Analytic methods in physics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin [u.a.]
Wiley-VCH
1999
|
| Edition: | 1. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 323 S. Ill. |
| ISBN: | 3527402160 |
Staff View
MARC
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| 245 | 1 | 0 | |a Analytic methods in physics |c Charlie Harper |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS 1 VECTOR ANALYSIS 13 1.1 INTRODUCTION 13 1.1.1 BACKGROUND 13
1.1.2 PROPERTIES AND NOTATIONS 14 1.1.3 GEOMETRIC ADDITION OF VECTORS 14
1.2 THE CARTESIAN COORDINATE SYSTEM 16 1.2.1 ORTHONORMAL BASIS VECTORS:
I, J, K 16 1.2.2 RECTANGULAR RESOLUTION OF VECTORS 16 1.2.3 DIRECTION
COSINES 18 1.2.4 VECTOR ALGEBRA 19 1.3 DIFFERENTIATION OF VECTOR
FUNCTIONS 26 1.3.1 THE DERIVATIVE OF A VECTOR FUNCTION 26 1.3.2 CONCEPTS
OF GRADIENT, DIVERGENCE, AND CURL 27 1.4 INTEGRATION OF VECTOR FUNCTIONS
31 1.4.1 LINE INTEGRALS 32 1.4.2 THE DIVERGENCE THEOREM DUE TO GAUSS 34
1.4.3 GREEN S THEOREM 40 1.4.4 THE CURL THEOREM DUE TO STOKES 41 1.5
ORTHOGONAL CURVILINEAR COORDINATES 43 1.5.1 INTRODUCTION 43 1.5.2 THE
GRADIENT IN ORTHOGONAL CURVILINEAR COORDINATES 46 1.5.3 DIVERGENCE AND
CURL IN ORTHOGONAL CURVILINEAR COORDINATES 46 1.5.4 THE LAPLACIAN IN
ORTHOGONAL CURVILINEAR COORDINATES 47 1.5.5 PLANE POLAR COORDINATES (R,
PHI ) 47 1.5.6 RIGHT CIRCULAR CYLINDRICAL COORDINATES (RHO, PHI, Z) 47
1.5.7 SPHERICAL POLAR COORDINATES (R, THETA ,PHI) 48 1.6 PROBLEMS 49 1.7
APPENDIX I: SYSTEME INTERNATIONAL (SI) UNITS 52 1.8 APPENDIX II:
