Mathematical methods for physics and engineering: a comprehensive guide
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2004
|
| Edition: | 2. ed., reprinted with corr. |
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXIII, 1232 S. graph. Darst. |
| ISBN: | 0521813727 0521890675 |
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| 245 | 1 | 0 | |a Mathematical methods for physics and engineering |b a comprehensive guide |c K. F. Riley, M. P. Hobson and S. J. Bence |
| 250 | |a 2. ed., reprinted with corr. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2004 | |
| 300 | |a XXIII, 1232 S. |b graph. Darst. | ||
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| 500 | |a Includes bibliographical references and index | ||
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| 700 | 1 | |a Bence, Stephen J. |d 1972- |e Verfasser |0 (DE-588)141008784 |4 aut | |
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| _version_ | 1804133237263433728 |
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| adam_text | MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING A COMPREHENSIVE GUIDE
SECOND EDITION K. F. RILEY, M. P. HOBSON AND S. J. BENCE CAMBRIDGE
UNIVERSITY PRESS CONTENTS PREFACE TO THE SECOND EDITION XIX PREFACE TO
THE FIRST EDITION XXI 1 PRELIMINARY ALGEBRA 1 1.1 SIMPLE FUNCTIONS AND
EQUATIONS 1 POLYNOMIAL EQUATIONS; FACTORISATION; PROPERTIES OF ROOTS 1.2
TRIGONOMETRIC IDENTITIES 10 SINGLE ANGLE; COMPOUND-ANGLES; DOUBLE- AND
HALF-ANGLE IDENTITIES 1.3 COORDINATE GEOMETRY 15 1.4 PARTIAL FRACTIONS
18 COMPLICATIONS AND SPECIAL CASES 1.5 BINOMIAL EXPANSION 25 1.6
PROPERTIES OF BINOMIAL COEFFICIENTS 27 1.7 SOME PARTICULAR METHODS OF
PROOF 30 PROOF BY INDUCTION; PROOF BY CONTRADICTION; NECESSARY AND
SUFFICIENT CONDITIONS 1.8 EXERCISES 36 1.9 HINTS AND ANSWERS 39 2
PRELIMINARY CALCULUS 42 2.1 DIFFERENTIATION 42 DIFFERENTIATION FROM
FIRST PRINCIPLES; PRODUCTS; THE CHAIN RULE; QUOTIENTS; IMPLICIT
DIFFERENTIATION; LOGARITHMIC DIFFERENTIATION; LEIBNITZ THEOREM; SPECIAL
POINTS OF A FUNCTION; CURVATURE; THEOREMS OF DIFFERENTIATION CONTENTS
2.2 INTEGRATION 60 INTEGRATION FROM FIRST PRINCIPLES; THE INVERSE OF
DIFFERENTIATION; BY INSPECTION; SINUSOIDAL FUNCTIONS; LOGARITHMIC
INTEGRATION; USING PARTIAL FRACTIONS; SUBSTITUTION METHOD; INTEGRATION
BY PARTS; REDUCTION FORMULAE; INFINITE AND IMPROPER INTEGRALS; PLANE
POLAR COORDINATES; INTEGRAL INEQUALITIES; APPLICATIONS OF INTEGRATION
2.3 EXERCISES 77 2.4 HINTS AND ANSWERS 82 3 COMPLEX NUMBERS AND
HYPERBOLIC FUNCTIONS 86 3.1 THE NEED FOR COMPLEX NUMBERS 86 3.2
MANIPULATION OF COMPLEX NUMBERS 88 ADDITION AND .SUBTRACTION; MODULUS
AND ARGUMENT; MULTIPLICATION; COMPLEX CONJUGATE; DIVISION 3.3 POLAR
REPRESENTATION OF COMPLEX NUMBERS 95 MULTIPLICATION AND DIVISION IN
POLAR FORM 3.4 DE MOIVRE S THEOREM 98 TRIGONOMETRIC IDENTITIES; FINDING
THE NTH ROOTS OF UNITY; SOLVING POLYNOMIAL EQUATIONS 3.5 COMPLEX
LOGARITHMS AND COMPLEX POWERS 102 3.6 APPLICATIONS TO DIFFERENTIATION
AND INTEGRATION 104 3.7 HYPERBOLIC FUNCTIONS 105 DEFINITIONS;
