Mathematical methods for physics and engineering:
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| Main Authors: | , , |
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| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2006
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| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Beschreibung für Leser Table of contents Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XXVII, 1333 S. graph. Darst. |
| ISBN: | 9780521861533 0521861535 9780521679718 0521679710 |
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MARC
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Record in the Search Index
| _version_ | 1810067045034754048 |
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| adam_text |
MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING THIRD EDITION K.F.
RILEY, M.P. HOBSON AND S.J. BENCE CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE TO THE THIRD EDITION PAGE XX PREFACE TO THE SECOND EDITION XXIII
PREFACE TO THE FIRST EDITION XXV 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 41 2.1 DIFFERENTIATION 41
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 59 INTEGRATION FROM FIRST
PRINCIPLES; THE INVERSE OF DIFFERENTIATION; BY INSPEC- TION; 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 76 2.4 HINTS AND ANSWERS 81 F
3 COMPLEX NUMBERS AND HYPERBOLIC FUNCTIONS 83 3.1 THE NEED FOR COMPLEX
NUMBERS 83 3.2 MANIPULATION OF COMPLEX NUMBERS 85 ADDITION AND
SUBTRACTION; MODULUS AND ARGUMENT; MULTIPLICATION; COMPLEX CONJUGATE;
DIVISION 3.3 POLAR REPRESENTATION OF COMPLEX NUMBERS 92 MULTIPLICATION
AND DIVISION IN POLAR FORM 3.4 DE MOIVRE'S THEOREM 95 TRIGONOMETRIC
IDENTITIES; FINDING THE NTH ROOTS OF UNITY; SOLVING POLYNOMIAL EQUATIONS
3.5 COMPLEX LOGARITHMS AND COMPLEX POWERS 99 3.6 APPLICATIONS TO
DIFFERENTIATION AND INTEGRATION 101 3.7 HYPERBOLIC FUNCTIONS 102
DEFINITIONS; HYPERBOLIC-TRIGONOMETRIC ANALOGIES; IDENTITIES OF
HYPERBOLIC FUNCTIONS; SOLVING HYPERBOLIC EQUATIONS; INVERSES OF
HYPERBOLIC FUNCTIONS; CALCULUS OF HYPERBOLIC FUNCTIONS 3.8 EXERCISES 109
3.9 HINTS AND ANSWERS 113 4 SERIES AND LIMITS 115 4.1 SERIES 115 4.2
SUMMATION OF SERIES 116 ARITHMETIC SERIES; GEOMETRIC SERIES;
ARITHMETICO-GEOMETRIC SERIES; THE DIFFERENCE METHOD; SERIES INVOLVING
NATURAL NUMBERS; TRANSFORMATION OF SERIES 4.3 CONVERGENCE OF INFINITE
SERIES 124 ABSOLUTE AND CONDITIONAL CONVERGENCE; SERIES CONTAINING ONLY
REAL POSITIVE TERMS; ALTERNATING SERIES TEST 4.4 OPERATIONS WITH SERIES
131 4.5 POWER SERIES 131 CONVERGENCE OF POWER SERIES; OPERATIONS WITH
POWER SERIES 4.6 TAYLOR SERIES 136 TAYLOR'S THEOREM; APPROXIMATION
ERRORS; STANDARD MACLAURIN SERIES 4.7 EVALUATION OF LIMITS 141 4.8
EXERCISES 144 4.9 HINTS AND ANSWERS 149 CONTENTS 5 PARTIAL
DIFFERENTIATION 151 5.1 DEFINITION OF THE PARTIAL DERIVATIVE 151 5.2 THE
TOTAL DIFFERENTIAL AND TOTAL DERIVATIVE 153 5.3 EXACT AND INEXACT
DIFFERENTIALS 155 5.4 USEFUL THEOREMS OF PARTIAL DIFFERENTIATION 157 5.5
THE CHAIN RULE 157 5.6 CHANGE OF VARIABLES 158 5.7 TAYLOR'S THEOREM FOR
MANY-VARIABLE FUNCTIONS 160 5.8 STATIONARY VALUES OF MANY-VARIABLE
FUNCTIONS 162 5.9 STATIONARY VALUES UNDER CONSTRAINTS 167 5.10 ENVELOPES
173 5.11 THERMODYNAMIC RELATIONS 176 5.12 DIFFERENTIATION OF INTEGRALS
178 5.13 EXERCISES 179 5.14 HINTS AND ANSWERS 185 6 MULTIPLE INTEGRALS
187 6.1 DOUBLE INTEGRALS 187 6.2 TRIPLE INTEGRALS 190 6.3 APPLICATIONS
OF MULTIPLE INTEGRALS 191 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 199 CHANGE OF
VARIABLES IN DOUBLE INTEGRALS; EVALUATION OF THE INTEGRAL I = JF R E~ X
' DX; CHANGE OF VARIABLES IN TRIPLE INTEGRALS; GENERAL PROPERTIES OF
JACOBIANS 6.5 EXERCISES 207 6.6 HINTS AND ANSWERS 211 7 VECTOR ALGEBRA
212 7.1 SCALARS AND VECTORS 212 7.2 ADDITION AND SUBTRACTION OF VECTORS
213 7.3 MULTIPLICATION BY A SCALAR 214 7.4 BASIS VECTORS AND COMPONENTS
217 7.5 MAGNITUDE OF A VECTOR 218 7.6 MULTIPLICATION OF VECTORS 219
SCALAR PRODUCT; VECTOR PRODUCT; SCALAR TRIPLE PRODUCT; VECTOR TRIPLE
PRODUCT CONTENTS 7.7 EQUATIONS OF LINES, PLANES AND SPHERES 226 7.8
USING VECTORS TO FIND DISTANCES 229 POINT TO LINE; POINT TO PLANE; LINE
TO LINE; LINE TO PLANE 7.9 RECIPROCAL VECTORS 233 7.10 EXERCISES 234
7.11 HINTS AND ANSWERS 240 8 MATRICES AND VECTOR SPACES 241 8.1 VECTOR
SPACES 242 BASIS VECTORS; INNER PRODUCT; SOME USEFUL INEQUALITIES 8.2
LINEAR OPERATORS 247 8.3 MATRICES 249 8.4 BASIC MATRIX ALGEBRA 250
MATRIX ADDITION; MULTIPLICATION BY A SCALAR; MATRIX MULTIPLICATION 8.5
FUNCTIONS OF MATRICES 255 8.6 THE TRANSPOSE OF A MATRIX 255 8.7 THE
COMPLEX AND HERMITIAN CONJUGATES OF A MATRIX 256 8.8 THE TRACE OF A
MATRIX 258 8.9 THE DETERMINANT OF A MATRIX 259 PROPERTIES OF
DETERMINANTS 8.10 THE INVERSE OF A MATRIX 263 8.11 THE RANK OF A MATRIX