PROPERTIES OF DETERMINANTS 53 1.8.1 INTRODUCTION 53 1.8.2 THE LAPLACE
DEVELOPMENT BY MINORS 55 1.9 SUMMARY OF SOME PROPERTIES OF DETERMINANTS
56 2 MODERN ALGEBRAIC METHODS IN PHYSICS 59 2.1 INTRODUCTION 59 2.2
MATRIX ANALYSIS 60 2.2.1 MATRIX OPERATIONS 61 2.2.2 PROPERTIES OF
ARBITRARY MATRICES 63 2.2.3 SPECIAL SQUARE MATRICES 64 2.2.4 THE
EIGENVALUE PROBLEM 68 2.2.5 ROTATIONS IN TWO AND THREE DIMENSIONS 69 2.3
ESSENTIALS OF VECTOR SPACES 71 2.3.1 BASIC DEFINITIONS 71 2.3.2 MAPPING
AND LINEAR OPERATORS 72 2.3.3 INNER PRODUCT AND NORM 74 2.3.4 THE
LEGENDRE TRANSFORMATION 75 2.3.5 TOPOLOGICAL SPACES 76 2.3.6 MANIFOLDS
79 2.4 ESSENTIAL ALGEBRAIC STRUCTURES 80 2.4.1 DEFINITION OF A GROUP 80
2.4.2 DEFINITIONS OF RINGS AND FIELDS 81 2.4.3 A PRIMER ON GROUP THEORY
IN PHYSICS 82 2.5 PROBLEMS 89 3 FUNCTIONS OF A COMPLEX VARIABLE 95 3.1
INTRODUCTION 95 3.2 COMPLEX VARIABLES AND THEIR REPRESENTATIONS 95 3.3
THE DE MOIVRE THEOREM 98 3.4 ANALYTIC FUNCTIONS OF A COMPLEX VARIABLE 99
3.5 CONTOUR INTEGRALS 102 3.6 THE TAYLOR SERIES AND ZEROS OF F(Z) 106
3.6.1 THE TAYLOR SERIES 106 3.6.2 ZEROS OF F(Z) 108 3.7 THE LAURENT
EXPANSION 108 3.8 PROBLEMS 113 3.9 APPENDIX: SERIES 115 3.9.1
INTRODUCTION 115 3.9.2 SIMPLE CONVERGENCE TESTS 116 3.9.3 SOME IMPORTANT
SERIES IN MATHEMATICAL PHYSICS 116 4 CALCULUS OF RESIDUES 119 4.1
ISOLATED SINGULAR POINTS 119 4.2 EVALUATION OF RESIDUES 121 4.2.1
M-TH-ORDER POLE 121 4.2.2 SIMPLE POLE 121 4.3 THE CAUCHY RESIDUE THEOREM
125 4.4 THE CAUCHY PRINCIPAL VALUE 126 4.5 EVALUATION OF DEFINITE
INTEGRALS 127 4.5.1 INTEGRALS OF THE FORM J 027R /(SIN(9,COS6 )D(9 127
4.5.2 INTEGRALS OF THE FORM J^ OO F(X)DX 128 4.5.3 A DIGRESSION ON
JORDAN S LEMMA 130 4.5.4 INTEGRALS OF THE FORM J^ OO F(X)E IMX DX 131
4.6 DISPERSION RELATIONS 132 4.7 CONFORMAL TRANSFORMATIONS 134 4.8
MULTI-VALUED FUNCTIONS 137 4.9 PROBLEMS 141 5 FOURIER SERIES 143 5.1
INTRODUCTION 143 5.2 THE FOURIER COSINE AND SINE SERIES 144 5.3 CHANGE
OF INTERVAL 144 5.4 COMPLEX FORM OF THE FOURIER SERIES 145 5.5
GENERALIZED FOURIER SERIES AND THE DIRAC DELTA FUNCTION 149 5.6
SUMMATION OF THE FOURIER SERIES 151 5.7 THE GIBBS PHENOMENON 153 5.8
SUMMARY OF SOME PROPERTIES OF FOURIER SERIES 154 5.9 PROBLEMS 155 6
FOURIER TRANSFORMS 157 6.1 INTRODUCTION 157 6.2 COSINE AND SINE
TRANSFORMS 159 6.3 THE TRANSFORMS OF DERIVATIVES 162 6.4 THE CONVOLUTION
THEOREM 164 6.5 PARSEVAL S RELATION 165 6.6 PROBLEMS 166 7 ORDINARY
DIFFERENTIAL EQUATIONS 167 7.1 INTRODUCTION 167 7.2 FIRST-ORDER LINEAR
DIFFERENTIAL EQUATIONS 168 7.2.1 SEPARABLE DIFFERENTIAL EQUATIONS 168
7.2.2 EXACT DIFFERENTIAL EQUATIONS 169 7.2.3 SOLUTION OF THE GENERAL
LINEAR DIFFERENTIAL EQUATION 170 7.3 THE BERNOULLI DIFFERENTIAL EQUATION
173 7.4 SECOND-ORDER LINEAR DIFFERENTIAL EQUATIONS 174 7.4.1 HOMOGENEOUS
DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS . . .175 7.4.2
NONHOMOGENEOUS DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS . 179
7.4.3 HOMOGENEOUS DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS . .
. .182 7.4.4 NONHOMOGENEOUS DIFFERENTIAL EQUATIONS WITH VARIABLE
COEFFICIENTS . . 184 7.5 SOME NUMERICAL METHODS 186 7.5.1 THE IMPROVED