HYPERBOLIC-TRIGONOMETRIC ANALOGIES; IDENTITIES OF HYPERBOLIC FUNCTIONS;
SOLVING HYPERBOLIC EQUATIONS; INVERSES OF HYPERBOLIC FUNCTIONS; CALCULUS
OF HYPERBOLIC FUNCTIONS 3.8 EXERCISES 112 3.9 HINTS AND ANSWERS 116 4
SERIES AND LIMITS 118 4.1 SERIES 118 4.2 SUMMATION OF SERIES 119
ARITHMETIC SERIES; GEOMETRIC SERIES; ARITHMETICO-GEOMETRIC SERIES; THE
DIFFERENCE METHOD; SERIES INVOLVING NATURAL NUMBERS; TRANSFORMATION OF
SERIES 4.3 CONVERGENCE OF INFINITE SERIES 127 ABSOLUTE AND CONDITIONAL
CONVERGENCE; SERIES CONTAINING ONLY REAL POSITIVE TERMS; ALTERNATING
SERIES TEST A A OPERATIONS WITH SERIES 134 4.5 POWER SERIES 134
CONVERGENCE OF POWER SERIES; OPERATIONS WITH POWER SERIES 4.6 TAYLOR
SERIES 139 TAYLOR S THEOREM; APPROXIMATION ERRORS; STANDARD MACLAURIN
SERIES 4.7 EVALUATION OF LIMITS 144 CONTENTS 4.8 EXERCISES 147 4.9 HINTS
AND ANSWERS 152 5 PARTIAL DIFFERENTIATION 154 5.1 DEFINITION OF THE
PARTIAL DERIVATIVE 154 5.2 THE TOTAL DIFFERENTIAL AND TOTAL DERIVATIVE
156 5.3 EXACT AND INEXACT DIFFERENTIALS 158 5.4 USEFUL THEOREMS OF
PARTIAL DIFFERENTIATION 160 5.5 THE CHAIN RULE 160 5.6 CHANGE OF
VARIABLES 161 5.7 TAYLOR S THEOREM FOR MANY-VARIABLE FUNCTIONS 163 5.8
STATIONARY VALUES OF MANY-VARIABLE FUNCTIONS 165 5.9 STATIONARY VALUES
UNDER CONSTRAINTS 170 5.10 ENVELOPES 176 5.11 THERMODYNAMIC RELATIONS
179 5.12 DIFFERENTIATION OF INTEGRALS 181 5.13 EXERCISES 182 5.14 HINTS
AND ANSWERS 188 6 MULTIPLE INTEGRALS 190 6.1 DOUBLE INTEGRALS 190 6.2
TRIPLE INTEGRALS 193 6.3 APPLICATIONS OF MULTIPLE INTEGRALS 194 AREAS
AND VOLUMES; MASSES, CENTRES OF MASS AND CENTROIDS; PAPPUS THEOREMS;
MOMENTS OF INERTIA; MEAN VALUES OF FUNCTIONS 6.4 CHANGE OF VARIABLES IN
MULTIPLE INTEGRALS 202 CHANGE OF VARIABLES IN DOUBLE INTEGRALS;
EVALUATION OF THE INTEGRAL I = F* M E~ X DX; CHANGE OF VARIABLES IN
TRIPLE INTEGRALS; GENERAL PROPERTIES OF JACOBIANS 6.5 EXERCISES 210 6.6
HINTS AND ANSWERS 214 7 VECTOR ALGEBRA 216 7.1 SCALARS AND VECTORS 216
7.2 ADDITION AND SUBTRACTION OF VECTORS 217 7.3 MULTIPLICATION BY A
SCALAR 218 7.4 BASIS VECTORS AND COMPONENTS 221 7.5 MAGNITUDE OF A
VECTOR 222 7.6 MULTIPLICATION OF VECTORS 223 SCALAR PRODUCT; VECTOR
PRODUCT; SCALAR TRIPLE PRODUCT; VECTOR TRIPLE PRODUCT VII CONTENTS 7.7
EQUATIONS OF LINES, PLANES AND SPHERES 230 7.8 USING VECTORS TO FIND
DISTANCES 233 POINT TO LINE; POINT TO PLANE; LINE TO LINE; LINE TO PLANE
7.9 RECIPROCAL VECTORS 237 7.10 EXERCISES 238 7.11 HINTS AND ANSWERS 244
8 MATRICES AND VECTOR SPACES 246 8.1 VECTOR SPACES 247 BASIS VECTORS;
INNER PRODUCT; SOME USEFUL INEQUALITIES 8.2 LINEAR OPERATORS 252 8.3
MATRICES 254 8.4 BASIC MATRIX ALGEBRA 255 MATRIX ADDITION;
MULTIPLICATION BY A SCALAR; MATRIX MULTIPLICATION 8.5 FUNCTIONS OF
MATRICES 260 8.6 THE TRANSPOSE OF A MATRIX 260 8.7 THE COMPLEX AND
HERMITIAN CONJUGATES OF A MATRIX 261 8.8 THE TRACE OF A MATRIX 263 8.9
THE DETERMINANT OF A MATRIX * 264 PROPERTIES OF DETERMINANTS 8.10 THE
INVERSE OF A MATRIX 268 8.11 THE RANK OF A MATRIX 272 8.12 SPECIAL TYPES