267 8.12 SPECIAL TYPES OF SQUARE MATRIX 268 DIAGONAL; TRIANGULAR;
SYMMETRIC AND ANTISYMMETRIC; ORTHOGONAL; HERMITIAN AND ANTI-HERMITIAN;
UNITARY; NORMAL 8.13 EIGENVECTORS AND EIGENVALUES 272 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 280 DEGENERATE EIGENVALUES 8.15 CHANGE OF BASIS AND
SIMILARITY TRANSFORMATIONS 282 8.16 DIAGONALISATION OF MATRICES 285 8.17
QUADRATIC AND HERMITIAN FORMS 288 STATIONARY PROPERTIES OF THE
EIGENVECTORS; QUADRATIC SURFACES 8.18 SIMULTANEOUS LINEAR EQUATIONS 292
RANGE; NULL SPACE; N SIMULTANEOUS LINEAR EQUATIONS IN N UNKNOWNS;
SINGULAR VALUE DECOMPOSITION 8.19 EXERCISES 307 8.20 HINTS AND ANSWERS
314 9 NORMAL MODES 316 9.1 TYPICAL OSCILLATORY SYSTEMS 317 9.2 SYMMETRY
AND NORMAL MODES 322 VIII CONTENTS 9.3 RAYLEIGH-RITZ METHOD 327 9.4
EXERCISES 329 9.5 HINTS AND ANSWERS 332 10 VECTOR CALCULUS 334 10.1
DIFFERENTIATION OF VECTORS 334 COMPOSITE VECTOR EXPRESSIONS;
DIFFERENTIAL OF A VECTOR 10.2 INTEGRATION OF VECTORS 339 10.3 SPACE
CURVES 340 10.4 VECTOR FUNCTIONS OF SEVERAL ARGUMENTS 344 10.5 SURFACES
345 10.6 SCALAR AND VECTOR FIELDS 347 10.7 VECTOR OPERATORS 347 GRADIENT
OF A SCALAR FIELD; DIVERGENCE OF A VECTOR FIELD; CURL OF A VECTOR FIELD
10.8 VECTOR OPERATOR FORMULAE 354 VECTOR OPERATORS ACTING ON SUMS AND
PRODUCTS; COMBINATIONS OF GRAD, DIV AND CURL 10.9 CYLINDRICAL AND
SPHERICAL POLAR COORDINATES 357 10.10 GENERAL CURVILINEAR COORDINATES
364 10.11 EXERCISES 369 10.12 HINTS AND ANSWERS 375 11 LINE, SURFACE AND
VOLUME INTEGRALS 377 11.1 LINE INTEGRALS 377 EVALUATING LINE INTEGRALS;
PHYSICAL EXAMPLES; LINE INTEGRALS WITH RESPECT TO A SCALAR 11.2
CONNECTIVITY OF REGIONS 383 11.3 GREEN'S THEOREM IN A PLANE 384 11.4
CONSERVATIVE FIELDS AND POTENTIALS 387 11.5 SURFACE INTEGRALS 389
EVALUATING SURFACE INTEGRALS; VECTOR AREAS OF SURFACES; PHYSICAL
EXAMPLES 11.6 VOLUME INTEGRALS 396 VOLUMES OF THREE-DIMENSIONAL REGIONS
11.7 INTEGRAL FORMS FOR GRAD, DIV AND CURL 398 11.8 DIVERGENCE THEOREM
AND RELATED THEOREMS 401 GREEN'S THEOREMS; OTHER RELATED INTEGRAL
THEOREMS; PHYSICAL APPLICATIONS 11.9 STOKES' THEOREM AND RELATED
THEOREMS 406 RELATED INTEGRAL THEOREMS; PHYSICAL APPLICATIONS 11.10
EXERCISES 409 11.11 HINTS AND ANSWERS 414 12 FOURIER SERIES 415 12.1 THE
DIRICHLET CONDITIONS 415 IX CONTENTS 12.2 THE FOURIER COEFFICIENTS 417
12.3 SYMMETRY CONSIDERATIONS 419 12.4 DISCONTINUOUS FUNCTIONS 420 12.5
NON-PERIODIC FUNCTIONS 422 12.6 INTEGRATION AND DIFFERENTIATION 424 12.7
COMPLEX FOURIER SERIES 424 12.8 PARSEVAL'S THEOREM 426 12.9 EXERCISES
427 12.10 HINTS AND ANSWERS 431 13 INTEGRAL TRANSFORMS 433 13.1 FOURIER
TRANSFORMS 433 THE UNCERTAINTY PRINCIPLE; FRAUNHOFER DIFFRACTION; THE
DIRAC D-FUNCTION; RELATION OF THE D-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
453 LAPLACE TRANSFORMS OF DERIVATIVES AND INTEGRALS; OTHER PROPERTIES OF
LAPLACE TRANSFORMS 13.3 CONCLUDING REMARKS 459 13.4 EXERCISES 460 13.5
HINTS AND ANSWERS 466 14 FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS 468
14.1 GENERAL FORM OF SOLUTION 469 14.2 FIRST-DEGREE FIRST-ORDER
EQUATIONS 470 SEPARABLE-VARIABLE EQUATIONS; EXACT EQUATIONS; INEXACT
EQUATIONS, INTEGRAT- ING FACTORS; LINEAR EQUATIONS; HOMOGENEOUS
EQUATIONS; ISOBARIC EQUATIONS; BERNOULLI'S EQUATION; MISCELLANEOUS
EQUATIONS 14.3 HIGHER-DEGREE FIRST-ORDER EQUATIONS 480 EQUATIONS SOLUBLE
FOR P; FOR X; FOR Y; CLAIRAUT'S EQUATION HA EXERCISES 484 14.5 HINTS AND
ANSWERS 488 15 HIGHER-ORDER ORDINARY DIFFERENTIAL EQUATIONS 490 15.1
LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 492 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 15.2 LINEAR EQUATIONS WITH VARIABLE
COEFFICIENTS 503 THE LEGENDRE AND EULER LINEAR EQUATIONS; EXACT
EQUATIONS; PARTIALLY KNOWN COMPLEMENTARY FUNCTION; VARIATION OF
PARAMETERS; GREEN'S FUNCTIONS; CANONICAL FORM FOR SECOND-ORDER EQUATIONS
CONTENTS 15.3 GENERAL ORDINARY DIFFERENTIAL EQUATIONS 518 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 523
15.5 HINTS AND ANSWERS 529 16 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL
EQUATIONS 531 16.1 SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
531 ORDINARY AND SINGULAR POINTS 16.2 SERIES SOLUTIONS ABOUT AN ORDINARY
POINT 535 16.3 SERIES SOLUTIONS ABOUT A REGULAR SINGULAR POINT 538
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 544 THE WRONSKIAN METHOD; THE DERIVATIVE METHOD;
SERIES FORM OF THE SECOND SOLUTION 16.5 POLYNOMIAL SOLUTIONS 548 16.6
EXERCISES 550 16.7 HINTS AND ANSWERS 553 17 EIGENFUNCTION METHODS FOR
DIFFERENTIAL EQUATIONS 554 17.1 SETS OF FUNCTIONS 556 SOME USEFUL
INEQUALITIES 17.2 ADJOINT, SELF-ADJOINT AND HERMITIAN OPERATORS 559 17.3
PROPERTIES OF HERMITIAN OPERATORS 561 REALITY OF THE EIGENVALUES;
ORTHOGONALITY OF THE EIGENFUNCTIONS; CONSTRUCTION OF REAL EIGENFUNCTIONS