EULER METHOD FOR FIRST-ORDER DIFFERENTIAL EQUATIONS . 186 7.5.2 THE
RUNGE-KUTTA METHOD FOR FIRST-ORDER DIFFERENTIAL EQUATIONS ... 188 7.5.3
SECOND-ORDER DIFFERENTIAL EQUATIONS 189 7.6 PROBLEMS 189 8 PARTIAL
DIFFERENTIAL EQUATIONS 195 8.1 INTRODUCTION 195 8.2 THE METHOD OF
SEPARATION OF VARIABLES 197 8.2.1 THE ONE-DIMENSIONAL HEAT CONDUCTION
EQUATION 200 8.2.2 THE ONE-DIMENSIONAL MECHANICAL WAVE EQUATION 201
8.2.3 THE TIME-INDEPENDENT SCHROEDINGER WAVE EQUATION 205 8.3 GREEN S
FUNCTIONS IN POTENTIAL THEORY 206 8.4 SOME NUMERICAL METHODS 208 8.4.1
FUNDAMENTAL RELATIONS IN FINITE DIFFERENCES 208 8.4.2 THE
TWO-DIMENSIONAL LAPLACE EQUATION: ELLIPTIC EQUATION 208 8.4.3 THE
ONE-DIMENSIONAL HEAT CONDUCTION EQUATION: PARABOLIC EQUATION 208 8.4.4
THE ONE-DIMENSIONAL WAVE EQUATION: HYPERBOLIC EQUATION 209 8.5 PROBLEMS
210 9 SPECIAL FUNCTIONS 215 9.1 INTRODUCTION 215 9.2 THE STURM-LIOUVILLE
THEORY 216 9.2.1 INTRODUCTION 216 9.2.2 HERMITIAN OPERATORS AND THEIR
EIGENVALUES 218 9.2.3 ORTHOGONALITY CONDITION AND COMPLETENESS OF
EIGENFUNCTIONS . . . .219 9.2.4 ORTHOGONAL POLYNOMIALS AND FUNCTIONS 220
9.3 THE HERMITE POLYNOMIALS 223 9.4 THE HELMHOLTZ DIFFERENTIAL EQUATION
IN SPHERICAL COORDINATES 225 9.4.1 INTRODUCTION 225 9.4.2 LEGENDRE
POLYNOMIALS AND ASSOCIATED LEGENDRE FUNCTIONS 227 9.4.3 LAGUERRE
POLYNOMIALS AND ASSOCIATED LAGUERRE POLYNOMIALS 230 9.5 THE HELMHOLTZ
DIFFERENTIAL EQUATION IN CYLINDRICAL COORDINATES 233 9.5.1 INTRODUCTION
233 9.5.2 SOLUTIONS OF BESSEL S DIFFERENTIAL EQUATION 233 9.5.3 BESSEL
FUNCTIONS OF THE FIRST KIND 234 9.5.4 NEUMANN FUNCTIONS 234 9.5.5 HANKEL
FUNCTIONS 235 9.5.6 MODIFIED BESSEL FUNCTIONS 236 9.5.7 SPHERICAL BESSEL
FUNCTIONS 236 9.6 THE HYPERGEOMETRIC FUNCTION 236 9.7 THE CONFLUENT
HYPERGEOMETRIC FUNCTION 239 9.8 OTHER SPECIAL FUNCTIONS USED IN PHYSICS
240 9.8.1 SOME OTHER SPECIAL FUNCTIONS OF TYPE 1 240 9.8.2 SOME OTHER
SPECIAL FUNCTIONS OF TYPE 2 241 9.9 PROBLEMS 242 9.9.1 WORKSHEET: THE
QUANTUM MECHANICAL LINEAR HARMONIC OSCILLATOR . . 244 9.9.2 WORKSHEET:
THE LEGENDRE DIFFERENTIAL EQUATION 247 9.9.3 WORKSHEET: THE LAGUERRE
DIFFERENTIAL EQUATION 249 9.9.4 WORKSHEET: THE BESSEL DIFFERENTIAL
EQUATION 250 9.9.5 WORKSHEET: THE HYPERGEOMETRIC DIFFERENTIAL EQUATION
251 10 INTEGRAL EQUATIONS 265 10.1 INTRODUCTION 265 10.2 INTEGRAL
EQUATIONS WITH SEPARABLE KERNELS 267 10.3 INTEGRAL EQUATIONS WITH
DISPLACEMENT KERNELS 269 10.4 THE NEUMANN SERIES METHOD 269 10.5 THE
ABEL PROBLEM 270 10.6 PROBLEMS 272 11 APPLIED FUNCTIONAL ANALYSIS 275
11.1 INTRODUCTION 275 11.2 STATIONARY VALUES OF CERTAIN FUNCTIONS AND
FUNCTIONALS 276 11.2.1 MAXIMA AND MINIMA OF FUNCTIONS 276 11.2.2 METHOD
OF LAGRANGE S MULTIPLIERS 276 11.2.3 MAXIMA AND MINIMA OF A CERTAIN
DEFINITE INTEGRAL 278 11.3 HAMILTON S VARIATIONAL PRINCIPLE IN MECHANICS
282 11.3.1 INTRODUCTION 282 11.3.2 GENERALIZED COORDINATES 282 11.3.3
LAGRANGE S EQUATIONS 283 11.3.4 FORMAT FOR SOLVING PROBLEMS BY USE OF
LAGRANGE S EQUATIONS 284 11.4 FORMULATION OF HAMILTONIAN MECHANICS 285
11.4.1 DERIVATION OF HAMILTON S CANONICAL EQUATIONS 285 11.4.2 FORMAT