OF SQUARE MATRIX 273 DIAGONAL; TRIANGULAR; SYMMETRIC AND ANTISYMMETRIC;
ORTHOGONAL; HERMITIAN AND ANTI-HERMITIAN; UNITARY; NORMAL 8.13
EIGENVECTORS AND EIGENVALUES 277 OF A NORMAL MATRIX; OF HERMITIAN AND
ANTI-HERMITIAN MATRICES; OF A UNITARY MATRIX; OF A GENERAL SQUARE MATRIX
8.14 DETERMINATION OF EIGENVALUES AND EIGENVECTORS 285 DEGENERATE
EIGENVALUES 8.15 CHANGE OF BASIS AND SIMILARITY TRANSFORMATIONS 288 8.16
DIAGONALISATION OF MATRICES 290 8.17 QUADRATIC AND HERMITIAN FORMS 293
STATIONARY PROPERTIES OF THE EIGENVECTORS; QUADRATIC SURFACES 8.18
SIMULTANEOUS LINEAR EQUATIONS 297 RANGE; NULL SPACE; N SIMULTANEOUS
LINEAR EQUATIONS IN N UNKNOWNS; SINGULAR VALUE DECOMPOSITION 8.19
EXERCISES 312 8.20 HINTS AND ANSWERS 319 9 NORMAL MODES 322 9.1 TYPICAL
OSCILLATORY SYSTEMS 323 CONTENTS 9.2 SYMMETRY AND NORMAL MODES 328 9.3
RAYLEIGH-RITZ METHOD 333 9.4 EXERCISES 335 9.5 HINTS AND ANSWERS 338 10
VECTOR CALCULUS 340 10.1 DIFFERENTIATION OF VECTORS 340 COMPOSITE VECTOR
EXPRESSIONS; DIFFERENTIAL OF A VECTOR 10.2 INTEGRATION OF VECTORS 345
10.3 SPACE CURVES 346 10.4 VECTOR FUNCTIONS OF SEVERAL ARGUMENTS 350
10.5 SURFACES 351 10.6 SCALAR AND VECTOR FIELDS 353 10.7 VECTOR
OPERATORS 353 GRADIENT OF A SCALAR FIELD; DIVERGENCE OF A VECTOR FIELD;
CURL OF A VECTOR FIELD 10.8 VECTOR OPERATOR FORMULAE 360 VECTOR
OPERATORS ACTING ON SUMS AND PRODUCTS; COMBINATIONS OF GRAD, DIV AND
CURL 10.9 CYLINDRICAL AND SPHERICAL POLAR COORDINATES 363 10.10 GENERAL
CURVILINEAR COORDINATES 370 10.11 EXERCISES 375 10.12 HINTS AND ANSWERS
381 11 LINE, SURFACE AND VOLUME INTEGRALS 383 11.1 LINE INTEGRALS 383
EVALUATING LINE INTEGRALS; PHYSICAL EXAMPLES; LINE INTEGRALS WITH
RESPECT TO A SCALAR * * * 11.2 CONNECTIVITY OF REGIONS 389 11.3 GREEN S
THEOREM IN A PLANE . 390 11.4 CONSERVATIVE FIELDS AND POTENTIALS 393
11.5 SURFACE INTEGRALS 395 EVALUATING SURFACE INTEGRALS; VECTOR AREAS OF
SURFACES; PHYSICAL EXAMPLES 11.6 VOLUME INTEGRALS 402 VOLUMES OF
THREE-DIMENSIONAL REGIONS 11.7 INTEGRAL FORMS FOR GRAD, DIV AND CURL 404
11.8 DIVERGENCE THEOREM AND RELATED THEOREMS 407 GREEN S THEOREMS; OTHER
RELATED INTEGRAL THEOREMS; PHYSICAL APPLICATIONS 11.9 STOKES THEOREM
AND RELATED THEOREMS 412 RELATED INTEGRAL THEOREMS; PHYSICAL
APPLICATIONS 11.10 EXERCISES 415 11.11 HINTS AND ANSWERS 420 IX CONTENTS
12 FOURIER SERIES 421 12.1 THE DIRICHLET CONDITIONS 421 12.2 THE FOURIER
COEFFICIENTS 423 12.3 SYMMETRY CONSIDERATIONS 425 12.4 DISCONTINUOUS
FUNCTIONS 426 12.5 NON-PERIODIC FUNCTIONS 428 12.6 INTEGRATION AND
DIFFERENTIATION 430 12.7 COMPLEX FOURIER SERIES . 430 12.8 PARSEVAL S
THEOREM 432 12.9 EXERCISES 433 12.10 HINTS AND ANSWERS . 437 13 INTEGRAL
TRANSFORMS 439 13.1 FOURIER TRANSFORMS 439 THE UNCERTAINTY PRINCIPLE;
FRAUNHOFER DIFFRACTION; THE DIRAC D-FUNCTION; RELATION OF THE 5-FUNCTION
TO FOURIER TRANSFORMS; PROPERTIES OF FOURIER TRANSFORMS; ODD AND EVEN
FUNCTIONS; CONVOLUTION AND DECONVOLUTION; CORRELATION FUNCTIONS AND
ENERGY SPECTRA; PARSEVAL S THEOREM; FOURIER TRANSFORMS IN HIGHER
DIMENSIONS 13.2 LAPLACE TRANSFORMS 459 LAPLACE TRANSFORMS OF DERIVATIVES
