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Informationen zum Autor David Z. Goodson , Associate Professor of Chemistry at the University of Massachusetts Dartmouth, has a BA in chemistry from Pomona College and a PhD in chemical physics from Harvard University. An interdisciplinary scientist, he is author of numerous articles on a wide range of topics including quantum chemistry, molecular spectroscopy, reaction rate theory, atomic physics, and applied mathematics. Klappentext Bridging the gap between undergraduate calculus and the mathematics of chemistry A focused presentation of statistical and advanced mathematical methods likely to be encountered by chemists, Mathematical Methods for Physical and Analytical Chemistry can serve as a text for a one-semester course at the undergraduate or graduate level, or as a resource for independent study by students and professionals in all areas of chemistry and in related fields such as environmental science, geochemistry, and chemical engineering. Mathematical Methods for Physical and Analytical Chemistry covers: CALCULUS -review of the basics, coordinate systems, degrees of freedom, special functions, numerical methods, complex numbers, singular points, improper integrals, Taylor series STATISTICS -probability theory, distribution functions, confidence intervals, propagation of error, significance of difference, ANOVA, method of least squares, calibration, model testing, fits with error in both variables, experiment design, randomization, optimization DIFFERENTIAL EQUATIONS -chemical reaction rate equations, Lagrangian and Hamiltonian mechanics, transport equations, the superposition principle, separation of variables, methods for exact, approximate, and numerical solutions LINEAR ALGEBRA -groups, Hilbert spaces, basis sets, matrices, determinants, orthogonal polynomials, spherical harmonics, Fourier series, eigenvalue equations, diagonalization, Fourier transform, spectral lineshapes, convolution, principles of quantum mechanics, Schrödinger's equation, hydrogen orbitals, hybrid orbitals, molecular orbitals Mathematical Methods for Physical and Analytical Chemistry features: Modern topics such as Monte Carlo simulation, robust estimation, and discrete Fourier transform, which are otherwise available only in more specialized texts Numerous figures and worked out examples and more than 200 exercises, many of which take advantage of computer algebra An annotated bibliography of references for further study Zusammenfassung Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate! post-calculus level. Inhaltsverzeichnis Preface xiii List of Examples xv Greek Alphabet xix Part I. Calculus 1 Functions: General Properties 3 1.1 Mappings 3 1.2 Differentials and Derivatives 4 1.3 Partial Derivatives 7 1.4 Integrals 9 1.5 Critical Points 14 2 Functions: Examples 19 2.1 Algebraic Functions 19 2.2 Transcendental Functions 21 2.3 Functional 31 3 Coordinate Systems 33 3.1 Points in Space 33 3.2 Coordinate Systems for Molecules 35 3.3 Abstract Coordinates 37 3.4 Constraints 39 3.5 Differential Operators in Polar Coordinates 43 4 Integration 47 4.1 Change of Variables in Integrands 47 4.2 Gaussian Integrals 51 4.3 Improper Integrals 53 4.4 Dirac Delta Function 56 4.5 Line Integrals 57 5 Numerical Methods 61 5.1 Interpolation 61 5.2 Numerical Differentiation 63 5.3 Numerical Integration 65 5.4 Random Numbers 70 5.5 Root Finding 71 5.6 Minimization* 74 6 Complex Numbers 79 6.1 Complex Arithmet...
