Mathematics for chemistry and physics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Diego
Academic Press
2002
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | xiv, 408 p. ill. : 24 cm |
| ISBN: | 0127050515 |
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Datensatz im Suchindex
| _version_ | 1804129302713729024 |
|---|---|
| adam_text | MATHEMATICS FOR CHEMISTRY AND PHYSICS GEORGE TURRELL UNIVERSITY OF
SCIENCE AND TECHNOLOGY, LILLE, FRANCE ACADEMIC PRESS AN ELSEVIER SCIENCE
IMPRINT SAN DIEGO SAN FRANCISCO NEW YORK BOSTON LONDON SYDNEY TOKYO
PREFACE XIII 1 VARIABLES AND FUNCTIONS 1 1.1 INTRODUCTION 1 1.2
FUNCTIONS 2 1.3 CLASSIFICATION AND PROPERTIES OF FUNCTIONS 6 1.4
EXPONENTIAL AND LOGARITHMIC FUNCTIONS 7 1.5 APPLICATIONS OF EXPONENTIAL
AND LOGARITHMIC FUNCTIONS 10 1.6 COMPLEX NUMBERS 12 1.7 CIRCULAR
TRIGONOMETRIC FUNCTIONS 14 1.8 HYPERBOLIC FUNCTIONS 16 PROBLEMS 17 2
LIMITS, DERIVATIVES AND SERIES 19 2.1 DEFINITION OF A LIMIT 19 2.2
CONTINUITY 21 2.3 THE DERIVATIVE 22 2.4 HIGHER DERIVATIVES 24 2.5
IMPLICIT AND PARAMETRIC RELATIONS 25 2.6 THE EXTREMA OF A FUNCTION AND
ITS CRITICAL POINTS 26 2.7 THE DIFFERENTIAL 28 2.8 THE MEAN-VALUE
THEOREM AND L HOSPITAL S RULE 30 2.9 TAYLOR S SERIES 32 2.10 BINOMIAL
EXPANSION 34 2.11 TESTS OF SERIES CONVERGENCE 35 2.12 FUNCTIONS OF
SEVERAL VARIABLES 37 2.13 EXACT DIFFERENTIALS 38 PROBLEMS 39 VI CONTENTS
3 INTEGRATION 43 3.1 THE INDEFINITE INTEGRAL 43 3.2 INTEGRATION FORMULAS
44 3.3 METHODS OF INTEGRATION 45 3.3.1 INTEGRATION BY SUBSTITUTION 45
3.3.2 INTEGRATION BY PARTS 46 3.3.3 INTEGRATION OF PARTIAL FRACTIONS 47
3.4 DEFINITE INTEGRALS 49 3.4.1 DEFINITION 49 3.4.2 PLANE AREA 50 3.4.3
LINE INTEGRALS 51 3.4.4 FIDO AND HIS MASTER 52 3.4.5 THE GAUSSIAN AND
ITS MOMENTS 54 3.5 INTEGRATING FACTORS 56 3.6 TABLES OF INTEGRALS 59
PROBLEMS 60 4 VECTOR ANALYSIS 63 4.1 INTRODUCTION 63 4.2 VECTOR ADDITION
64 4.3 SCALAR PRODUCT 66 4.4 VECTOR PRODUCT 67 4.5 TRIPLE PRODUCTS 69
4.6 RECIPROCAL BASES 71 4.7 DIFFERENTIATION OF VECTORS 72 4.8 SCALAR AND
VECTOR FIELDS 73 4.9 THE GRADIENT 74 4.10 THE DIVERGENCE 75 4.11 THE
CURL OR ROTATION 75 4.12 THE LAPLACIAN 76 4.13 MAXWELL S EQUATIONS 77
4.14 LINE INTEGRALS 80 4.15 CURVILINEAR COORDINATES 81 PROBLEMS 83 5
ORDINARY DIFFERENTIAL EQUATIONS 85 5.1 FIRST-ORDER DIFFERENTIAL
EQUATIONS 85 5.2 SECOND-ORDER DIFFERENTIAL EQUATIONS 87 5.2.1 SERIES
SOLUTION 87 CONTENTS VII 5.2.2 THE CLASSICAL HARMONIC OSCILLATOR 89
5.2.3 THE DAMPED OSCILLATOR 91 5.3 THE DIFFERENTIAL OPERATOR 93 5.3.1
HARMONIC OSCILLATOR 93 5.3.2 INHOMOGENEOUS EQUATIONS 94 5.3.3 FORCED
VIBRATIONS 95 5:4 APPLICATIONS IN QUANTUM MECHANICS 96 5.4.1 THE
PARTICLE IN A BOX 96 5.4.2 SYMMETRIC BOX 99 5.4.3 RECTANGULAR BARRIER:
THE TUNNEL EFFECT 100 5.4.4 THE HARMONIC OSCILLATOR IN QUANTUM MECHANICS
102 5.5 SPECIAL FUNCTIONS 104 5.5.1 HERMITE POLYNOMIALS 104 5.5.2