AND INTEGRALS; OTHER PROPERTIES OF LAPLACE TRANSFORMS 13.3 CONCLUDING
REMARKS 465 13.4 EXERCISES 466 13.5 HINTS AND ANSWERS 472 14 FIRST-ORDER
ORDINARY DIFFERENTIAL EQUATIONS 474 14.1 GENERAL FORM OF SOLUTION 475
14.2 FIRST-DEGREE FIRST-ORDER EQUATIONS 476 SEPARABLE-VARIABLE
EQUATIONS; EXACT EQUATIONS; INEXACT EQUATIONS, INTEGRATING FACTORS;
LINEAR EQUATIONS; HOMOGENEOUS EQUATIONS; ISOBARIC EQUATIONS; BERNOULLI S
EQUATION; MISCELLANEOUS EQUATIONS 14.3 HIGHER-DEGREE FIRST-ORDER
EQUATIONS 486 EQUATIONS SOLUBLE FOR P; FOR X; FOR Y; CLAIRAUT S EQUATION
14.4 EXERCISES 490 14.5 HINTS AND ANSWERS 494 15 HIGHER-ORDER ORDINARY
DIFFERENTIAL EQUATIONS . 496 15.1 LINEAR EQUATIONS WITH CONSTANT
COEFFICIENTS 498 FINDING THE COMPLEMENTARY FUNCTION Y C (X); FINDING THE
PARTICULAR INTEGRAL Y P (X); CONSTRUCTING THE GENERAL SOLUTION Y C (X) +
Y P (X); LINEAR RECURRENCE RELATIONS; LAPLACE TRANSFORM METHOD CONTENTS
15.2 LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS 509 THE LEGENDRE AND
EULER LINEAR EQUATIONS; EXACT EQUATIONS; PARTIALLY KNOWN COMPLEMENTARY
FUNCTION; VARIATION OF PARAMETERS; GREEN S FUNCTIONS; CANONICAL FORM FOR
SECOND-ORDER EQUATIONS 15.3 GENERAL ORDINARY DIFFERENTIAL EQUATIONS 524
DEPENDENT VARIABLE ABSENT; INDEPENDENT VARIABLE ABSENT; NON-LINEAR EXACT
EQUATIONS; ISOBARIC OR HOMOGENEOUS EQUATIONS; EQUATIONS HOMOGENEOUS IN X
OR Y ALONE; EQUATIONS HAVING Y = AE X AS A SOLUTION 15.4 EXERCISES 529
15.5 HINTS AND ANSWERS 535 16 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL
EQUATIONS 537 16.1 SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
537 ORDINARY AND SINGULAR POINTS 16.2 SERIES SOLUTIONS ABOUT AN ORDINARY
POINT 541 16.3 SERIES SOLUTIONS ABOUT A REGULAR SINGULAR POINT 544
DISTINCT ROOTS NOT DIFFERING BY AN INTEGER; REPEATED ROOT OF THE
INDICIAL EQUATION; DISTINCT ROOTS DIFFERING BY AN INTEGER 16.4 OBTAINING
A SECOND SOLUTION 549 THE WRONSKIAN METHOD; THE DERIVATIVE METHOD;
SERIES FORM OF THE SECOND SOLUTION 16.5 POLYNOMIAL SOLUTIONS 554 16.6
LEGENDRE S EQUATION 555 GENERAL SOLUTION FOR INTEGER (; PROPERTIES OF
LEGENDRE POLYNOMIALS 16.7 BESSEL S EQUATION 564 GENERAL SOLUTION FOR
NON-INTEGER V; GENERAL SOLUTION FOR INTEGER V; PROPERTIES OF BESSEL
FUNCTIONS 16.8 GENERAL REMARKS 575 16.9 EXERCISES 575 16.10 HINTS AND
ANSWERS 579 17 EIGENFUNCTION METHODS FOR DIFFERENTIAL EQUATIONS 581 17.1
SETS OF FUNCTIONS 583 SOME USEFUL INEQUALITIES 17.2 ADJOINT AND
HERMITIAN OPERATORS 587 XI CONTENTS 17.3 THE PROPERTIES OF HERMITIAN
OPERATORS 588 REALITY OF THE EIGENVALUES; ORTHOGONALITY OF THE
EIGENFUNCTIONS; CONSTRUCTION OF REAL EIGENFUNCTIONS 11A STURM-LIOUVILL E
EQUATIONS 591 VALID BOUNDARY CONDITIONS; PUTTING AN EQUATION INTO
STURM-LIOUVILLE FORM 17.5 EXAMPLES OF STURM-LIOUVILLE EQUATIONS 593
LEGENDRE S EQUATION; THE ASSOCIATED LEGENDRE EQUATION; BESSEL S
EQUATION; THE SIMPLE HARMONIC EQUATION; HERMITE S EQUATION; LAGUERRE S
EQUATION; CHEBYSHEV S EQUATION 17.6 SUPERPOSITION OF EIGENFUNCTIONS:
GREEN S FUNCTIONS 597 17.7 A USEFUL GENERALISATION 601 17.8 EXERCISES
