Mathematics for Physical Chemistry

Mathematics for Physical Chemistry

4th Edition - June 7, 2013

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  • Author: Robert Mortimer
  • Paperback ISBN: 9780124158092
  • eBook ISBN: 9780123978455

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Description

Mathematics for Physical Chemistry is the ideal supplementary text for practicing chemists and students who want to sharpen their mathematics skills while enrolled in general through physical chemistry courses. This book specifically emphasizes the use of mathematics in the context of physical chemistry, as opposed to being simply a mathematics text. This 4e includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The early chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. A final chapter discusses mathematical topics needed in the analysis of experimental data.

Key Features

  • Numerous examples and problems interspersed throughout the presentations
  • Each extensive chapter contains a preview and objectives
  • Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory
  • Provides chemistry-specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics

Readership

New chemistry researchers; freshmen through juniors, seniors and graduates students enrolled in general through physical chemistry courses; especially students in lower- and upper-division honors chemistry courses

Table of Contents

  • 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

Product details

  • No. of pages: 272
  • Language: English
  • Copyright: © Elsevier 2013
  • Published: June 7, 2013
  • Imprint: Elsevier
  • Paperback ISBN: 9780124158092
  • eBook ISBN: 9780123978455

About the Author

Robert Mortimer

Robert Mortimer
Robert Mortimer has been a professor of chemistry at Rhodes College since 1981. He is the recipient of a Woodrow Wilson National Fellowship as well as a National Science Foundation Predoctoral Fellowship.

Affiliations and Expertise

Rhodes College, Memphis, TN, USA

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