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Mathematical Methods for Physical and Analytical Chemistry

ISBN-10: 0470473541
ISBN-13: 9780470473542
Edition: 2011
Authors: David Z. Goodson
List price: $165.95
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Description: This text 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  More...

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Book details

List price: $165.95
Copyright year: 2011
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/22/2011
Binding: Hardcover
Pages: 408
Size: 6.50" wide x 9.75" long x 1.00" tall
Weight: 1.540
Language: English

This text 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.

Preface
List of Examples
Greek Alphabet
Calculus
Functions: General Properties
Mappings
Differentials and Derivatives
Partial Derivatives
Integrals
Critical Points
Functions: Examples
Algebraic Functions
Transcendental Functions
Logarithm and Exponential
Circular Functions
Gamma and Beta Functions
Functionals
Coordinate Systems
Points in Space
Coordinate Systems for Molecules
Abstract Coordinates
Constraints
Degrees of Freedom
Constrained Extrema*
Differential Operators in Polar Coordinates
Integration
Change of Variables in Integrands
Change of Variable: Examples
Jacobian Determinant
Gaussian Integrals
Improper Integrals
Dirac Delta Function
Line Integrals
Numerical Methods
Interpolation
Numerical Differentiation
Numerical Integration
Random Numbers
Root Finding
Minimization*
Complex Numbers
Complex Arithmetic
Fundamental Theorem of Algebra
The Argand Diagram
Functions of a Complex Variable*
Branch Cuts*
Extrapolation
Taylor Series
Partial Sums
Applications of Taylor Series
Convergence
Summation Approximants*
Statistics
Estimation
Error and Estimation
Probability Distributions
Probability Distribution Functions
The Normal Distribution
The Poisson Distribution
The Binomial Distribution*
The Boltzmann Distribution*
Outliers
Robust Estimation
Analysis of Significance
Confidence Intervals
Propagation of Error
Monte Carlo Simulation of Error
Significance of Difference
Distribution Testing*
Fitting
Method of Least Squares
Polynomial Fitting
Weighted Least Squares
Generalizations of the Least-Squares Method*
Fitting with Error in Both Variables
Uncontrolled Error in x
Controlled Error in x
Nonlinear Fitting
Quality of Fit
Confidence Intervals for Parameters
Confidence Band for a Calibration Line
Outliers and Leverage Points
Robust Fitting*
Model Testing
Experiment Design
Risk Assessment
Randomization
Multiple Comparisons
ANOVA*
Post-Hoc Tests*
Optimization*
Differential Equations
Examples of Differential Equations
Chemical Reaction Rates
Classical Mechanics
Newtonian Mechanics
Lagrangian and Hamiltonian Mechanics
Angular Momentum
Differentials in Thermodynamics
Transport Equations
Solving Differential Equations, I
Basic Concepts
The Superposition Principle
First-Order ODE's
Higher-Order ODE's
Partial Differential Equations
Solving Differential Equations, II
Numerical Solution
Basic Algorithms
The Leapfrog Method*
Systems of Differential Equations
Chemical Reaction Mechanisms
Approximation Methods
Taylor Series*
Perturbation Theory*
Linear Algebra
Vector Spaces
Cartesian Coordinate Vectors
Sets
Groups
Vector Spaces
Functions as Vectors
Hilbert Spaces
Basis Sets
Spaces of Functions
Orthogonal Polynomials
Function Resolution
Fourier Series
Spherical Harmonics
Matrices
Matrix Representation of Operators
Matrix Algebra
Matrix Operations
Pseudoinverse*
Determinants
Orthogonal and Unitary Matrices
Simultaneous Linear Equations
Eigenvalue Equations
Matrix Eigenvalue Equations
Matrix Diagonalization
Differential Eigenvalue Equations
Hermitian Operators
The Variational Principle*
Schr�dinger's Equation
Quantum Mechanics
Quantum Mechanical Operators
The Wavefunction
The Basic Postulates*
Atoms and Molecules
The One-Electron Atom
Orbitals
The Radial Equation*
Hybrid Orbitals
Antisymmetry*
Molecular Orbitals*
Fourier Analysis
The Fourier Transform
Spectral Line Shapes*
Discrete Fourier Transform*
Signal Processing
Noise Filtering*
Convolution*
Computer Programs
Robust Estimators
FREML
Nelder-Mead Simplex Optimization
Answers to Selected Exercises
Bibliography
Index

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