602 17.9 HINTS AND ANSWERS 606 18 PARTIAL DIFFERENTIAL EQUATIONS:
GENERAL AND PARTICULAR SOLUTIONS 608 18.1 IMPORTANT PARTIAL DIFFERENTIAL
EQUATIONS 609 THE WAVE EQUATION; THE DIFFUSION EQUATION; LAPLACE S
EQUATION; POISSON S EQUATION; SCHRODINGER S EQUATION 18.2 GENERAL FORM
OF SOLUTION 613 18.3 GENERAL AND PARTICULAR SOLUTIONS 614 FIRST-ORDER
EQUATIONS; INHOMOGENEOUS EQUATIONS AND PROBLEMS; SECOND-ORDER EQUATIONS
18.4 THE WAVE EQUATION 626 18.5 THE DIFFUSION EQUATION ^628 18.6
CHARACTERISTICS AND THE EXISTENCE OF SOLUTIONS 632 FIRST-ORDER
EQUATIONS; SECOND-ORDER EQUATIONS 18.7 UNIQUENESS OF SOLUTIONS 638 18.8
EXERCISES 640 18.9 HINTS AND ANSWERS 644 19 PARTIAL DIFFERENTIAL
EQUATIONS: SEPARATION OF VARIABLES AND OTHER METHODS 646 19.1 SEPARATION
OF VARIABLES: THE GENERAL METHOD 646 19.2 SUPERPOSITION OF SEPARATED
SOLUTIONS 650 19.3 SEPARATION OF VARIABLES IN POLAR COORDINATES 658
LAPLACE S EQUATION IN POLAR COORDINATES; SPHERICAL HARMONICS; OTHER
EQUATIONS IN POLAR COORDINATES; SOLUTION BY EXPANSION; SEPARATION OF
VARIABLES FOR INHOMOGENEOUS EQUATIONS 19A INTEGRAL TRANSFORM METHODS 681
19.5 INHOMOGENEOUS PROBLEMS - GREEN S FUNCTIONS 686 SIMILARITIES TO
GREEN S FUNCTIONS FOR ORDINARY DIFFERENTIAL EQUATIONS; GENERAL
BOUNDARY-VALUE PROBLEMS; DIRICHLET PROBLEMS; NEUMANN PROBLEMS XII
CONTENTS 19.6 EXERCISES 702 19.7 HINTS AND ANSWERS 708 20 COMPLEX
VARIABLES 710 20.1 FUNCTIONS OF A COMPLEX VARIABLE 711 20.2 THE
CAUCHY-RIEMANN RELATIONS 713 20.3 POWER SERIES IN A COMPLEX VARIABLE 716
20.4 SOME ELEMENTARY FUNCTIONS 718 20.5 MULTIVALUED FUNCTIONS AND BRANCH
CUTS 721 20.6 SINGULARITIES AND ZEROES OF COMPLEX FUNCTIONS 723 20.7
COMPLEX POTENTIALS 725 20.8 CONFORMAL TRANSFORMATIONS 730 20.9
APPLICATIONS OF CONFORMAL TRANSFORMATIONS 735 20.10 COMPLEX INTEGRALS
738 20.11 CAUCHY S THEOREM 742 20.12 CAUCHY S INTEGRAL FORMULA 745 20.13
TAYLOR AND LAURENT SERIES 747 20.14 RESIDUE THEOREM 752 20.15 LOCATION
OF ZEROES 754 20.16 INTEGRALS OF SINUSOIDAL FUNCTIONS 758 20.17 SOME
INFINITE INTEGRALS 759 20.18 INTEGRALS OF MULTIVALUED FUNCTIONS 762
20.19 SUMMATION OF SERIES 764 20.20 INVERSE LAPLACE TRANSFORM 765 20.21
EXERCISES 768 20.22 HINTS AND ANSWERS 773 21 TENSORS 776 21.1 SOME
NOTATION 777 21.2 CHANGE OF BASIS 778 21.3 CARTESIAN TENSORS 779 21.4
FIRST- AND ZERO-ORDER CARTESIAN TENSORS 781 21.5 SECOND- AND
HIGHER-ORDER CARTESIAN TENSORS 784 21.6 THE ALGEBRA OF TENSORS 787 21.7
THE QUOTIENT LAW 788 21.8 THE TENSORS (5Y AND E T J K 790 21.9 ISOTROPIC
TENSORS 793 21.10 IMPROPER ROTATIONS AND PSEUDOTENSORS 795 21.11 DUAL
TENSORS 798 21.12 PHYSICAL APPLICATIONS OF TENSORS 799 21.13 INTEGRAL
THEOREMS FOR TENSORS 803 21.14 NON-CARTESIAN COORDINATES 804 XIII
CONTENTS 21.15 THE METRIC TENSOR 806 21.16 GENERAL COORDINATE
TRANSFORMATIONS AND TENSORS 809 21.17 RELATIVE TENSORS 812 21.18
DERIVATIVES OF BASIS VECTORS AND CHRISTOFFEL SYMBOLS 814 21.19 COVARIANT
DIFFERENTIATION 817 21.20 VECTOR OPERATORS IN TENSOR FORM . . 820 21.21
ABSOLUTE DERIVATIVES ALONG CURVES 824 21.22 GEODESIES 825 21.23