FOR SOLVING PROBLEMS BY USE OF HAMILTON S EQUATIONS 286 11.4.3 POISSON S
BRACKETS 287 11.5 CONTINUOUS MEDIA AND FIELDS 288 11.6 TRANSITIONS TO
QUANTUM MECHANICS 288 11.6.1 INTRODUCTION 288 11.6.2 THE HEISENBERG
PICTURE 289 11.6.3 THE SCHROEDINGER PICTURE 289 11.6.4 THE FEYNMAN PATH
INTEGRAL 290 11.7 PROBLEMS 291 12 GEOMETRICAL METHODS IN PHYSICS 293
12.1 INTRODUCTION 293 12.2 TRANSFORMATION OF COORDINATES IN LINEAR
SPACES 294 12.3 CONTRAVARIANT AND COVARIANT TENSORS 296 12.3.1 TENSORS
OF RANK ONE 296 12.3.2 HIGHER-RANK TENSORS 297 12.3.3 SYMMETRIC AND
ANTISYMMETRIC TENSORS 298 12.3.4 POLAR AND AXIAL VECTORS 299 12.4 TENSOR
ALGEBRA 299 12.4.1 ADDITION (SUBTRACTION) 299 12.4.2 MULTIPLICATION
(OUTER PRODUCT) 299 12.4.3 CONTRACTION 300 12.4.4 INNER PRODUCT 300
12.4.5 THE QUOTIENT LAW 300 12.5 THE LINE ELEMENT 301 12.5.1 THE
FUNDAMENTAL METRIC TENSOR 301 12.5.2 ASSOCIATE TENSORS 302 12.6 TENSOR
CALCULUS 302 12.6.1 INTRODUCTION 302 12.6.2 CHRISTOFFEL SYMBOLS 303
12.6.3 COVARIANT DIFFERENTIATION OF TENSORS 304 12.7 THE EQUATION OF THE
GEODESIC LINE 306 12.8 SPECIAL EQUATIONS INVOLVING THE METRIC TENSOR 307
12.8.1 THE RIEMANN-CHRISTOFFEL TENSOR 308 12.8.2 THE CURVATURE TENSOR
309 12.8.3 THE RICCI TENSOR 309 12.8.4 THE EINSTEIN TENSOR AND EQUATIONS
OF GENERAL RELATIVITY 309 12.9 EXTERIOR DIFFERENTIAL FORMS 310 12.9.1
INTRODUCTION 310 12.9.2 EXTERIOR PRODUCT 312 12.9.3 EXTERIOR DERIVATIVE
313 12.9.4 THE EXTERIOR PRODUCT AND EXTERIOR DERIVATIVE IN E 3 313
12.9.5 THE GENERALIZED STOKES THEOREM 315 12.10PROBLEMS 315 BIBLIOGRAPHY
317 INDEX 320
|
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| indexdate | 2024-07-09T18:32:25Z |
| institution | BVB |
| isbn | 3527402160 |
| language | German |
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| physical | 323 S. Ill. |
| publishDate | 1999 |
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| spelling | Harper, Charlie Verfasser aut Analytic methods in physics Charlie Harper 1. ed. Berlin [u.a.] Wiley-VCH 1999 323 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematische Physik Mathematical analysis Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008644532&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harper, Charlie Analytic methods in physics Mathematische Physik Mathematical analysis Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4123623-3 |
| title | Analytic methods in physics |
| title_auth | Analytic methods in physics |
| title_exact_search | Analytic methods in physics |
| title_full | Analytic methods in physics Charlie Harper |
| title_fullStr | Analytic methods in physics Charlie Harper |
| title_full_unstemmed | Analytic methods in physics Charlie Harper |
| title_short | Analytic methods in physics |
| title_sort | analytic methods in physics |
| topic | Mathematische Physik Mathematical analysis Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathematische Physik Mathematical analysis Mathematical physics Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008644532&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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