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050 4 QC20 -- .G66 2011eb
082 0 541.0151
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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