17.4 STURM-LIOUVILLE EQUATIONS 564 VALID BOUNDARY CONDITIONS; PUTTING AN
EQUATION INTO STURM-LIOUVILLE FORM 17.5 SUPERPOSITION OF EIGENFUNCTIONS:
GREEN'S FUNCTIONS 569 17.6 A USEFUL GENERALISATION 572 17.7 EXERCISES
573 17.8 HINTS AND ANSWERS 576 18 SPECIAL FUNCTIONS 577 18.1 LEGENDRE
FUNCTIONS 577 GENERAL SOLUTION FOR INTEGER F; PROPERTIES OF LEGENDRE
POLYNOMIALS 18.2 ASSOCIATED LEGENDRE FUNCTIONS 587 18.3 SPHERICAL
HARMONICS 593 18.4 CHEBYSHEV FUNCTIONS 595 18.5 BESSEL FUNCTIONS 602
GENERAL SOLUTION FOR NON-INTEGER V; GENERAL SOLUTION FOR INTEGER V;
PROPERTIES OF BESSEL FUNCTIONS CONTENTS 18.6 SPHERICAL BESSEL FUNCTIONS
614 18.7 LAGUERRE FUNCTIONS 616 18.8 ASSOCIATED LAGUERRE FUNCTIONS 621
18.9 HERMITE FUNCTIONS 624 18.10 HYPERGEOMETRIC FUNCTIONS 628 18.11
CONFLUENT HYPERGEOMETRIC FUNCTIONS 633 18.12 THE GAMMA FUNCTION AND
RELATED FUNCTIONS 635 18.13 EXERCISES 640 18.14 HINTS AND ANSWERS 646 19
QUANTUM OPERATORS 648 19.1 OPERATOR FORMALISM 648 COMMUTATORS 19.2
PHYSICAL EXAMPLES OF OPERATORS 656 UNCERTAINTY PRINCIPLE; ANGULAR
MOMENTUM; CREATION AND ANNIHILATION OPERATORS 19.3 EXERCISES 671 19.4
HINTS AND ANSWERS 674 20 PARTIAL DIFFERENTIAL EQUATIONS: GENERAL AND
PARTICULAR SOLUTIONS 675 20.1 IMPORTANT PARTIAL DIFFERENTIAL EQUATIONS
676 THE WAVE EQUATION; THE DIFFUSION EQUATION; LAPLACE'S EQUATION;
POISSON'S EQUATION; SCHRODINGER'S EQUATION 20.2 GENERAL FORM OF SOLUTION
680 20.3 GENERAL AND PARTICULAR SOLUTIONS 681 FIRST-ORDER EQUATIONS;
INHOMOGENEOUS EQUATIONS AND PROBLEMS; SECOND-ORDER EQUATIONS 20.4 THE
WAVE EQUATION 693 20.5 THE DIFFUSION EQUATION 695 20.6 CHARACTERISTICS
AND THE EXISTENCE OF SOLUTIONS 699 FIRST-ORDER EQUATIONS; SECOND-ORDER
EQUATIONS 20.7 UNIQUENESS OF SOLUTIONS 705 20.8 EXERCISES 707 20.9 HINTS
AND ANSWERS 711 21 PARTIAL DIFFERENTIAL EQUATIONS: SEPARATION OF
VARIABLES AND OTHER METHODS 713 21.1 SEPARATION OF VARIABLES: THE
GENERAL METHOD 713 21.2 SUPERPOSITION OF SEPARATED SOLUTIONS 717 21.3
SEPARATION OF VARIABLES IN POLAR COORDINATES 725 LAPLACE'S EQUATION IN
POLAR COORDINATES; SPHERICAL HARMONICS; OTHER EQUATIONS IN POLAR
COORDINATES; SOLUTION BY EXPANSION; SEPARATION OF VARIABLES FOR
INHOMOGENEOUS EQUATIONS 21A INTEGRAL TRANSFORM METHODS 747 XII CONTENTS
21.5 INHOMOGENEOUS PROBLEMS - GREEN'S FUNCTIONS 751 SIMILARITIES TO
GREEN'S FUNCTIONS FOR ORDINARY DIFFERENTIAL EQUATIONS; GENERAL
BOUNDARY-VALUE PROBLEMS; DIRICHLET PROBLEMS; NEUMANN PROBLEMS 21.6
EXERCISES 767 21.7 HINTS AND ANSWERS 773 22 CALCULUS OF VARIATIONS 775
22.1 THE EULER-LAGRANGE EQUATION 776 22.2 SPECIAL CASES 777 F DOES NOT
CONTAIN Y EXPLICITLY; F DOES NOT CONTAIN X EXPLICITLY 22.3 SOME
EXTENSIONS 781 SEVERAL DEPENDENT VARIABLES; SEVERAL INDEPENDENT
VARIABLES; HIGHER-ORDER DERIVATIVES; VARIABLE END-POINTS 22.4
CONSTRAINED VARIATION 785 22.5 PHYSICAL VARIATIONAL PRINCIPLES 787
FERMAT'S PRINCIPLE IN OPTICS; HAMILTON'S PRINCIPLE IN MECHANICS 22.6
GENERAL EIGENVALUE PROBLEMS 790 22.7 ESTIMATION OF EIGENVALUES AND
EIGENFUNCTIONS 792 22.8 ADJUSTMENT OF PARAMETERS 795 22.9 EXERCISES 797
22.10 HINTS AND ANSWERS 801 23 INTEGRAL EQUATIONS 803 23.1 OBTAINING AN
INTEGRAL EQUATION FROM A DIFFERENTIAL EQUATION 803 23.2 TYPES OF
INTEGRAL EQUATION 804 23.3 OPERATOR NOTATION AND THE EXISTENCE OF
SOLUTIONS 805 23.4 CLOSED-FORM SOLUTIONS 806 SEPARABLE KERNELS; INTEGRAL
TRANSFORM METHODS; DIFFERENTIATION 23.5 NEUMANN SERIES 813 23.6 FREDHOLM
THEORY 815 23.7 SCHMIDT-HILBERT THEORY 816 23.8 EXERCISES 819 23.9 HINTS
AND ANSWERS 823 24 COMPLEX VARIABLES 824 24.1 FUNCTIONS OF A COMPLEX
VARIABLE 825 24.2 THE CAUCHY-RIEMANN RELATIONS 827 24.3 POWER SERIES IN
A COMPLEX VARIABLE 830 24.4 SOME ELEMENTARY FUNCTIONS 832 24.5
MULTIVALUED FUNCTIONS AND BRANCH CUTS 835 24.6 SINGULARITIES AND ZEROS
OF COMPLEX FUNCTIONS 837 24.7 CONFORMAL TRANSFORMATIONS 839 24.8 COMPLEX
INTEGRALS 845 CONTENTS 24.9 CAUCHY'S THEOREM 849 24.10 CAUCHY'S INTEGRAL
FORMULA 851 24.11 TAYLOR AND LAURENT SERIES 853 24.12 RESIDUE THEOREM
858 24.13 DEFINITE INTEGRALS USING CONTOUR INTEGRATION 861 24.14
EXERCISES 867 24.15 HINTS AND ANSWERS 870 25 APPLICATIONS OF COMPLEX
VARIABLES 871 25.1 COMPLEX POTENTIALS 871 25.2 APPLICATIONS OF CONFORMAL
TRANSFORMATIONS 876 25.3 LOCATION OF ZEROS 879 25.4 SUMMATION OF SERIES
882 25.5 INVERSE LAPLACE TRANSFORM 884 25.6 STOKES' EQUATION AND AIRY
INTEGRALS 888 25.7 WKB METHODS 895 25.8 APPROXIMATIONS TO INTEGRALS 905
LEVEL LINES AND SADDLE POINTS; STEEPEST DESCENTS; STATIONARY PHASE 25.9
EXERCISES 920 25.10 HINTS AND ANSWERS 925 26 TENSORS 927 26.1 SOME
NOTATION 928 26.2 CHANGE OF BASIS 929 26.3 CARTESIAN TENSORS 930 26.4
FIRST- AND ZERO-ORDER CARTESIAN TENSORS 932 26.5 SECOND- AND
HIGHER-ORDER CARTESIAN TENSORS 935 26.6 THE ALGEBRA OF TENSORS 938 26.7