ASSOCIATED LEGENDRE POLYNOMIALS 107 5.5.3 THE ASSOCIATED LAGUERRE
POLYNOMIALS ILL 5.5.4 THE GAMMA FUNCTION 112 5.5.5 BESSEL FUNCTIONS 113
5.5.6 MATHIEU FUNCTIONS 114 5.5.7 THE HYPERGEOMETRIC FUNCTIONS 115
PROBLEMS 116 6 PARTIAL DIFFERENTIAL EQUATIONS 119 6.1 THE VIBRATING
STRING 119 6.1.1 THE WAVE EQUATION 119 6.1.2 SEPARATION OF VARIABLES 120
6.1.3 BOUNDARY CONDITIONS 121 6.1.4 INITIAL CONDITIONS 123 6.2 THE
THREE-DIMENSIONAL HARMONIC OSCILLATOR 125 6.2.1 QUANTUM-MECHANICAL
APPLICATIONS 125 6.2.2 DEGENERACY 127 6.3 THE TWO-BODY PROBLEM 129 6.3.1
CLASSICAL MECHANICS 129 6.3.2 QUANTUM MECHANICS 130 6.4 CENTRAL FORCES
132 6.4.1 SPHERICAL COORDINATES -. 132 6.4.2 SPHERICAL HARMONICS 134 6.5
THE DIATOMIC MOLECULE 135 6.5.1 THE RIGID ROTATOR 136 VIII CONTENTS
6.5.2 THE VIBRATING ROTATOR 136 6.5.3 CENTRIFUGAL FORCES 137 6.6 THE
HYDROGEN ATOM 138 6.6.1 ENERGY 139 6.6.2 WAVEFUNCTIONS AND THE
PROBABILITY DENSITY .... 140 6.7 BINARY COLLISIONS 142 6.7.1
CONSERVATION OF ANGULAR MOMENTUM 142 6.7.2 CONSERVATION OF ENERGY 143
6.7.3 INTERACTION POTENTIAL: LJ (6-12) 143 6.7.4 ANGLE OF DEFLECTION 145
6.7.5 QUANTUM MECHANICAL DESCRIPTION: THE PHASE SHIFT 146 PROBLEMS 147 7
OPERATORS AND MATRICES 149 7.1 THE ALGEBRA OF OPERATORS 149 7.2
HERMITIAN OPERATORS AND THEIR EIGENVALUES 151 7.3 MATRICES 153 7.4 THE
DETERMINANT 157 7.5 PROPERTIES OF DETERMINANTS 158 7.6 JACOBIANS 159 7.7
VECTORS AND MATRICES 161 7.8 LINEAR EQUATIONS 163 7.9 PARTITIONING OF
MATRICES 163 7.10 MATRIX FORMULATION OF THE EIGENVALUE PROBLEM 164 7.11
COUPLED OSCILLATORS 166 7.12 GEOMETRIC OPERATIONS 170 7.13 THE MATRIX
METHOD IN QUANTUM MECHANICS 172 7.14 THE HARMONIC OSCILLATOR 175
PROBLEMS 177 8 GROUP THEORY 181 8.1 DEFINITION OF A GROUP 181 8.2
EXAMPLES 182 8.3 PERMUTATIONS 184 8.4 CONJUGATE ELEMENTS AND CLASSES 185
8.5 MOLECULAR SYMMETRY 187 8.6 THE CHARACTER 195 8.7 IRREDUCIBLE
REPRESENTATIONS 196 8.8 CHARACTER TABLES 198 CONTENTS IX 8.9 REDUCTION
OF A REPRESENTATION: THE MAGIC FORMULA 200 8.10 THE DIRECT PRODUCT
REPRESENTATION 202 8.11 SYMMETRY-ADAPTED FUNCTIONS: PROJECTION OPERATORS
. . . 204 8.12 HYBRIDIZATION OF ATOMIC ORBITALS 207 8.13 CRYSTAL
SYMMETRY 209 PROBLEMS 212 9 MOLECULAR MECHANICS 215 9.1 KINETIC ENERGY
215 9.2 MOLECULAR ROTATION 217 9.2.1 EULER S ANGLES 218 9.2.2
CLASSIFICATION OF ROTATORS 220 9.2.3 ANGULAR MOMENTA 221 9.2.4 THE
SYMMETRIC TOP IN QUANTUM MECHANICS .... 222 9.3 VIBRATIONAL ENERGY 224
9.3.1 KINETIC ENERGY 225 9.3.2 INTERNAL COORDINATES: THE G MATRIX 226
9.3.3 POTENTIAL ENERGY 227 9.3.4 NORMAL COORDINATES 227 9.3.5 SECULAR
DETERMINANT : 228 9.3.6 AN EXAMPLE: THE WATER MOLECULE 229 9.3.7
SYMMETRY COORDINATES 231 9.3.8 APPLICATION TO MOLECULAR VIBRATIONS 233
9.3.9 FORM OF NORMAL MODES 234 9.4 NONRIGID MOLECULES 236 9.4.1
MOLECULAR INVERSION 236 9.4.2 INTERNAL ROTATION 238 9.4.3 MOLECULAR
