Front Cover -- Mathematics for Chemistry and Physics -- Copyright Page -- Contents -- Preface -- Chapter 1. Variables and Functions -- 1.1 Introduction -- 1.2 Functions -- 1.3 Classification and properties of functions -- 1.4 Exponential and logarithmic functions -- 1.5 Applications of exponential and logarithmic functions -- 1.6 Complex numbers -- 1.7 Circular trigonometric functions -- 1.8 Hyperbolic functions -- Problems -- Chapter 2. Limits, Derivatives and Series -- 2.1 Definition of a limit -- 2.2 Continuity -- 2.3 The derivative -- 2.4 Higher derivatives -- 2.5 Implicit and parametric relations -- 2.6 The extrema of a function and its critical points -- 2.7 The differential -- 2.8 The mean-value theorem and L'Hospital's rule -- 2.9 Taylor's series -- 2.10 Binomial expansion -- 2.11 Tests of series convergence -- 2.12 Functions of several variables -- 2.13 Exact differentials -- Problems -- Chapter 3. Integration -- 3.1 The indefinite integral -- 3.2 Integration formulas -- 3.3 Methods of integration -- 3.4 Definite integrals -- 3.5 Integrating factors -- 3.6 Tables of integrals -- Problems -- Chapter 4. Vector Analysis -- 4.1 Introduction -- 4.2 Vector addition -- 4.3 Scalar product -- 4.4 Vector product -- 4.5 Triple products -- 4.6 Reciprocal bases -- 4.7 Differentiation of vectors -- 4.8 Scalar and vector fields -- 4.9 The gradient -- 4.10 The divergence -- 4.11 The curl or rotation -- 4.12 The Laplacian -- 4.13 Maxwell's equations -- 4.14 Line integrals -- 4.15 Curvilinear coordinates -- Problems -- Chapter 5. Ordinary Differential Equations -- 5.1 First-order differential equations -- 5.2 Second-order differential equations -- 5.3 The differential operator -- 5.4 Applications in quantum mechanics -- 5.5 Special functions -- Problems -- Chapter 6. Partial Differential Equations -- 6.1 The vibrating string.

6.2 The three-dimensional harmonic oscillator -- 6.3 The two-body problem -- 6.4 Central forces -- 6.5 The diatomic molecule -- 6.6 The hydrogen atom -- 6.7 Binary collisions -- Problems -- Chapter 7. Operators and Matrices -- 7.1 The algebra of operators -- 7.2 Hermitian operators and their eigenvalues -- 7.3 Matrices -- 7.4 The determinant -- 7.5 Properties of determinants -- 7.6 Jacobians -- 7.7 Vectors and matrices -- 7.8 Linear equations -- 7.9 Partitioning of matrices -- 7.10 Matrix formulation of the eigenvalue problem -- 7.11 Coupled oscillators -- 7.12 Geometric operations -- 7.13 The matrix method in quantum mechanics -- 7.14 The harmonic oscillator -- Problems -- Chapter 8. Group Theory -- 8.1 Definition of a group -- 8.2 Examples -- 8.3 Permutations -- 8.4 Conjugate elements and classes -- 8.5 Molecular symmetry -- 8.6 The character -- 8.7 Irreducible representations -- 8.8 Character tables -- 8.9 Reduction of a representation: The "magic formula" -- 8.10 The direct product representation -- 8.11 Symmetry-adapted functions: Projection operators -- 8.12 Hybridization of atomic orbitals -- 8.13 Crystal symmetry -- Problems -- Chapter 9. Molecular Mechanics -- 9.1 Kinetic energy -- 9.2 Molecular rotation -- 9.3 Vibrational energy -- 9.4 Nonrigid molecules -- Problems -- Chapter 10. Probability and Statistics -- 10.1 Permutations -- 10.2 Combinations -- 10.3 Probability -- 10.4 Stirling's approximation -- 10.5 Statistical mechanics -- 10.6 The Lagrange multipliers -- 10.7 The partition function -- 10.8 Molecular energies -- 10.9 Quantum statistics -- 10.10 Ortho- and para-hydrogen -- Problems -- Chapter 11. Integral Transforms -- 11.1 The Fourier transform -- 11.2 The Laplace transform -- Problems -- Chapter 12. Approximation Methods in Quantum Mechanics -- 12.1 The Born-Oppenheimer approximation -- 12.2 Perturbation theory: Stationary states.

12.3 Time-dependent perturbations -- 12.4 The variation method -- Problems -- 13. Numerical Analysis -- 13.1 Errors -- 13.2 The method of least squares -- 13.3 Polynomial interpolation and smoothing -- 13.4 The Fourier transform -- 13.5 Numerical integration -- 13.6 Zeros of functions -- Problems -- Appendices -- I The Greek alphabet -- II Dimensions and units -- III Atomic orbitals -- IV Radial wavefunctions for hydrogenlike species -- V The Laplacian operator in spherical coordinates -- VI The divergence theorem -- VII Determination of the molecular symmetry group -- Appendix VIII: Character Tables for Some of the More Common Point Groups -- Appendix IX: Matrix Elements for the Harmonic Oscillator -- Appendix X: Further Reading -- Author Index -- Subject Index.