THE QUOTIENT LAW 939 26.8 THE TENSORS 5,-Y AND E,^ 941 26.9 ISOTROPIC
TENSORS 944 26.10 IMPROPER ROTATIONS AND PSEUDOTENSORS 946 26.11 DUAL
TENSORS 949 26.12 PHYSICAL APPLICATIONS OF TENSORS 950 26.13 INTEGRAL
THEOREMS FOR TENSORS 954 26.14 NON-CARTESIAN COORDINATES 955 26.15 THE
METRIC TENSOR 957 26.16 GENERAL COORDINATE TRANSFORMATIONS AND TENSORS
960 26.17 RELATIVE TENSORS 963 26.18 DERIVATIVES OF BASIS VECTORS AND
CHRISTOFFEL SYMBOLS 965 26.19 COVARIANT DIFFERENTIATION 968 26.20 VECTOR
OPERATORS IN TENSOR FORM 971 CONTENTS 26.21 ABSOLUTE DERIVATIVES ALONG
CURVES 975 26.22 GEODESIES 976 26.23 EXERCISES 977 26.24 HINTS AND
ANSWERS 982 27 NUMERICAL METHODS 984 27.1 ALGEBRAIC AND TRANSCENDENTAL
EQUATIONS 985 REARRANGEMENT OF THE EQUATION; LINEAR INTERPOLATION;
BINARY CHOPPING; NEWTON-RAPHSON METHOD 27.2 CONVERGENCE OF ITERATION
SCHEMES 992 27.3 SIMULTANEOUS LINEAR EQUATIONS 994 GAUSSIAN ELIMINATION;
GAUSS-SEIDEL ITERATION; TRIDIAGONAL MATRICES 21A NUMERICAL INTEGRATION
1000 TRAPEZIUM RULE; SIMPSON'S RULE; GAUSSIAN INTEGRATION; MONTE CARLO
METHODS 27.5 FINITE DIFFERENCES 1019 27.6 DIFFERENTIAL EQUATIONS 1020
DIFFERENCE EQUATIONS; TAYLOR SERIES SOLUTIONS; PREDICTION AND
CORRECTION; RUNGE-KUTTA METHODS; ISOCLINES 27.7 HIGHER-ORDER EQUATIONS
1028 27.8 PARTIAL DIFFERENTIAL EQUATIONS 1030 27.9 EXERCISES 1033 27.10
HINTS AND ANSWERS 1039 28 GROUP THEORY 1041 28.1 GROUPS 1041 DEFINITION
OF A GROUP; EXAMPLES OF GROUPS 28.2 FINITE GROUPS 1049 28.3 NON-ABELIAN
GROUPS 1052 28.4 PERMUTATION GROUPS 1056 28.5 MAPPINGS BETWEEN GROUPS
1059 28.6 SUBGROUPS 1061 28.7 SUBDIVIDING A GROUP 1063 EQUIVALENCE
RELATIONS AND CLASSES; CONGRUENCE AND COSETS; CONJUGATES AND CLASSES
28.8 EXERCISES 1070 28.9 HINTS AND ANSWERS 1074 29 REPRESENTATION THEORY
1076 29.1 DIPOLE MOMENTS OF MOLECULES 1077 29.2 CHOOSING AN APPROPRIATE
FORMALISM 1078 29.3 EQUIVALENT REPRESENTATIONS 1084 29.4 REDUCIBILITY OF
A REPRESENTATION 1086 29.5 THE ORTHOGONALITY THEOREM FOR IRREDUCIBLE
REPRESENTATIONS 1090 CONTENTS 29.6 CHARACTERS 1092 ORTHOGONALITY
PROPERTY OF CHARACTERS 29.7 COUNTING IRREPS USING CHARACTERS 1095
SUMMATION RULES FOR IRREPS 29.8 CONSTRUCTION OF A CHARACTER TABLE 1100
29.9 GROUP NOMENCLATURE 1102 29.10 PRODUCT REPRESENTATIONS 1103 29.11
PHYSICAL APPLICATIONS OF GROUP THEORY 1105 BONDING IN MOLECULES; MATRIX
ELEMENTS IN QUANTUM MECHANICS; DEGENERACY OF NORMALSNODES; BREAKING OF
DEGENERACIES 29.12 EXERCISES 1113 29.13 HINTS AND ANSWERS 1117 30
PROBABILITY 1119 30.1 VENN DIAGRAMS 1119 30.2 PROBABILITY 1124 AXIOMS
AND THEOREMS; CONDITIONAL PROBABILITY; BAYES' THEOREM 30.3 PERMUTATIONS
AND COMBINATIONS 1133 30.4 RANDOM VARIABLES AND DISTRIBUTIONS 1139
DISCRETE RANDOM VARIABLES; CONTINUOUS RANDOM VARIABLES 30.5 PROPERTIES
OF DISTRIBUTIONS 1143 MEAN; MODE AND MEDIAN; VARIANCE AND STANDARD
DEVIATION; MOMENTS; CENTRAL MOMENTS 30.6 FUNCTIONS OF RANDOM VARIABLES
1150 30.7 GENERATING FUNCTIONS 1157 PROBABILITY GENERATING FUNCTIONS;
MOMENT GENERATING FUNCTIONS; CHARACTERISTIC FUNCTIONS; CUMULANT
GENERATING FUNCTIONS 30.8 IMPORTANT DISCRETE DISTRIBUTIONS 1168
BINOMIAL; GEOMETRIC; NEGATIVE BINOMIAL; HYPERGEOMETRIC; POISSON 30.9
IMPORTANT CONTINUOUS DISTRIBUTIONS 1179 GAUSSIAN; LOG-NORMAL;
EXPONENTIAL; GAMMA; CHI-SQUARED; CAUCHY; BREIT- WIGNER; UNIFORM 30.10
THE CENTRAL LIMIT THEOREM 1195 30.11 JOINT DISTRIBUTIONS 1196 DISCRETE
BIVARIATE; CONTINUOUS BIVARIATE; MARGINAL AND CONDITIONAL DISTRIBUTIONS
30.12 PROPERTIES OF JOINT DISTRIBUTIONS 1199 MEANS; VARIANCES;
COVARIANCE AND CORRELATION 30.13 GENERATING FUNCTIONS FOR JOINT
DISTRIBUTIONS 1205 30.14 TRANSFORMATION OF VARIABLES IN JOINT
DISTRIBUTIONS 1206 30.15 IMPORTANT JOINT DISTRIBUTIONS 1207
MULTINOMINAL; MULTIVARIATE GAUSSIAN 30.16 EXERCISES 1211 30.17 HINTS AND
ANSWERS 1219 CONTENTS 31 STATISTICS 1221 31.1 EXPERIMENTS, SAMPLES AND
POPULATIONS 1221 31.2 SAMPLE STATISTICS 1222 AVERAGES; VARIANCE AND
STANDARD DEVIATION; MOMENTS; COVARIANCE AND CORRELA- TION 31.3
ESTIMATORS AND SAMPLING DISTRIBUTIONS 1229 CONSISTENCY, BIAS AND
EFFICIENCY; FISHER'S INEQUALITY; STANDARD ERRORS; CONFI- DENCE LIMITS
31.4 SOME BASIC ESTIMATORS 1243 MEAN; VARIANCE; STANDARD DEVIATION;
MOMENTS; COVARIANCE AND CORRELATION 31.5 MAXIMUM-LIKELIHOOD METHOD 1255
ML ESTIMATOR; TRANSFORMATION INVARIANCE AND BIAS; EFFICIENCY; ERRORS AND
CONFIDENCE LIMITS; BAYESIAN INTERPRETATION; LARGE-N BEHAVIOUR; EXTENDED
ML METHOD 31.6 THE METHOD OF LEAST SQUARES 1271 LINEAR LEAST SQUARES;
NON-LINEAR LEAST SQUARES 31.7 HYPOTHESIS TESTING 1277 SIMPLE AND
COMPOSITE HYPOTHESES; STATISTICAL TESTS; NEYMAN-PEARSON; GENER- ALISED
LIKELIHOOD-RATIO; STUDENT'S T; FISHER'S F; GOODNESS OF FIT 31.8
EXERCISES 1298 31.9 HINTS AND ANSWERS 1303 INDEX 1305 XVN |
| adam_txt |
MATHEMATICAL METHODS FOR PHYSICS AND ENGINEERING THIRD EDITION K.F.
