Mathematics for Chemistry and Physics (eBook)

George Turrell (Autor)

eBook Download: PDF

2001 | 1. Auflage
424 Seiten
Elsevier Science (Verlag)
978-0-08-051127-6 (ISBN)

Infos

Chemistry and physics share a common mathematical foundation. From elementary calculus to vector analysis and group theory, Mathematics for Chemistry and Physics aims to provide a comprehensive reference for students and researchers pursuing these scientific fields. The book is based on the authors many classroom experience.

Designed as a reference text, Mathematics for Chemistry and Physics will prove beneficial for students at all university levels in chemistry, physics, applied mathematics, and theoretical biology. Although this book is not computer-based, many references to current applications are included, providing the background to what goes on behind the screen in computer experiments.

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Chemistry and physics share a common mathematical foundation. From elementary calculus to vector analysis and group theory, Mathematics for Chemistry and Physics aims to provide a comprehensive reference for students and researchers pursuing these scientific fields. The book is based on the authors many classroom experience. Designed as a reference text, Mathematics for Chemistry and Physics will prove beneficial for students at all university levels in chemistry, physics, applied mathematics, and theoretical biology. Although this book is not computer-based, many references to current applications are included, providing the background to what goes on "e;behind the screen"e; in computer experiments.

Inhalt

Cover 1
Contents 6
Preface 14
Chapter 1. Variables and Functions 16
1.1 Introduction 16
1.2 Functions 17
1.3 Classification and properties of functions 21
1.4 Exponential and logarithmic functions 22
1.5 Applications of exponential and logarithmic functions 25
1.6 Complex numbers 27
1.7 Circular trigonometric functions 29
1.8 Hyperbolic functions 31
Problems 32
Chapter 2. Limits, Derivatives and Series 34
2.1 Definition of a limit 34
2.2 Continuity 36
2.3 The derivative 37
2.4 Higher derivatives 39
2.5 Implicit and parametric relations 40
2.6 The extrema of a function and its critical points 41
2.7 The differential 43
2.8 The mean-value theorem and L’Hospital’s rule 45
2.9 Taylor’s series 47
2.10 Binomial expansion 49
2.11 Tests of series convergence 50
2.12 Functions of several variables 52
2.13 Exact differentials 53
Problems 54
Chapter 3. Integration 58
3.1 The indefinite integral 58
3.2 Integration formulas 59
3.3 Methods of integration 60
3.4 Definite integrals 64
3.5 Integrating factors 71
3.6 Tables of integrals 74
Problems 75
Chapter 4. Vector Analysis 78
4.1 Introduction 78
4.2 Vector addition 79
4.3 Scalar product 81
4.4 Vector product 82
4.5 Triple products 84
4.6 Reciprocal bases 86
4.7 Differentiation of vectors 87
4.8 Scalar and vector fields 88
4.9 The gradient 89
4.10 The divergence 90
4.11 The curl or rotation 90
4.12 The Laplacian 91
4.13 Maxwell’s equations 92
4.14 Line integrals 95
4.15 Curvilinear coordinates 96
Problems 98
Chapter 5. Ordinary Differential Equations 100
5.1 First-order differential equations 100
5.2 Second-order differential equations 102
5.3 The differential operator 108
5.4 Applications in quantum mechanics 111
5.5 Special functions 119
Problems 131
Chapter 6. Partial Differential Equations 134
6.1 The vibrating string 134
6.2 The three-dimensional harmonic oscillator 140
6.3 The two-body problem 144
6.4 Central forces 147
6.5 The diatomic molecule 150
6.6 The hydrogen atom 153
6.7 Binary collisions 157
Problems 162
Chapter 7. Operators and Matrices 164
7.1 The algebra of operators 164
7.2 Hermitian operators and their eigenvalues 166
7.3 Matrices 168
7.4 The determinant 172
7.5 Properties of determinants 173
7.6 Jacobians 174
7.7 Vectors and matrices 176
7.8 Linear equations 178
7.9 Partitioning of matrices 178
7.10 Matrix formulation of the eigenvalue problem 179
7.11 Coupled oscillators 181
7.12 Geometric operations 185
7.13 The matrix method in quantum mechanics 187
7.14 The harmonic oscillator 190
Problems 192
Chapter 8. Group Theory 196
8.1 Definition of a group 196
8.2 Examples 197
8.3 Permutations 199
8.4 Conjugate elements and classes 200
8.5 Molecular symmetry 202
8.6 The character 210
8.7 Irreducible representations 211
8.8 Character tables 213
8.9 Reduction of a representation: The magic formulaŽ 215
8.10 The direct product representation 217
8.11 Symmetry-adapted functions: Projection operators 219
8.12 Hybridization of atomic orbitals 222
8.13 Crystal symmetry 224
Problems 227
Chapter 9. Molecular Mechanics 230
9.1 Kinetic energy 230
9.2 Molecular rotation 232
9.3 Vibrational energy 239
9.4 Nonrigid molecules 251
Problems 257
Chapter 10. Probability and Statistics 260
10.1 Permutations 260
10.2 Combinations 262
10.3 Probability 264
10.4 Stirling’s approximation 266
10.5 Statistical mechanics 268
10.6 The Lagrange multipliers 270
10.7 The partition function 271
10.8 Molecular energies 272
10.9 Quantum statistics 277
10.10 Ortho- and para-hydrogen 282
Problems 285
Chapter 11. Integral Transforms 286
11.1 The Fourier transform 286
11.2 The Laplace transform 294
Problems 301
Chapter 12. Approximation Methods in Quantum Mechanics 302
12.1 The Born–Oppenheimer approximation 302
12.2 Perturbation theory: Stationary states 305
12.3 Time-dependent perturbations 315
12.4 The variation method 323
Problems 337
13. Numerical Analysis 340
13.1 Errors 340
13.2 The method of least squares 343
13.3 Polynomial interpolation and smoothing 345
13.4 The Fourier transform 349
13.5 Numerical integration 356
13.6 Zeros of functions 360
Problems 362
Appendices 364
I The Greek alphabet 364
II Dimensions and units 366
III Atomic orbitals 370
IV Radial wavefunctions for hydrogenlike species 376
V The Laplacian operator in spherical coordinates 378
VI The divergence theorem 382
VII Determination of the molecular symmetry group 384
Appendix VIII: Character Tables for Some of the More Common Point Groups 388
Appendix IX: Matrix Elements for the Harmonic Oscillator 400
Appendix X: Further Reading 402
Author Index 408
Subject Index 410

Produkt-Details

• Erscheint lt. Verlag: 4.12.2001
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Algebra
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Naturwissenschaften ► Chemie ► Technische Chemie
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Umwelttechnik / Biotechnologie
• ISBN-10: 0-08-051127-9 / 0080511279
• ISBN-13: 978-0-08-051127-6 / 9780080511276