CONFORMATION: THE MOLECULAR MECHANICS METHOD 240 PROBLEMS 242 10
PROBABILITY AND STATISTICS 245 10.1 PERMUTATIONS 245 10.2 COMBINATIONS
246 10.3 PROBABILITY , . . . 249 10.4 STIRLING S APPROXIMATION 251 10.5
STATISTICAL MECHANICS 253 10.6 THE LAGRANGE MULTIPLIERS 255 X CONTENTS
10.7 THE PARTITION FUNCTION 256 10.8 MOLECULAR ENERGIES 257 10.8.1
TRANSLATION 258 10.8.2 ROTATION 259 10.8.3 VIBRATION 261 10.9 QUANTUM
STATISTICS 262 10.9.1 THE INDISTINGUISHABILITY OF IDENTICAL PARTICLES
262 10.9.2 THE EXCLUSION PRINCIPLE 263 10.9.3 FERMI-DIRAC STATISTICS 264
10.9.4 BOSE-EINSTEIN STATISTICS 266 10.10 ORTHO- AND PARA-HYDROGEN 267
PROBLEMS 270 11 INTEGRAL TRANSFORMS 271 11.1 THE FOURIER TRANSFORM 271
11.1.1 CONVOLUTION 272 11.1.2 FOURIER TRANSFORM PAIRS 273 11.2 THE
LAPLACE TRANSFORM 279 11.2.1 EXAMPLES OF SIMPLE LAPLACE TRANSFORMS 279
11.2.2 THE TRANSFORM OF DERIVATIVES 281 11.2.3 SOLUTION OF DIFFERENTIAL
EQUATIONS 282 11.2.4 LAPLACE TRANSFORMS: CONVOLUTION AND INVERSION 283
11.2.5 GREEN S FUNCTIONS . . . 284 PROBLEMS 286 12 APPROXIMATION METHODS
IN QUANTUM MECHANICS 287 12.1 THE BORN-OPPENHEIMER APPROXIMATION 287
12.2 PERTURBATION THEORY: STATIONARY STATES 290 12.2.1 NONDEGENERATE
SYSTEMS 290 12.2.2 FIRST-ORDER APPROXIMATION 291 12.2.3 SECOND-ORDER
APPROXIMATION 293 12.2.4 THE ANHARMONIC OSCILLATOR 293 12.2.5 DEGENERATE
SYSTEMS 296 12.2.6 THE STARK EFFECT OF THE HYDROGEN ATOM 298 12.3
TIME-DEPENDENT PERTURBATIONS 300 12.3.1 THE SCHRODINGER EQUATION 300
12.3.2 INTERACTION OF LIGHT AND MATTER 301 CONTENTS * XI 12.3.3
SPECTROSCOPIC SELECTION RULES 305 12.4 THE VARIATION METHOD 308 12.4.1
THE VARIATION THEOREM 308 12.4.2 AN EXAMPLE: THE PARTICLE IN A BOX 309
12.4.3 LINEAR VARIATION FUNCTIONS 311 12.4.4 LINEAR COMBINATIONS OF
ATOMIC ORBITALS (LCAO) 312 12.4.5 THE HIICKEL APPROXIMATION 316 PROBLEMS
322 13 NUMERICAL ANALYSIS 325 13.1 ERRORS 325 13.1.1 THE GAUSSIAN
DISTRIBUTION 326 13.1.2 THE POISSON DISTRIBUTION 327 13.2 THE METHOD OF
LEAST SQUARES 328 13.3 POLYNOMIAL INTERPOLATION AND SMOOTHING 330 13.4
THE FOURIER TRANSFORM 334 13.4.1 THE DISCRETE FOURIER TRANSFORM (DFT)
334 13.4.2 THE FAST FOURIER TRANSFORM (FFT) 336 13.4.3 AN APPLICATION:
INTERPOLATION AND SMOOTHING 339 13.5 NUMERICAL INTEGRATION 341 13.5.1
THE TRAPEZOID RULE 342 13.5.2 SIMPSON S RULE 343 13.5.3 THE METHOD OF
ROMBERG 343 13.6 ZEROS OF FUNCTIONS 345 13.6.1 NEWTON S METHOD 345
13.6.2 THE BISECTION METHOD 346 13.6.3 THE ROOTS: AN EXAMPLE 346
PROBLEMS 347 APPENDICES I THE GREEK ALPHABET . 349 II DIMENSIONS AND
UNITS 351 III ATOMIC ORBITALS 355 IV RADIAL WAVEFUNCTIONS FOR
HYDROGENLIKE SPECIES 361 V THE LAPLACIAN OPERATOR IN SPHERICAL
COORDINATES 363 VI THE DIVERGENCE THEOREM . . . 367 VII DETERMINATION
OF THE MOLECULAR SYMMETRY GROUP 369 XII CONTENTS VIII CHARACTER TABLES