RILEY, M.P. HOBSON AND S.J. BENCE CAMBRIDGE UNIVERSITY PRESS CONTENTS
PREFACE TO THE THIRD EDITION PAGE XX PREFACE TO THE SECOND EDITION XXIII
PREFACE TO THE FIRST EDITION XXV 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 41 2.1 DIFFERENTIATION 41
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 59 INTEGRATION FROM FIRST
PRINCIPLES; THE INVERSE OF DIFFERENTIATION; BY INSPEC- TION; 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 76 2.4 HINTS AND ANSWERS 81 F
3 COMPLEX NUMBERS AND HYPERBOLIC FUNCTIONS 83 3.1 THE NEED FOR COMPLEX
NUMBERS 83 3.2 MANIPULATION OF COMPLEX NUMBERS 85 ADDITION AND
SUBTRACTION; MODULUS AND ARGUMENT; MULTIPLICATION; COMPLEX CONJUGATE;
DIVISION 3.3 POLAR REPRESENTATION OF COMPLEX NUMBERS 92 MULTIPLICATION
AND DIVISION IN POLAR FORM 3.4 DE MOIVRE'S THEOREM 95 TRIGONOMETRIC
IDENTITIES; FINDING THE NTH ROOTS OF UNITY; SOLVING POLYNOMIAL EQUATIONS
3.5 COMPLEX LOGARITHMS AND COMPLEX POWERS 99 3.6 APPLICATIONS TO
DIFFERENTIATION AND INTEGRATION 101 3.7 HYPERBOLIC FUNCTIONS 102
DEFINITIONS; HYPERBOLIC-TRIGONOMETRIC ANALOGIES; IDENTITIES OF
HYPERBOLIC FUNCTIONS; SOLVING HYPERBOLIC EQUATIONS; INVERSES OF
HYPERBOLIC FUNCTIONS; CALCULUS OF HYPERBOLIC FUNCTIONS 3.8 EXERCISES 109
3.9 HINTS AND ANSWERS 113 4 SERIES AND LIMITS 115 4.1 SERIES 115 4.2
SUMMATION OF SERIES 116 ARITHMETIC SERIES; GEOMETRIC SERIES;
ARITHMETICO-GEOMETRIC SERIES; THE DIFFERENCE METHOD; SERIES INVOLVING
NATURAL NUMBERS; TRANSFORMATION OF SERIES 4.3 CONVERGENCE OF INFINITE
SERIES 124 ABSOLUTE AND CONDITIONAL CONVERGENCE; SERIES CONTAINING ONLY
REAL POSITIVE TERMS; ALTERNATING SERIES TEST 4.4 OPERATIONS WITH SERIES
131 4.5 POWER SERIES 131 CONVERGENCE OF POWER SERIES; OPERATIONS WITH
POWER SERIES 4.6 TAYLOR SERIES 136 TAYLOR'S THEOREM; APPROXIMATION
ERRORS; STANDARD MACLAURIN SERIES 4.7 EVALUATION OF LIMITS 141 4.8
EXERCISES 144 4.9 HINTS AND ANSWERS 149 CONTENTS 5 PARTIAL
DIFFERENTIATION 151 5.1 DEFINITION OF THE PARTIAL DERIVATIVE 151 5.2 THE
TOTAL DIFFERENTIAL AND TOTAL DERIVATIVE 153 5.3 EXACT AND INEXACT
DIFFERENTIALS 155 5.4 USEFUL THEOREMS OF PARTIAL DIFFERENTIATION 157 5.5
THE CHAIN RULE 157 5.6 CHANGE OF VARIABLES 158 5.7 TAYLOR'S THEOREM FOR
MANY-VARIABLE FUNCTIONS 160 5.8 STATIONARY VALUES OF MANY-VARIABLE
FUNCTIONS 162 5.9 STATIONARY VALUES UNDER CONSTRAINTS 167 5.10 ENVELOPES
173 5.11 THERMODYNAMIC RELATIONS 176 5.12 DIFFERENTIATION OF INTEGRALS
178 5.13 EXERCISES 179 5.14 HINTS AND ANSWERS 185 6 MULTIPLE INTEGRALS
187 6.1 DOUBLE INTEGRALS 187 6.2 TRIPLE INTEGRALS 190 6.3 APPLICATIONS
OF MULTIPLE INTEGRALS 191 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 199 CHANGE OF
VARIABLES IN DOUBLE INTEGRALS; EVALUATION OF THE INTEGRAL I = JF R E~ X
' DX; CHANGE OF VARIABLES IN TRIPLE INTEGRALS; GENERAL PROPERTIES OF
JACOBIANS 6.5 EXERCISES 207 6.6 HINTS AND ANSWERS 211 7 VECTOR ALGEBRA
212 7.1 SCALARS AND VECTORS 212 7.2 ADDITION AND SUBTRACTION OF VECTORS
213 7.3 MULTIPLICATION BY A SCALAR 214 7.4 BASIS VECTORS AND COMPONENTS
217 7.5 MAGNITUDE OF A VECTOR 218 7.6 MULTIPLICATION OF VECTORS 219
SCALAR PRODUCT; VECTOR PRODUCT; SCALAR TRIPLE PRODUCT; VECTOR TRIPLE
PRODUCT CONTENTS 7.7 EQUATIONS OF LINES, PLANES AND SPHERES 226 7.8
USING VECTORS TO FIND DISTANCES 229 POINT TO LINE; POINT TO PLANE; LINE
TO LINE; LINE TO PLANE 7.9 RECIPROCAL VECTORS 233 7.10 EXERCISES 234
7.11 HINTS AND ANSWERS 240 8 MATRICES AND VECTOR SPACES 241 8.1 VECTOR
SPACES 242 BASIS VECTORS; INNER PRODUCT; SOME USEFUL INEQUALITIES 8.2
LINEAR OPERATORS 247 8.3 MATRICES 249 8.4 BASIC MATRIX ALGEBRA 250
MATRIX ADDITION; MULTIPLICATION BY A SCALAR; MATRIX MULTIPLICATION 8.5
FUNCTIONS OF MATRICES 255 8.6 THE TRANSPOSE OF A MATRIX 255 8.7 THE
COMPLEX AND HERMITIAN CONJUGATES OF A MATRIX 256 8.8 THE TRACE OF A
MATRIX 258 8.9 THE DETERMINANT OF A MATRIX 259 PROPERTIES OF
DETERMINANTS 8.10 THE INVERSE OF A MATRIX 263 8.11 THE RANK OF A MATRIX
267 8.12 SPECIAL TYPES OF SQUARE MATRIX 268 DIAGONAL; TRIANGULAR;
SYMMETRIC AND ANTISYMMETRIC; ORTHOGONAL; HERMITIAN AND ANTI-HERMITIAN;
UNITARY; NORMAL 8.13 EIGENVECTORS AND EIGENVALUES 272 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 280 DEGENERATE EIGENVALUES 8.15 CHANGE OF BASIS AND
SIMILARITY TRANSFORMATIONS 282 8.16 DIAGONALISATION OF MATRICES 285 8.17
QUADRATIC AND HERMITIAN FORMS 288 STATIONARY PROPERTIES OF THE
EIGENVECTORS; QUADRATIC SURFACES 8.18 SIMULTANEOUS LINEAR EQUATIONS 292
RANGE; NULL SPACE; N SIMULTANEOUS LINEAR EQUATIONS IN N UNKNOWNS;
SINGULAR VALUE DECOMPOSITION 8.19 EXERCISES 307 8.20 HINTS AND ANSWERS
314 9 NORMAL MODES 316 9.1 TYPICAL OSCILLATORY SYSTEMS 317 9.2 SYMMETRY
AND NORMAL MODES 322 VIII CONTENTS 9.3 RAYLEIGH-RITZ METHOD 327 9.4
EXERCISES 329 9.5 HINTS AND ANSWERS 332 10 VECTOR CALCULUS 334 10.1
DIFFERENTIATION OF VECTORS 334 COMPOSITE VECTOR EXPRESSIONS;
DIFFERENTIAL OF A VECTOR 10.2 INTEGRATION OF VECTORS 339 10.3 SPACE
CURVES 340 10.4 VECTOR FUNCTIONS OF SEVERAL ARGUMENTS 344 10.5 SURFACES
345 10.6 SCALAR AND VECTOR FIELDS 347 10.7 VECTOR OPERATORS 347 GRADIENT
OF A SCALAR FIELD; DIVERGENCE OF A VECTOR FIELD; CURL OF A VECTOR FIELD
10.8 VECTOR OPERATOR FORMULAE 354 VECTOR OPERATORS ACTING ON SUMS AND
PRODUCTS; COMBINATIONS OF GRAD, DIV AND CURL 10.9 CYLINDRICAL AND
SPHERICAL POLAR COORDINATES 357 10.10 GENERAL CURVILINEAR COORDINATES
364 10.11 EXERCISES 369 10.12 HINTS AND ANSWERS 375 11 LINE, SURFACE AND
VOLUME INTEGRALS 377 11.1 LINE INTEGRALS 377 EVALUATING LINE INTEGRALS;
PHYSICAL EXAMPLES; LINE INTEGRALS WITH RESPECT TO A SCALAR 11.2
