapter 15. Integral Transforms
  142. 15.1 Integral Transforms
  143. 15.2 Development of the Fourier Integral
  144. 15.3 Fourier Transforms—Inversion Theorem
  145. 15.4 Fourier Transform of Derivatives
  146. 15.5 Convolution Theorem
  147. 15.6 Momentum Representation
  148. 15.7 Transfer Functions
  149. 15.8 Laplace Transforms
  150. 15.9 Laplace Transform of Derivatives
  151. 15.10 Other Properties
  152. 15.11 Convolution (Faltungs) Theorem
  153. 15.12 Inverse Laplace Transform
  154. Additional Readings
  155. Chapter 16. Integral Equations
  156. 16.1 Introduction
  157. 16.2 Integral Transforms, Generating Functions
  158. 16.3 Neumann Series, Separable (Degenerate) Kernels
  159. 16.4 Hilbert–Schmidt Theory
  160. Additional Readings
  161. Chapter 17. Calculus of Variations
  162. 17.1 A Dependent and an Independent Variable
  163. 17.2 Applications of the Euler Equation
  164. 17.3 Several Dependent Variables
  165. 17.4 Several Independent Variables
  166. 17.5 Several Dependent and Independent Variables
  167. 17.6 Lagrangian Multipliers
  168. 17.7 Variation with Constraints
  169. 17.8 Rayleigh–Ritz Variational Technique
  170. Additional Readings
  171. Chapter 18. Nonlinear Methods and Chaos
  172. 18.1 Introduction
  173. 18.2 The Logistic Map
  174. 18.3 Sensitivity to Initial Conditions and Parameters
  175. 18.4 Nonlinear Differential Equations
  176. Additional Readings
  177. Chapter 19. Probability
  178. 19.1 Definitions, Simple Properties
  179. 19.2 Random Variables
  180. 19.3 Binomial Distribution
  181. 19.4 Poisson Distribution
  182. 19.5 Gauss’ Normal Distribution
  183. 19.6 Statistics
  184. Additional Readings
  185. General References
  186. Index

 

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