EXERCISES * 826 2O4 HINTS AND ANSWERS 831 22 CALCULUS OF VARIATIONS 834
22.1 THE EULER-LAGRANGE EQUATION 835 22.2 SPECIAL CASES 836 F DOES NOT
CONTAIN Y EXPLICITLY; F DOES NOT CONTAIN X EXPLICITLY 22.3 SOME
EXTENSIONS 840 SEVERAL DEPENDENT VARIABLES; SEVERAL INDEPENDENT
VARIABLES ; HIGHER-ORDER DERIVATIVES; VARIABLE END-POINTS 22.4
CONSTRAINED VARIATION 844 22.5 PHYSICAL VARIATIONAL PRINCIPLES 846
FERMAT S PRINCIPLE IN OPTICS; HAMILTON S PRINCIPLE IN MECHANICS 22.6
GENERAL EIGENVALUE PROBLEMS 849 22.7 ESTIMATION OF EIGENVALUES AND
EIGENFUNCTIONS 851 22.8 ADJUSTMENT OF PARAMETERS 854 22.9 EXERCISES .
856 22.10 HINTS AND ANSWERS 860 23 INTEGRAL EQUATIONS 862 23.1 OBTAINING
AN INTEGRAL EQUATION FROM A DIFFERENTIAL EQUATION 862 23.2 TYPES OF
INTEGRAL EQUATION 863 23.3 OPERATOR NOTATION AND THE EXISTENCE OF
SOLUTIONS 864 23.4 CLOSED-FORM SOLUTIONS 865 SEPARABLE KERNELS; INTEGRAL
TRANSFORM METHODS; DIFFERENTIATION 23.5 NEUMANN SERIES 872 23.6 FREDHOLM
THEORY 874 23.7 SCHMIDT-HILBERT THEORY 875 23.8 EXERCISES 878 23.9
HINTS AND ANSWERS 882 24 GROUP THEORY 883 24.1 GROUPS 883 DEFINITION OF
A GROUP; EXAMPLES OF GROUPS CONTENTS 24.2 FINITE GROUPS 891 24.3
NON-ABELIAN GROUPS 894 24.4 PERMUTATION GROUPS 898 24.5 MAPPINGS BETWEEN
GROUPS 901 24.6 SUBGROUPS 903 24.7 SUBDIVIDING A GROUP 905 EQUIVALENCE
RELATIONS AND CLASSES; CONGRUENCE AND COSETS; CONJUGATES AND CLASSES
24.8 EXERCISES 912 24.9 HINTS AND ANSWERS 915 25 REPRESENTATION THEORY
918 25.1 DIPOLE MOMENTS OF MOLECULES 919 25.2 CHOOSING AN APPROPRIATE
FORMALISM 920 25.3 EQUIVALENT REPRESENTATIONS 926 25.4 REDUCIBILITY OF A
REPRESENTATION 928 25.5 THE ORTHOGONALITY THEOREM FOR IRREDUCIBLE
REPRESENTATIONS 932 25.6 CHARACTERS 934 ORTHOGONALITY PROPERTY OF
CHARACTERS 25.7 COUNTING IRREPS USING CHARACTERS 937 SUMMATION RULES FOR
IRREPS 25.8 CONSTRUCTION OF A CHARACTER TABLE 942 25.9 GROUP
NOMENCLATURE 944 25.10 PRODUCT REPRESENTATIONS 945 25.11 PHYSICAL
APPLICATIONS OF GROUP THEORY 947 BONDING IN MOLECULES; MATRIX ELEMENTS
IN QUANTUM MECHANICS; DEGENERACY OF NORMAL MODES; BREAKING OF
DEGENERACIES 25.12 EXERCISES 955 25.13 HINTS AND ANSWERS 959 26
PROBABILITY 961 26.1 VENN DIAGRAMS 961 26.2 PROBABILITY 966 AXIOMS AND
THEOREMS; CONDITIONAL PROBABILITY; BAYES THEOREM 26.3 PERMUTATIONS AND
COMBINATIONS 975 26.4 RANDOM VARIABLES AND DISTRIBUTIONS 981 DISCRETE
RANDOM VARIABLES; CONTINUOUS RANDOM VARIABLES 26.5 PROPERTIES OF
DISTRIBUTIONS 985 MEAN; MODE AND MEDIAN; VARIANCE AND STANDARD
DEVIATION; MOMENTS; CENTRAL MOMENTS 26.6 FUNCTIONS OF RANDOM VARIABLES
992 XV CONTENTS 26.7 GENERATING FUNCTIONS 999 PROBABILITY GENERATING
FUNCTIONS; MOMENT GENERATING FUNCTIONS; CHARACTERIS- TIC FUNCTIONS;
CUMULANT GENERATING FUNCTIONS 26.8 IMPORTANT DISCRETE DISTRIBUTIONS 1009
BINOMIAL; GEOMETRIC; NEGATIVE BINOMIAL; HYPERGEOMETRIC; POISSON 26.9
IMPORTANT CONTINUOUS DISTRIBUTIONS 1021 GAUSSIAN; LOG-NORMAL;
EXPONENTIAL; GAMMA; CHI-SQUARED; CAUCHY; BREIT- WIGNER; UNIFORM 26.10
THE CENTRAL LIMIT THEOREM 1036 26.11 JOINT DISTRIBUTIONS 1038 DISCRETE
