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100 1  Goodson, David Z 
245 10 Mathematical Methods for Physical and Analytical Chemistry
250    1st ed 
264  1 Hoboken :|bJohn Wiley & Sons, Incorporated,|c2011 
264  4 |c©2011 
300    1 online resource (404 pages) 
336    text|btxt|2rdacontent 
337    computer|bc|2rdamedia 
338    online resource|bcr|2rdacarrier 
505 0  Intro -- 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 Freedom
       -- 3.4.2 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 
       Variable -- 6.5 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 
505 8  9.3 Monte Carlo Simulation of Error -- 9.4 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 Randomization -- 12.3 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 -- 15 Solving Differential 
       Equations, II -- 15.1 Numerical Solution -- 15.1.1 Basic 
       Algorithms -- 15.1.2 The Leapfrog Method -- 15.1.3 Systems
       of Differential Equations -- 15.2 Chemical Reaction 
       Mechanisms -- 15.3 Approximation Methods -- 15.3.1 Taylor 
       Series -- 15.3.2 Perturbation Theory -- Part IV. Linear 
       Algebra -- 16 Vector Spaces -- 16.1 Cartesian Coordinate 
       Vectors -- 16.2 Sets -- 16.3 Groups -- 16.4 Vector Spaces 
       -- 16.5 Functions as Vectors -- 16.6 Hilbert Spaces -- 
       16.7 Basis Sets -- 17 Spaces of Functions -- 17.1 
       Orthogonal Polynomials -- 17.2 Function Resolution -- 17.3
       Fourier Series -- 17.4 Spherical Harmonics 
505 8  18 Matrices -- 18.1 Matrix Representation of Operators -- 
       18.2 Matrix Algebra -- 18.3 Matrix Operations -- 18.4 
       Pseudoinverse -- 18.5 Determinants -- 18.6 Orthogonal and 
       Unitary Matrices -- 18.7 Simultaneous Linear Equations -- 
       19 Eigenvalue Equations -- 19.1 Matrix Eigenvalue 
       Equations -- 19.2 Matrix Diagonalization -- 19.3 
       Differential Eigenvalue Equations -- 19.4 Hermitian 
       Operators -- 19.5 The Variational Principle -- 20 
       Schrödinger's Equation -- 20.1 Quantum Mechanics -- 20.1.1
       Quantum Mechanical Operators -- 20.1.2 The Wavefunction --
       20.1.3 The Basic Postulates -- 20.2 Atoms and Molecules --
       20.3 The One-Electron Atom -- 20.3.1 Orbitals -- 20.3.2 
       The Radial Equation -- 20.4 Hybrid Orbitals -- 20.5 
       Antisymmetry -- 20.6 Molecular Orbitals -- 21 Fourier 
       Analysis -- 21.1 The Fourier Transform -- 21.2 Spectral 
       Line Shapes -- 21.3 Discrete Fourier Transform -- 21.4 
       Signal Processing -- 21.4.1 Noise Filtering -- 21.4.2 
       Convolution -- A Computer Programs -- A.1 Robust 
       Estimators -- A.2 FREML -- A.3 Nelder-Mead Simplex 
       Optimization -- B Answers to Selected Exercises -- C 
       Bibliography -- Index 
520    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.
       With numerous example problems and helpful anecdotes, this
       text gives chemistry students the mathematical knowledge 
       they need to understand the analytical and physical 
       chemistry professional literature 
588    Description based on publisher supplied metadata and other
       sources 
590    Electronic reproduction. Ann Arbor, Michigan : ProQuest 
       Ebook Central, 2020. Available via World Wide Web. Access 
       may be limited to ProQuest Ebook Central affiliated 
       libraries 
650  0 Mathematical physics.;Chemometrics 
655  4 Electronic books 
700 1  Goodson, David Z 
776 08 |iPrint version:|aGoodson, David Z.|tMathematical Methods 
       for Physical and Analytical Chemistry|dHoboken : John 
       Wiley & Sons, Incorporated,c2011|z9781118135204 
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