Elsevier S & T

Mathematics for Chemistry & Physics

Turrell, George

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Table of contents
  • Cover
  • Contentsv
  • Prefacexiii
  • Chapter 1. Variables and Functions1
  • 1.1 Introduction1
  • 1.2 Functions2
  • 1.3 Classification and properties of functions6
  • 1.4 Exponential and logarithmic functions7
  • 1.5 Applications of exponential and logarithmic functions10
  • 1.6 Complex numbers12
  • 1.7 Circular trigonometric functions14
  • 1.8 Hyperbolic functions16
  • Problems17
  • Chapter 2. Limits, Derivatives and Series19
  • 2.1 Definition of a limit19
  • 2.2 Continuity21
  • 2.3 The derivative22
  • 2.4 Higher derivatives24
  • 2.5 Implicit and parametric relations25
  • 2.6 The extrema of a function and its critical points26
  • 2.7 The differential28
  • 2.8 The mean-value theorem and L’Hospital’s rule30
  • 2.9 Taylor’s series32
  • 2.10 Binomial expansion34
  • 2.11 Tests of series convergence35
  • 2.12 Functions of several variables37
  • 2.13 Exact differentials38
  • Problems39
  • Chapter 3. Integration43
  • 3.1 The indefinite integral43
  • 3.2 Integration formulas44
  • 3.3 Methods of integration45
  • 3.4 Definite integrals49
  • 3.5 Integrating factors56
  • 3.6 Tables of integrals59
  • Problems60
  • Chapter 4. Vector Analysis63
  • 4.1 Introduction63
  • 4.2 Vector addition64
  • 4.3 Scalar product66
  • 4.4 Vector product67
  • 4.5 Triple products69
  • 4.6 Reciprocal bases71
  • 4.7 Differentiation of vectors72
  • 4.8 Scalar and vector fields73
  • 4.9 The gradient74
  • 4.10 The divergence75
  • 4.11 The curl or rotation75
  • 4.12 The Laplacian76
  • 4.13 Maxwell’s equations77
  • 4.14 Line integrals80
  • 4.15 Curvilinear coordinates81
  • Problems83
  • Chapter 5. Ordinary Differential Equations85
  • 5.1 First-order differential equations85
  • 5.2 Second-order differential equations87
  • 5.3 The differential operator93
  • 5.4 Applications in quantum mechanics96
  • 5.5 Special functions104
  • Problems116
  • Chapter 6. Partial Differential Equations119
  • 6.1 The vibrating string119
  • 6.2 The three-dimensional harmonic oscillator125
  • 6.3 The two-body problem129
  • 6.4 Central forces132
  • 6.5 The diatomic molecule135
  • 6.6 The hydrogen atom138
  • 6.7 Binary collisions142
  • Problems147
  • Chapter 7. Operators and Matrices149
  • 7.1 The algebra of operators149
  • 7.2 Hermitian operators and their eigenvalues151
  • 7.3 Matrices153
  • 7.4 The determinant157
  • 7.5 Properties of determinants158
  • 7.6 Jacobians159
  • 7.7 Vectors and matrices161
  • 7.8 Linear equations163
  • 7.9 Partitioning of matrices163
  • 7.10 Matrix formulation of the eigenvalue problem164
  • 7.11 Coupled oscillators166
  • 7.12 Geometric operations170
  • 7.13 The matrix method in quantum mechanics172
  • 7.14 The harmonic oscillator175
  • Problems177
  • Chapter 8. Group Theory181
  • 8.1 Definition of a group181
  • 8.2 Examples182
  • 8.3 Permutations184
  • 8.4 Conjugate elements and classes185
  • 8.5 Molecular symmetry187
  • 8.6 The character195
  • 8.7 Irreducible representations196
  • 8.8 Character tables198
  • 8.9 Reduction of a representation: The magic formulaŽ200
  • 8.10 The direct product representation202
  • 8.11 Symmetry-adapted functions: Projection operators204
  • 8.12 Hybridization of atomic orbitals207
  • 8.13 Crystal symmetry209
  • Problems212
  • Chapter 9. Molecular Mechanics215
  • 9.1 Kinetic energy215
  • 9.2 Molecular rotation217
  • 9.3 Vibrational energy224
  • 9.4 Nonrigid molecules236
  • Problems242
  • Chapter 10. Probability and Statistics245
  • 10.1 Permutations245
  • 10.2 Combinations247
  • 10.3 Probability249
  • 10.4 Stirling’s approximation251
  • 10.5 Statistical mechanics253
  • 10.6 The Lagrange multipliers255
  • 10.7 The partition function256
  • 10.8 Molecular energies257
  • 10.9 Quantum statistics262
  • 10.10 Ortho- and para-hydrogen267
  • Problems270
  • Chapter 11. Integral Transforms271
  • 11.1 The Fourier transform271
  • 11.2 The Laplace transform279
  • Problems286
  • Chapter 12. Approximation Methods in Quantum Mechanics287
  • 12.1 The Born–Oppenheimer approximation287
  • 12.2 Perturbation theory: Stationary states290
  • 12.3 Time-dependent perturbations300
  • 12.4 The variation method308
  • Problems322
  • 13. Numerical Analysis325
  • 13.1 Errors325
  • 13.2 The method of least squares328
  • 13.3 Polynomial interpolation and smoothing330
  • 13.4 The Fourier transform334
  • 13.5 Numerical integration341
  • 13.6 Zeros of functions345
  • Problems347
  • Appendices349
  • I The Greek alphabet349
  • II Dimensions and units351
  • III Atomic orbitals355
  • IV Radial wavefunctions for hydrogenlike species361
  • V The Laplacian operator in spherical coordinates363
  • VI The divergence theorem367
  • VII Determination of the molecular symmetry group369
  • Appendix VIII: Character Tables for Some of the More Common Point Groups373
  • Appendix IX: Matrix Elements for the Harmonic Oscillator385
  • Appendix X: Further Reading387
  • Author Index393
  • Subject Index395
Book details
  • Vendor Elsevier S & T
  • SKU 9780127050515
  • ISBN-13 9780080511276
  • Author Turrell, George
  • Category Mathematics
  • Subject Applied

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Description eBook delivery & access Reviews
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.