Goodson, David Z. 1958- creator text bibliography Electronic books. Electronic books. nju Hoboken, N.J Wiley ©2011 2011 monographic eng

electronic resource

1 online resource (xix, 382 pages) : illustrations "Mathematical Methods for Physical and Analytical Chemistry presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton's method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations"-- Mathematical Methods for Physical and Analytical Chemistry; Contents; Preface; List of Examples; Greek Alphabet; Part I. Calculus; 1 Functions: General Properties; 1.1 Mappings; 1.2 Differentials and Derivatives; 1.3 Partial Derivatives; 1.4 Integrals; 1.5 Critical Points; 2 Functions: Examples; 2.1 Algebraic Functions; 2.2 Transcendental Functions; 2.2.1 Logarithm and Exponential; 2.2.2 Circular Functions; 2.2.3 Gamma and Beta Functions; 2.3 Functionals; 3 Coordinate Systems; 3.1 Points in Space; 3.2 Coordinate Systems for Molecules; 3.3 Abstract Coordinates; 3.4 Constraints. 3.4.1 Degrees of Freedom3.4.2 Constrained Extrema; 3.5 Differential Operators in Polar Coordinates; 4 Integration; 4.1 Change of Variables in Integrands; 4.1.1 Change of Variable: Examples; 4.1.2 Jacobian Determinant; 4.2 Gaussian Integrals; 4.3 Improper Integrals; 4.4 Dirac Delta Function; 4.5 Line Integrals; 5 Numerical Methods; 5.1 Interpolation; 5.2 Numerical Differentiation; 5.3 Numerical Integration; 5.4 Random Numbers; 5.5 Root Finding; 5.6 Minimization; 6 Complex Numbers; 6.1 Complex Arithmetic; 6.2 Fundamental Theorem of Algebra; 6.3 The Argand Diagram. 6.4 Functions of a Complex Variable6.5 Branch Cuts; 7 Extrapolation; 7.1 Taylor Series; 7.2 Partial Sums; 7.3 Applications of Taylor Series; 7.4 Convergence; 7.5 Summation Approximants; Part II. Statistics; 8 Estimation; 8.1 Error and Estimation; 8.2 Probability Distributions; 8.2.1 Probability Distribution Functions; 8.2.2 The Normal Distribution; 8.2.3 The Poisson Distribution; 8.2.4 The Binomial Distribution; 8.2.5 The Boltzmann Distribution; 8.3 Outliers; 8.4 Robust Estimation; 9 Analysis of Significance; 9.1 Confidence Intervals; 9.2 Propagation of Error. 9.3 Monte Carlo Simulation of Error9.4 Significance of Difference; 9.5 Distribution Testing; 10 Fitting; 10.1 Method of Least Squares; 10.1.1 Polynomial Fitting; 10.1.2 Weighted Least Squares; 10.1.3 Generalizations of the Least-Squares Method; 10.2 Fitting with Error in Both Variables; 10.2.1 Uncontrolled Error in x; 10.2.2 Controlled Error in x; 10.3 Nonlinear Fitting; 11 Quality of Fit; 11.1 Confidence Intervals for Parameters; 11.2 Confidence Band for a Calibration Line; 11.3 Outliers and Leverage Points; 11.4 Robust Fitting; 11.5 Model Testing; 12 Experiment Design; 12.1 Risk Assessment. 12.2 Randomization12.3 Multiple Comparisons; 12.3.1 ANOVA; 12.3.2 Post-Hoc Tests; 12.4 Optimization; Part III. Differential Equations; 13 Examples of Differential Equations; 13.1 Chemical Reaction Rates; 13.2 Classical Mechanics; 13.2.1 Newtonian Mechanics; 13.2.2 Lagrangian and Hamiltonian Mechanics; 13.2.3 Angular Momentum; 13.3 Differentials in Thermodynamics; 13.4 Transport Equations; 14 Solving Differential Equations, I; 14.1 Basic Concepts; 14.2 The Superposition Principle; 14.3 First-Order ODE's; 14.4 Higher-Order ODE's; 14.5 Partial Differential Equations. David Z. Goodson. Includes bibliographical references and index. Mathematical physics Chemometrics SCIENCE Energy SCIENCE Mechanics General SCIENCE Physics General Chemometrics Mathematical physics QC20 .G66 2011eb 530.15 9781118135204 1118135202 9781118135174 1118135172 1283337479 9781283337472 333747 MIL http://onlinelibrary.wiley.com/book/10.1002/9781118135204 http://onlinelibrary.wiley.com/book/10.1002/9781118135204 CDX 110622 20171116090542.0 ocn767949531 eng