CONNECTIVITY OF REGIONS 383 11.3 GREEN'S THEOREM IN A PLANE 384 11.4
CONSERVATIVE FIELDS AND POTENTIALS 387 11.5 SURFACE INTEGRALS 389
EVALUATING SURFACE INTEGRALS; VECTOR AREAS OF SURFACES; PHYSICAL
EXAMPLES 11.6 VOLUME INTEGRALS 396 VOLUMES OF THREE-DIMENSIONAL REGIONS
11.7 INTEGRAL FORMS FOR GRAD, DIV AND CURL 398 11.8 DIVERGENCE THEOREM
AND RELATED THEOREMS 401 GREEN'S THEOREMS; OTHER RELATED INTEGRAL
THEOREMS; PHYSICAL APPLICATIONS 11.9 STOKES' THEOREM AND RELATED
THEOREMS 406 RELATED INTEGRAL THEOREMS; PHYSICAL APPLICATIONS 11.10
EXERCISES 409 11.11 HINTS AND ANSWERS 414 12 FOURIER SERIES 415 12.1 THE
DIRICHLET CONDITIONS 415 IX CONTENTS 12.2 THE FOURIER COEFFICIENTS 417
12.3 SYMMETRY CONSIDERATIONS 419 12.4 DISCONTINUOUS FUNCTIONS 420 12.5
NON-PERIODIC FUNCTIONS 422 12.6 INTEGRATION AND DIFFERENTIATION 424 12.7
COMPLEX FOURIER SERIES 424 12.8 PARSEVAL'S THEOREM 426 12.9 EXERCISES
427 12.10 HINTS AND ANSWERS 431 13 INTEGRAL TRANSFORMS 433 13.1 FOURIER
TRANSFORMS 433 THE UNCERTAINTY PRINCIPLE; FRAUNHOFER DIFFRACTION; THE
DIRAC D-FUNCTION; RELATION OF THE D-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
453 LAPLACE TRANSFORMS OF DERIVATIVES AND INTEGRALS; OTHER PROPERTIES OF
LAPLACE TRANSFORMS 13.3 CONCLUDING REMARKS 459 13.4 EXERCISES 460 13.5
HINTS AND ANSWERS 466 14 FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS 468
14.1 GENERAL FORM OF SOLUTION 469 14.2 FIRST-DEGREE FIRST-ORDER
EQUATIONS 470 SEPARABLE-VARIABLE EQUATIONS; EXACT EQUATIONS; INEXACT
EQUATIONS, INTEGRAT- ING FACTORS; LINEAR EQUATIONS; HOMOGENEOUS
EQUATIONS; ISOBARIC EQUATIONS; BERNOULLI'S EQUATION; MISCELLANEOUS
EQUATIONS 14.3 HIGHER-DEGREE FIRST-ORDER EQUATIONS 480 EQUATIONS SOLUBLE
FOR P; FOR X; FOR Y; CLAIRAUT'S EQUATION HA EXERCISES 484 14.5 HINTS AND
ANSWERS 488 15 HIGHER-ORDER ORDINARY DIFFERENTIAL EQUATIONS 490 15.1
LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS 492 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 15.2 LINEAR EQUATIONS WITH VARIABLE
COEFFICIENTS 503 THE LEGENDRE AND EULER LINEAR EQUATIONS; EXACT
EQUATIONS; PARTIALLY KNOWN COMPLEMENTARY FUNCTION; VARIATION OF
PARAMETERS; GREEN'S FUNCTIONS; CANONICAL FORM FOR SECOND-ORDER EQUATIONS
CONTENTS 15.3 GENERAL ORDINARY DIFFERENTIAL EQUATIONS 518 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 523
15.5 HINTS AND ANSWERS 529 16 SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL
EQUATIONS 531 16.1 SECOND-ORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS
531 ORDINARY AND SINGULAR POINTS 16.2 SERIES SOLUTIONS ABOUT AN ORDINARY
POINT 535 16.3 SERIES SOLUTIONS ABOUT A REGULAR SINGULAR POINT 538
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 544 THE WRONSKIAN METHOD; THE DERIVATIVE METHOD;
SERIES FORM OF THE SECOND SOLUTION 16.5 POLYNOMIAL SOLUTIONS 548 16.6
EXERCISES 550 16.7 HINTS AND ANSWERS 553 17 EIGENFUNCTION METHODS FOR
DIFFERENTIAL EQUATIONS 554 17.1 SETS OF FUNCTIONS 556 SOME USEFUL
INEQUALITIES 17.2 ADJOINT, SELF-ADJOINT AND HERMITIAN OPERATORS 559 17.3
PROPERTIES OF HERMITIAN OPERATORS 561 REALITY OF THE EIGENVALUES;
ORTHOGONALITY OF THE EIGENFUNCTIONS; CONSTRUCTION OF REAL EIGENFUNCTIONS
17.4 STURM-LIOUVILLE EQUATIONS 564 VALID BOUNDARY CONDITIONS; PUTTING AN
EQUATION INTO STURM-LIOUVILLE FORM 17.5 SUPERPOSITION OF EIGENFUNCTIONS:
GREEN'S FUNCTIONS 569 17.6 A USEFUL GENERALISATION 572 17.7 EXERCISES
573 17.8 HINTS AND ANSWERS 576 18 SPECIAL FUNCTIONS 577 18.1 LEGENDRE
FUNCTIONS 577 GENERAL SOLUTION FOR INTEGER F; PROPERTIES OF LEGENDRE
POLYNOMIALS 18.2 ASSOCIATED LEGENDRE FUNCTIONS 587 18.3 SPHERICAL
HARMONICS 593 18.4 CHEBYSHEV FUNCTIONS 595 18.5 BESSEL FUNCTIONS 602
GENERAL SOLUTION FOR NON-INTEGER V; GENERAL SOLUTION FOR INTEGER V;
PROPERTIES OF BESSEL FUNCTIONS CONTENTS 18.6 SPHERICAL BESSEL FUNCTIONS
614 18.7 LAGUERRE FUNCTIONS 616 18.8 ASSOCIATED LAGUERRE FUNCTIONS 621
18.9 HERMITE FUNCTIONS 624 18.10 HYPERGEOMETRIC FUNCTIONS 628 18.11
CONFLUENT HYPERGEOMETRIC FUNCTIONS 633 18.12 THE GAMMA FUNCTION AND
RELATED FUNCTIONS 635 18.13 EXERCISES 640 18.14 HINTS AND ANSWERS 646 19
QUANTUM OPERATORS 648 19.1 OPERATOR FORMALISM 648 COMMUTATORS 19.2
PHYSICAL EXAMPLES OF OPERATORS 656 UNCERTAINTY PRINCIPLE; ANGULAR
MOMENTUM; CREATION AND ANNIHILATION OPERATORS 19.3 EXERCISES 671 19.4
HINTS AND ANSWERS 674 20 PARTIAL DIFFERENTIAL EQUATIONS: GENERAL AND
PARTICULAR SOLUTIONS 675 20.1 IMPORTANT PARTIAL DIFFERENTIAL EQUATIONS
676 THE WAVE EQUATION; THE DIFFUSION EQUATION; LAPLACE'S EQUATION;
POISSON'S EQUATION; SCHRODINGER'S EQUATION 20.2 GENERAL FORM OF SOLUTION
680 20.3 GENERAL AND PARTICULAR SOLUTIONS 681 FIRST-ORDER EQUATIONS;
INHOMOGENEOUS EQUATIONS AND PROBLEMS; SECOND-ORDER EQUATIONS 20.4 THE
WAVE EQUATION 693 20.5 THE DIFFUSION EQUATION 695 20.6 CHARACTERISTICS
AND THE EXISTENCE OF SOLUTIONS 699 FIRST-ORDER EQUATIONS; SECOND-ORDER
EQUATIONS 20.7 UNIQUENESS OF SOLUTIONS 705 20.8 EXERCISES 707 20.9 HINTS
AND ANSWERS 711 21 PARTIAL DIFFERENTIAL EQUATIONS: SEPARATION OF
VARIABLES AND OTHER METHODS 713 21.1 SEPARATION OF VARIABLES: THE
GENERAL METHOD 713 21.2 SUPERPOSITION OF SEPARATED SOLUTIONS 717 21.3
SEPARATION OF VARIABLES IN POLAR COORDINATES 725 LAPLACE'S EQUATION IN
POLAR COORDINATES; SPHERICAL HARMONICS; OTHER EQUATIONS IN POLAR
COORDINATES; SOLUTION BY EXPANSION; SEPARATION OF VARIABLES FOR
INHOMOGENEOUS EQUATIONS 21A INTEGRAL TRANSFORM METHODS 747 XII CONTENTS
21.5 INHOMOGENEOUS PROBLEMS - GREEN'S FUNCTIONS 751 SIMILARITIES TO
GREEN'S FUNCTIONS FOR ORDINARY DIFFERENTIAL EQUATIONS; GENERAL
