Mathematics for Physical Chemistry, 4th Edition

Dedication

Preface

Chapter 1. Problem Solving and Numerical Mathematics

1.1 Problem Solving

1.2 Numbers and Measurements

1.3 Numerical Mathematical Operations

1.4 Units of Measurement

1.5 The Factor-Label Method

1.6 Measurements, Accuracy, and Significant Digits

Problems

Chapter 2. Mathematical Functions

2.1 Mathematical Functions in Physical Chemistry

2.2 Important Families of Functions

2.3 Generating Approximate Graphs

Problems

Chapter 3. Problem Solving and Symbolic Mathematics: Algebra

3.1 The Algebra of Real Scalar Variables

3.2 Coordinate Systems In Two Dimensions

3.3 Coordinate Systems in Three Dimensions

3.4 Imaginary and Complex Numbers

3.5 Problem Solving and Symbolic Mathematics

Problems

Chapter 4. Vectors and Vector Algebra

4.1 Vectors in Two Dimensions

4.2 Vectors in Three Dimensions

4.3 Physical Examples of Vector Products

Problems

Chapter 5. Problem Solving and the Solution of Algebraic Equations

5.1 Algebraic Methods for Solving One Equation with One Unknown

5.2 Numerical Solution of Algebraic Equations

5.3 A Brief Introduction to Mathematica

5.4 Simultaneous Equations: Two Equations with Two Unknowns

Problems

Chapter 6. Differential Calculus

6.1 The Tangent Line and the Derivative of a Function

6.2 Differentials

6.3 Some Useful Derivative Identities

6.4 Newton’s Method

6.5 Higher-Order Derivatives

6.6 Maximum–Minimum Problems

6.7 Limiting Values of Functions

6.8 l’Hôpital’s Rule

Chapter 7. Integral Calculus

7.1 The Antiderivative of a Function

7.1.1 Position, Velocity, and Acceleration

7.2 The Process of Integration

7.2.1 The Definite Integral as an Area

7.2.2 Facts about Integrals

7.2.3 Derivatives of Definite Integrals

7.3 Tables of Indefinite Integrals

7.4 Improper Integrals

7.5 Techniques of Integration

7.6 Numerical Integration

Problems

Chapter 8. Differential Calculus with Several Independent Variables

8.1 Functions of Several Independent Variables

8.2 Changes in a Function of Several Variables, Partial Derivatives

8.3 Change of Variables

8.4 Useful Partial Derivative Identities

8.5 Thermodynamic Variables Related to Partial Derivatives

8.6 Exact and Inexact Differentials

8.7 Maximum and Minimum Values of Functions of Several Variables

8.8 Vector Derivative Operators

Problems

Chapter 9. Integral Calculus with Several Independent Variables

9.1 Line Integrals

9.2 Multiple Integrals

Problems

Chapter 10. Mathematical Series

10.1 Constant Series

10.2 Power Series

10.3 Mathematical Operations on Series

10.4 Power Series with More than One Independent Variable

Chapter 11. Functional Series and Integral Transforms

11.1 Fourier Series

11.2 Other Functional Series with Orthogonal Basis Sets

11.3 Integral Transforms

Problems

Chapter 12. Differential Equations

12.1 Differential Equations and Newton’s Laws of Motion

12.2 Homogeneous Linear Differential Equations with Constant Coefficients

12.3 Inhomogeneous Linear Differential Equations: The Forced Harmonic Oscillator

12.4 Differential Equations with Separable Variables

12.5 Exact Differential Equations

12.6 Solution of Inexact Differential Equations Using Integrating Factors

12.7 Partial Differential Equations

12.8 Solution of Differential Equations using Laplace Transforms

12.9 Numerical Solution of Differential Equations

Problems

Chapter 13. Operators, Matrices, and Group Theory

13.1 Mathematical Operators

13.2 Symmetry Operators

13.3 The Operation of Symmetry Operators on Functions

13.4 Matrix Algebra

13.5 Determinants

13.6 Matrix Algebra with Mathematica

13.7 An Elementary Introduction to Group Theory

13.8 Symmetry Operators and Matrix Representations

Chapter 14. The Solution of Simultaneous Algebraic Equations with More than Two Unknowns

14.1 Cramer’s Rule

14.2 Linear Dependence and Inconsistency

14.3 Solution by Matrix Inversion

14.4 Gauss–Jordan Elimination

14.5 Linear Homogeneous Equations

14.6 Matrix Eigenvalues and Eigenvectors

14.7 The Use of Mathematica to Solve Simultaneous Equations

14.8 The Use of Mathematica to Find Matrix Eigenvalues and Eigenvectors

Problems

Chapter 15. Probability, Statistics, and Experimental Errors

15.1 Experimental Errors in Measured Quantities

15.2 Probability Theory

15.3 Statistics and the Properties of a Sample

15.4 Numerical Estimation of Random Errors

Problems

Chapter 16. Data Reduction and the Propagation of Errors

16.1 The Combination of Errors

16.2 Curve Fitting

16.3 Data Reduction With A Derivative

Problems

Appendices

Appendix A Values of Physical Constants

Appendix B Some Mathematical Formulas and Identities

Appendix C Infinite Series

Appendix D A Short Table of Derivatives

Appendix E A Short Table of Indefinite Integrals

Appendix F A Short Table of Definite Integrals

Appendix G Some Integrals with Exponentials in the Integrands: The Error Function

Appendix H Answers to Selected Numerical Exercises and Problems

Chapter 16

Additional Reading

Books on Mathematics for Science

Calculus Textbooks

Books on Numerical Analysis

Advanced Mathematics Books

Books on Group Theory

Books on Experimental Data Analysis

Computer Books

Problem-Solving and Problem Books

Mathematical Tables

Websites

Index