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Mathematical methods for physical and analytical chemistry / David Z. Goodson.

By: Material type: TextTextPublication details: Hoboken, N.J. : Wiley, ©2011.Description: 1 online resource (xix, 382 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781118135204
  • 1118135202
  • 9781118135174
  • 1118135172
  • 1283337479
  • 9781283337472
Subject(s): Genre/Form: Additional physical formats: Print version:: No titleDDC classification:
  • 530.15 23
LOC classification:
  • QC20 .G66 2011eb
Online resources:
Contents:
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.
Summary: "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"-- Provided by publisher.
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Includes bibliographical references and index.

Print version record.

"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"-- Provided by publisher.

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.

Physical Science