BOUNDARY-VALUE PROBLEMS; DIRICHLET PROBLEMS; NEUMANN PROBLEMS 21.6
EXERCISES 767 21.7 HINTS AND ANSWERS 773 22 CALCULUS OF VARIATIONS 775
22.1 THE EULER-LAGRANGE EQUATION 776 22.2 SPECIAL CASES 777 F DOES NOT
CONTAIN Y EXPLICITLY; F DOES NOT CONTAIN X EXPLICITLY 22.3 SOME
EXTENSIONS 781 SEVERAL DEPENDENT VARIABLES; SEVERAL INDEPENDENT
VARIABLES; HIGHER-ORDER DERIVATIVES; VARIABLE END-POINTS 22.4
CONSTRAINED VARIATION 785 22.5 PHYSICAL VARIATIONAL PRINCIPLES 787
FERMAT'S PRINCIPLE IN OPTICS; HAMILTON'S PRINCIPLE IN MECHANICS 22.6
GENERAL EIGENVALUE PROBLEMS 790 22.7 ESTIMATION OF EIGENVALUES AND
EIGENFUNCTIONS 792 22.8 ADJUSTMENT OF PARAMETERS 795 22.9 EXERCISES 797
22.10 HINTS AND ANSWERS 801 23 INTEGRAL EQUATIONS 803 23.1 OBTAINING AN
INTEGRAL EQUATION FROM A DIFFERENTIAL EQUATION 803 23.2 TYPES OF
INTEGRAL EQUATION 804 23.3 OPERATOR NOTATION AND THE EXISTENCE OF
SOLUTIONS 805 23.4 CLOSED-FORM SOLUTIONS 806 SEPARABLE KERNELS; INTEGRAL
TRANSFORM METHODS; DIFFERENTIATION 23.5 NEUMANN SERIES 813 23.6 FREDHOLM
THEORY 815 23.7 SCHMIDT-HILBERT THEORY 816 23.8 EXERCISES 819 23.9 HINTS
AND ANSWERS 823 24 COMPLEX VARIABLES 824 24.1 FUNCTIONS OF A COMPLEX
VARIABLE 825 24.2 THE CAUCHY-RIEMANN RELATIONS 827 24.3 POWER SERIES IN
A COMPLEX VARIABLE 830 24.4 SOME ELEMENTARY FUNCTIONS 832 24.5
MULTIVALUED FUNCTIONS AND BRANCH CUTS 835 24.6 SINGULARITIES AND ZEROS
OF COMPLEX FUNCTIONS 837 24.7 CONFORMAL TRANSFORMATIONS 839 24.8 COMPLEX
INTEGRALS 845 CONTENTS 24.9 CAUCHY'S THEOREM 849 24.10 CAUCHY'S INTEGRAL
FORMULA 851 24.11 TAYLOR AND LAURENT SERIES 853 24.12 RESIDUE THEOREM
858 24.13 DEFINITE INTEGRALS USING CONTOUR INTEGRATION 861 24.14
EXERCISES 867 24.15 HINTS AND ANSWERS 870 25 APPLICATIONS OF COMPLEX
VARIABLES 871 25.1 COMPLEX POTENTIALS 871 25.2 APPLICATIONS OF CONFORMAL
TRANSFORMATIONS 876 25.3 LOCATION OF ZEROS 879 25.4 SUMMATION OF SERIES
882 25.5 INVERSE LAPLACE TRANSFORM 884 25.6 STOKES' EQUATION AND AIRY
INTEGRALS 888 25.7 WKB METHODS 895 25.8 APPROXIMATIONS TO INTEGRALS 905
LEVEL LINES AND SADDLE POINTS; STEEPEST DESCENTS; STATIONARY PHASE 25.9
EXERCISES 920 25.10 HINTS AND ANSWERS 925 26 TENSORS 927 26.1 SOME
NOTATION 928 26.2 CHANGE OF BASIS 929 26.3 CARTESIAN TENSORS 930 26.4
FIRST- AND ZERO-ORDER CARTESIAN TENSORS 932 26.5 SECOND- AND
HIGHER-ORDER CARTESIAN TENSORS 935 26.6 THE ALGEBRA OF TENSORS 938 26.7
THE QUOTIENT LAW 939 26.8 THE TENSORS 5,-Y AND E,^ 941 26.9 ISOTROPIC
TENSORS 944 26.10 IMPROPER ROTATIONS AND PSEUDOTENSORS 946 26.11 DUAL
TENSORS 949 26.12 PHYSICAL APPLICATIONS OF TENSORS 950 26.13 INTEGRAL
THEOREMS FOR TENSORS 954 26.14 NON-CARTESIAN COORDINATES 955 26.15 THE
METRIC TENSOR 957 26.16 GENERAL COORDINATE TRANSFORMATIONS AND TENSORS
960 26.17 RELATIVE TENSORS 963 26.18 DERIVATIVES OF BASIS VECTORS AND
CHRISTOFFEL SYMBOLS 965 26.19 COVARIANT DIFFERENTIATION 968 26.20 VECTOR
OPERATORS IN TENSOR FORM 971 CONTENTS 26.21 ABSOLUTE DERIVATIVES ALONG
CURVES 975 26.22 GEODESIES 976 26.23 EXERCISES 977 26.24 HINTS AND
ANSWERS 982 27 NUMERICAL METHODS 984 27.1 ALGEBRAIC AND TRANSCENDENTAL
EQUATIONS 985 REARRANGEMENT OF THE EQUATION; LINEAR INTERPOLATION;
BINARY CHOPPING; NEWTON-RAPHSON METHOD 27.2 CONVERGENCE OF ITERATION
SCHEMES 992 27.3 SIMULTANEOUS LINEAR EQUATIONS 994 GAUSSIAN ELIMINATION;
GAUSS-SEIDEL ITERATION; TRIDIAGONAL MATRICES 21A NUMERICAL INTEGRATION
1000 TRAPEZIUM RULE; SIMPSON'S RULE; GAUSSIAN INTEGRATION; MONTE CARLO
METHODS 27.5 FINITE DIFFERENCES 1019 27.6 DIFFERENTIAL EQUATIONS 1020
DIFFERENCE EQUATIONS; TAYLOR SERIES SOLUTIONS; PREDICTION AND
CORRECTION; RUNGE-KUTTA METHODS; ISOCLINES 27.7 HIGHER-ORDER EQUATIONS
1028 27.8 PARTIAL DIFFERENTIAL EQUATIONS 1030 27.9 EXERCISES 1033 27.10
HINTS AND ANSWERS 1039 28 GROUP THEORY 1041 28.1 GROUPS 1041 DEFINITION
OF A GROUP; EXAMPLES OF GROUPS 28.2 FINITE GROUPS 1049 28.3 NON-ABELIAN
GROUPS 1052 28.4 PERMUTATION GROUPS 1056 28.5 MAPPINGS BETWEEN GROUPS
1059 28.6 SUBGROUPS 1061 28.7 SUBDIVIDING A GROUP 1063 EQUIVALENCE
RELATIONS AND CLASSES; CONGRUENCE AND COSETS; CONJUGATES AND CLASSES
28.8 EXERCISES 1070 28.9 HINTS AND ANSWERS 1074 29 REPRESENTATION THEORY
1076 29.1 DIPOLE MOMENTS OF MOLECULES 1077 29.2 CHOOSING AN APPROPRIATE
FORMALISM 1078 29.3 EQUIVALENT REPRESENTATIONS 1084 29.4 REDUCIBILITY OF
A REPRESENTATION 1086 29.5 THE ORTHOGONALITY THEOREM FOR IRREDUCIBLE
REPRESENTATIONS 1090 CONTENTS 29.6 CHARACTERS 1092 ORTHOGONALITY
PROPERTY OF CHARACTERS 29.7 COUNTING IRREPS USING CHARACTERS 1095
SUMMATION RULES FOR IRREPS 29.8 CONSTRUCTION OF A CHARACTER TABLE 1100
29.9 GROUP NOMENCLATURE 1102 29.10 PRODUCT REPRESENTATIONS 1103 29.11
PHYSICAL APPLICATIONS OF GROUP THEORY 1105 BONDING IN MOLECULES; MATRIX
ELEMENTS IN QUANTUM MECHANICS; DEGENERACY OF NORMALSNODES; BREAKING OF
DEGENERACIES 29.12 EXERCISES 1113 29.13 HINTS AND ANSWERS 1117 30
PROBABILITY 1119 30.1 VENN DIAGRAMS 1119 30.2 PROBABILITY 1124 AXIOMS
AND THEOREMS; CONDITIONAL PROBABILITY; BAYES' THEOREM 30.3 PERMUTATIONS
AND COMBINATIONS 1133 30.4 RANDOM VARIABLES AND DISTRIBUTIONS 1139
DISCRETE RANDOM VARIABLES; CONTINUOUS RANDOM VARIABLES 30.5 PROPERTIES
OF DISTRIBUTIONS 1143 MEAN; MODE AND MEDIAN; VARIANCE AND STANDARD
DEVIATION; MOMENTS; CENTRAL MOMENTS 30.6 FUNCTIONS OF RANDOM VARIABLES
1150 30.7 GENERATING FUNCTIONS 1157 PROBABILITY GENERATING FUNCTIONS;
MOMENT GENERATING FUNCTIONS; CHARACTERISTIC FUNCTIONS; CUMULANT
GENERATING FUNCTIONS 30.8 IMPORTANT DISCRETE DISTRIBUTIONS 1168
BINOMIAL; GEOMETRIC; NEGATIVE BINOMIAL; HYPERGEOMETRIC; POISSON 30.9
IMPORTANT CONTINUOUS DISTRIBUTIONS 1179 GAUSSIAN; LOG-NORMAL;