BIVARIATE; CONTINUOUS BIVARIATE; MARGINAL AND CONDITIONAL DISTRIBU-
TIONS 26.12 PROPERTIES OF JOINT DISTRIBUTIONS 1041 MEANS; VARIANCES;
COVARIANCE AND CORRELATION 26.13 GENERATING FUNCTIONS FOR JOINT
DISTRIBUTIONS 1047 26.14 TRANSFORMATION OF VARIABLES IN JOINT
DISTRIBUTIONS 1048 26.15 IMPORTANT JOINT DISTRIBUTIONS 1049
MULTINOMINAL; MULTIVARIATE GAUSSIAN 26.16 EXERCISES 1053 26.17 HINTS AND
ANSWERS 1061 27 STATISTICS 1064 27.1 EXPERIMENTS, SAMPLES AND
POPULATIONS 1064 27.2 SAMPLE STATISTICS 1065 AVERAGES; VARIANCE AND
STANDARD DEVIATION; MOMENTS; COVARIANCE AND CORRELATION 27.3 ESTIMATORS
AND SAMPLING DISTRIBUTIONS 1072 CONSISTENCY, BIAS AND EFFICIENCY;
FISHER S INEQUALITY; STANDARD ERRORS; CONFIDENCE LIMITS 21A SOME BASIC
ESTIMATORS 1086 MEAN; VARIANCE; STANDARD DEVIATION; MOMENTS; COVARIANCE
AND CORRELATION 27.5 MAXIMUM-LIKELIHOOD METHOD 1097 ML ESTIMATOR;
TRANSFORMATION INVARIANCE AND BIAS; EFFICIENCY; ERRORS AND CONFIDENCE
LIMITS; BAYESIAN INTERPRETATION; LARGE-N BEHAVIOUR; EXTENDED ML METHOD
27.6 THE METHOD OF LEAST SQUARES 1113 LINEAR LEAST SQUARES; NON-LINEAR
LEAST SQUARES 27.7 HYPOTHESIS TESTING 1119 SIMPLE AND COMPOSITE
HYPOTHESES; STATISTICAL TESTS; NEYMAN-PEARSON; GENERALISED
LIKELIHOOD-RATIO; STUDENT S T; FISHER S F; GOODNESS OF FIT 27.8
EXERCISES 1140 27.9 HINTS AND ANSWERS 1145 XVI CONTENTS 28 NUMERICAL
METHODS 1148 28.1 ALGEBRAIC AND TRANSCENDENTAL EQUATIONS 1149
REARRANGEMENT OF THE EQUATION; LINEAR INTERPOLATION; BINARY CHOPPING;
NEWTON-RAPHSON METHOD 28.2 CONVERGENCE OF ITERATION SCHEMES 1156 28.3
SIMULTANEOUS LINEAR EQUATIONS 1158 GAUSSIAN ELIMINATION; GAUSS-SEIDEL
ITERATION; TRIDIAGONAL MATRICES 28.4 NUMERICAL INTEGRATION 1164
TRAPEZIUM RULE; SIMPSON S RULE; GAUSSIAN INTEGRATION; MONTE CARLO
METHODS 28.5 FINITE DIFFERENCES 1179 28.6 DIFFERENTIAL EQUATIONS 1180
DIFFERENCE EQUATIONS; TAYLOR SERIES SOLUTIONS; PREDICTION AND
CORRECTION; RUNGE-KUTTA METHODS; ISOCLINES 28.7 HIGHER-ORDER EQUATIONS
1188 28.8 PARTIAL DIFFERENTIAL EQUATIONS 1190 28.9 EXERCISES 1193 28.10
HINTS AND ANSWERS 1198 APPENDIX GAMMA, BETA AND ERROR FUNCTIONS 1201 A
1.1 THE GAMMA FUNCTION 1201 A1.2 THE BETA FUNCTION 1203 A1.3 THE ERROR
FUNCTION 1204 INDEX 1206 XVN
|
| any_adam_object | 1 |
| author | Riley, Kenneth F. 1936- Hobson, Michael P. 1967- Bence, Stephen J. 1972- |
| author_GND | (DE-588)123286387 (DE-588)141007885 (DE-588)141008784 |
| author_facet | Riley, Kenneth F. 1936- Hobson, Michael P. 1967- Bence, Stephen J. 1972- |
| author_role | aut aut aut |
| author_sort | Riley, Kenneth F. 1936- |
| author_variant | k f r kf kfr m p h mp mph s j b sj sjb |
| building | Verbundindex |
| bvnumber | BV019761041 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 |
| callnumber-search | QA300 |
| callnumber-sort | QA 3300 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 |
| classification_tum | MAT 021f |
| ctrlnum | (OCoLC)254827927 (DE-599)BVBBV019761041 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., reprinted with corr. |
| format | Book |