FOR SOME OF THE MORE COMMON POINT GROUPS 373 IX MATRIX ELEMENTS FOR THE
HARMONIC OSCILLATOR 385 X FURTHER READING 387 APPLIED MATHEMATICS 387
CHEMICAL PHYSICS 390 AUTHOR INDEX 393 SUBJECT INDEX 395
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| id | DE-604.BV014470625 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:02:59Z |
| institution | BVB |
| isbn | 0127050515 |
| language | English |
| lccn | 2001091916 |
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| owner_facet | DE-703 DE-526 DE-634 |
| physical | xiv, 408 p. ill. : 24 cm |
| publishDate | 2002 |
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| publisher | Academic Press |
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| spelling | Turrell, George Verfasser aut Mathematics for chemistry and physics George Turrell San Diego Academic Press 2002 xiv, 408 p. ill. : 24 cm txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Chimie - Mathématiques Physique mathématique Química (métodos matemáticos) larpcal Chemie Mathematik Mathematische Physik Chemistry Mathematics Mathematical physics Mathematics Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematische Chemie (DE-588)4246882-6 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 s DE-604 Mathematische Chemie (DE-588)4246882-6 s GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009878158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Turrell, George Mathematics for chemistry and physics Chimie - Mathématiques Physique mathématique Química (métodos matemáticos) larpcal Chemie Mathematik Mathematische Physik Chemistry Mathematics Mathematical physics Mathematics Mathematische Physik (DE-588)4037952-8 gnd Mathematische Chemie (DE-588)4246882-6 gnd |
| subject_GND | (DE-588)4037952-8 (DE-588)4246882-6 |
| title | Mathematics for chemistry and physics |
| title_auth | Mathematics for chemistry and physics |
| title_exact_search | Mathematics for chemistry and physics |
| title_full | Mathematics for chemistry and physics George Turrell |
| title_fullStr | Mathematics for chemistry and physics George Turrell |
| title_full_unstemmed | Mathematics for chemistry and physics George Turrell |
| title_short | Mathematics for chemistry and physics |
| title_sort | mathematics for chemistry and physics |
| topic | Chimie - Mathématiques Physique mathématique Química (métodos matemáticos) larpcal Chemie Mathematik Mathematische Physik Chemistry Mathematics Mathematical physics Mathematics Mathematische Physik (DE-588)4037952-8 gnd Mathematische Chemie (DE-588)4246882-6 gnd |
| topic_facet | Chimie - Mathématiques Physique mathématique Química (métodos matemáticos) Chemie Mathematik Mathematische Physik Chemistry Mathematics Mathematical physics Mathematics Mathematische Chemie |
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