EXPONENTIAL; GAMMA; CHI-SQUARED; CAUCHY; BREIT- WIGNER; UNIFORM 30.10
THE CENTRAL LIMIT THEOREM 1195 30.11 JOINT DISTRIBUTIONS 1196 DISCRETE
BIVARIATE; CONTINUOUS BIVARIATE; MARGINAL AND CONDITIONAL DISTRIBUTIONS
30.12 PROPERTIES OF JOINT DISTRIBUTIONS 1199 MEANS; VARIANCES;
COVARIANCE AND CORRELATION 30.13 GENERATING FUNCTIONS FOR JOINT
DISTRIBUTIONS 1205 30.14 TRANSFORMATION OF VARIABLES IN JOINT
DISTRIBUTIONS 1206 30.15 IMPORTANT JOINT DISTRIBUTIONS 1207
MULTINOMINAL; MULTIVARIATE GAUSSIAN 30.16 EXERCISES 1211 30.17 HINTS AND
ANSWERS 1219 CONTENTS 31 STATISTICS 1221 31.1 EXPERIMENTS, SAMPLES AND
POPULATIONS 1221 31.2 SAMPLE STATISTICS 1222 AVERAGES; VARIANCE AND
STANDARD DEVIATION; MOMENTS; COVARIANCE AND CORRELA- TION 31.3
ESTIMATORS AND SAMPLING DISTRIBUTIONS 1229 CONSISTENCY, BIAS AND
EFFICIENCY; FISHER'S INEQUALITY; STANDARD ERRORS; CONFI- DENCE LIMITS
31.4 SOME BASIC ESTIMATORS 1243 MEAN; VARIANCE; STANDARD DEVIATION;
MOMENTS; COVARIANCE AND CORRELATION 31.5 MAXIMUM-LIKELIHOOD METHOD 1255
ML ESTIMATOR; TRANSFORMATION INVARIANCE AND BIAS; EFFICIENCY; ERRORS AND
CONFIDENCE LIMITS; BAYESIAN INTERPRETATION; LARGE-N BEHAVIOUR; EXTENDED
ML METHOD 31.6 THE METHOD OF LEAST SQUARES 1271 LINEAR LEAST SQUARES;
NON-LINEAR LEAST SQUARES 31.7 HYPOTHESIS TESTING 1277 SIMPLE AND
COMPOSITE HYPOTHESES; STATISTICAL TESTS; NEYMAN-PEARSON; GENER- ALISED
LIKELIHOOD-RATIO; STUDENT'S T; FISHER'S F; GOODNESS OF FIT 31.8
EXERCISES 1298 31.9 HINTS AND ANSWERS 1303 INDEX 1305 XVN |
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| any_adam_object_boolean | 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 | BV021510863 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 QA401 |
| callnumber-search | QA300 QA401 |
| callnumber-sort | QA 3300 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SK 950 |
| classification_tum | MAT 021f |
| ctrlnum | (OCoLC)62532900 (DE-599)BVBBV021510863 |
| dewey-full | 515.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.1 |
| dewey-search | 515.1 |
| dewey-sort | 3515.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV021510863 |
| illustrated | Illustrated |
| index_date | 2024-07-02T14:18:46Z |
| indexdate | 2024-09-13T08:00:51Z |
| institution | BVB |
| isbn | 9780521861533 0521861535 9780521679718 0521679710 |
| language | English |
| lccn | 2006280779 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014727489 |
| oclc_num | 62532900 |
| open_access_boolean | |
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| physical | XXVII, 1333 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Riley, Kenneth F. 1936- Verfasser (DE-588)123286387 aut Mathematical methods for physics and engineering K. F. Riley ; M. P. Hobson and S. J. Bence 3. ed. Cambridge [u.a.] Cambridge Univ. Press 2006 XXVII, 1333 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Analyse mathématique Mathématiques de l'ingénieur Physique mathématique Mathematische Physik Engineering mathematics Mathematical analysis Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 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 Ergänzung Riley, Kenneth Franklin Student solutions manual for Mathematical methods for physics and engineering (DE-604)BV021667241 text/html http://www.loc.gov/catdir/enhancements/fy0665/2006280779-t.html Inhaltsverzeichnis text/html http://www.loc.gov/catdir/enhancements/fy0665/2006280779-d.html Beschreibung für Leser text/html 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=014727489&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 Analyse mathématique Mathématiques de l'ingénieur Physique mathématique Mathematische Physik Engineering mathematics Mathematical analysis Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4045956-1 (DE-588)4155620-3 (DE-588)4137304-2 (DE-588)4142443-8 |
| title | Mathematical methods for physics and engineering |
| title_auth | Mathematical methods for physics and engineering |
| title_exact_search | Mathematical methods for physics and engineering |
| title_exact_search_txtP | Mathematical methods for physics and engineering |
| title_full | Mathematical methods for physics and engineering K. F. Riley ; M. P. Hobson and S. J. Bence |
| title_fullStr | Mathematical methods for physics and engineering K. F. Riley ; M. P. Hobson and S. J. Bence |
| title_full_unstemmed | Mathematical methods for physics and engineering 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 |
| topic | Analyse mathématique Mathématiques de l'ingénieur Physique mathématique Mathematische Physik Engineering mathematics Mathematical analysis Mathematical physics Mathematische Physik (DE-588)4037952-8 gnd Physik (DE-588)4045956-1 gnd Mathematische Methode (DE-588)4155620-3 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Analyse mathématique Mathématiques de l'ingénieur Physique mathématique Mathematische Physik Engineering mathematics Mathematical analysis Mathematical physics Physik Mathematische Methode Ingenieurwissenschaften Angewandte Mathematik |
| url | http://www.loc.gov/catdir/enhancements/fy0665/2006280779-t.html http://www.loc.gov/catdir/enhancements/fy0665/2006280779-d.html 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=014727489&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT rileykennethf mathematicalmethodsforphysicsandengineering AT hobsonmichaelp mathematicalmethodsforphysicsandengineering AT bencestephenj mathematicalmethodsforphysicsandengineering |
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