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