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| id | DE-604.BV019761041 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:05:31Z |
| institution | BVB |
| isbn | 0521813727 0521890675 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013087398 |
| oclc_num | 254827927 |
| open_access_boolean | |
| owner | DE-703 DE-573 |
| owner_facet | DE-703 DE-573 |
| physical | XXIII, 1232 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Riley, Kenneth F. 1936- Verfasser (DE-588)123286387 aut Mathematical methods for physics and engineering a comprehensive guide K. F. Riley, M. P. Hobson and S. J. Bence 2. ed., reprinted with corr. Cambridge [u.a.] Cambridge Univ. Press 2004 XXIII, 1232 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Angewandte Mathematik (DE-588)4142443-8 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 s Mathematische Methode (DE-588)4155620-3 s DE-604 Physik (DE-588)4045956-1 s Angewandte Mathematik (DE-588)4142443-8 s Mathematische Physik (DE-588)4037952-8 s 1\p DE-604 Hobson, Michael P. 1967- Verfasser (DE-588)141007885 aut Bence, Stephen J. 1972- Verfasser (DE-588)141008784 aut http://www.loc.gov/catdir/toc/cam021/2002018922.html Table of contents HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013087398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Riley, Kenneth F. 1936- Hobson, Michael P. 1967- Bence, Stephen J. 1972- Mathematical methods for physics and engineering a comprehensive guide Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Physik (DE-588)4045956-1 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4155620-3 (DE-588)4137304-2 (DE-588)4045956-1 (DE-588)4142443-8 |
| title | Mathematical methods for physics and engineering a comprehensive guide |
| title_auth | Mathematical methods for physics and engineering a comprehensive guide |
| title_exact_search | Mathematical methods for physics and engineering a comprehensive guide |
| title_full | Mathematical methods for physics and engineering a comprehensive guide K. F. Riley, M. P. Hobson and S. J. Bence |
| title_fullStr | Mathematical methods for physics and engineering a comprehensive guide K. F. Riley, M. P. Hobson and S. J. Bence |
| title_full_unstemmed | Mathematical methods for physics and engineering a comprehensive guide K. F. Riley, M. P. Hobson and S. J. Bence |
| title_short | Mathematical methods for physics and engineering |
| title_sort | mathematical methods for physics and engineering a comprehensive guide |
| title_sub | a comprehensive guide |
| topic | Mathematische Physik (DE-588)4037952-8 gnd Mathematische Methode (DE-588)4155620-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Physik (DE-588)4045956-1 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Mathematische Physik Mathematische Methode Ingenieurwissenschaften Physik Angewandte Mathematik |
| url | http://www.loc.gov/catdir/toc/cam021/2002018922.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013087398&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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