Mathematics for Physical Chemistry
- 5th Edition - February 20, 2023
- Imprint: Elsevier
- Authors: Robert G. Mortimer, S.M. Blinder
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 1 8 9 4 5 - 6
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 1 8 9 4 6 - 3
Mathematics for Physical Chemistry, Fifth Edition includes exercises that enable readers to test their understanding and put theory into practice. Chapters are constructed around… Read more
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Request a sales quoteMathematics for Physical Chemistry, Fifth Edition includes exercises that enable readers to test their understanding and put theory into practice. Chapters are constructed around a sequence of mathematical topics, progressing gradually into more advanced material, before discussing key mathematical skills, including the analysis of experimental data and—new to this edition—complex variables. Includes additional new content on Mathematica and its advanced applications. Drawing on the experience of its expert authors, this book is the ideal supplementary text for practicing chemists and students wanting to sharpen their mathematics skills and understanding of key mathematical concepts for applications across physical chemistry.
- Includes updated coverage of key topics, including a review of general algebra and an introduction to group theory
- Features previews, objectives, and numerous examples and problems throughout the text to aid learning
- Provides chemistry-specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics
- Includes new chapters on complex variables and Mathematica for advanced applications
Students and teachers enrolled in general through physical chemistry courses, and researchers across chemistry interested in brushing up their skills
- Cover image
- Title page
- Table of Contents
- Copyright
- Preface
- Chapter 1: Problem Solving and Numerical Mathematics
- Abstract
- 1.1. Problem Solving
- 1.2. Measurements
- 1.3. Numerical Mathematical Operations
- 1.4. Units of Measurement
- 1.5. The Factor-Label Method
- 1.6. Measurements, Accuracy, and Significant Digits
- 1.7. Problems
- Chapter 2: Mathematical Functions
- Abstract
- 2.1. Mathematical Functions in Physical Chemistry
- 2.2. Important Families of Functions
- 2.3. Generating Approximate Graphs
- 2.4. Problems
- Chapter 3: Symbolic Mathematics: Algebra
- Abstract
- 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
- 3.6. Problems
- Chapter 4: Vectors and Vector Algebra
- Abstract
- 4.1. Vectors in Two Dimensions
- 4.2. Vectors in Three Dimensions
- 4.3. Physical Examples of Vector Products
- 4.4. Problems
- Chapter 5: The Solution of Algebraic Equations
- Abstract
- 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
- Chapter 6: Differential Calculus
- Abstract
- 6.1. The Tangent Line and the Derivative of a Function
- 6.2. Differentials
- 6.3. Some Derivative Identities
- 6.4. Higher-Order Derivatives
- 6.5. Newton's Method
- 6.6. Maximum-Minimum Problems
- 6.7. Locating Inflection Points
- 6.8. Limiting Values of Functions
- 6.9. L'Hôpital's Rule
- Chapter 7: Integral Calculus
- Abstract
- 7.1. The Antiderivative of a Function
- 7.2. The Process of Integration
- 7.3. Tables of Indefinite Integrals
- 7.4. Improper Integrals
- 7.5. Techniques of Integration
- 7.6. Numerical Integration
- Chapter 8: Differential Calculus With Several Independent Variables
- Abstract
- 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
- Chapter 9: Integral Calculus With Several Independent Variables
- Abstract
- 9.1. Line Integrals
- 9.2. Multiple Integrals
- Chapter 10: Mathematical Series
- Abstract
- 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
- Abstract
- 11.1. Fourier Series
- 11.2. Other Functional Series With Orthogonal Basis Sets
- 11.3. Integral Transforms
- Chapter 12: Differential Equations
- Abstract
- 12.1. Differential Equations and Newton's Laws of Motion
- 12.2. Ordinary Linear Differential Equations With Constant Coefficients
- 12.3. Differential Equations With Separable Variables
- 12.4. Exact Differential Equations
- 12.5. Inexact Differential Equations
- 12.6. Partial Differential Equations
- 12.7. Solution of Differential Equations Using Laplace Transforms
- 12.8. Numerical Solution of Differential Equations
- Chapter 13: Operators, Matrices, and Group Theory
- Abstract
- 13.1. Mathematical Operators
- 13.2. Symmetry Operators
- 13.3. The Operation of Symmetry Operators on Functions
- 13.4. Matrices and Matrix Algebra
- 13.5. Matrices in Quantum Mechanics
- 13.6. Determinants
- 13.7. Matrix Algebra With Mathematica
- 13.8. An Elementary Introduction to Group Theory
- 13.9. Matrix Representations of Symmetry Operators
- Chapter 14: The Solution of Simultaneous Algebraic Equations With More Than Two Unknowns
- Abstract
- 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
- Chapter 15: Complex Variables
- Abstract
- 15.1. Mapping in the Complex Plane
- 15.2. Cauchy–Riemann Equations
- 15.3. Contour Integration
- 15.4. Cauchy's Theorem
- 15.5. Cauchy's Integral Formula
- 15.6. Taylor Series
- 15.7. Laurent Expansions
- 15.8. Calculus of Residues
- 15.9. Trigonometric Integrals
- 15.10. Improper Integrals
- 15.11. Multivalued Functions
- 15.12. Integrals Using Branch Cuts
- 15.13. Problems
- Chapter 16: Probability, Statistics, and Experimental Errors
- Abstract
- 16.1. Experimental Errors in Measured Quantities
- 16.2. Probability Theory
- 16.3. Statistics and the Properties of a Sample
- 16.4. Numerical Estimation of Random Errors
- Chapter 17: Data Reduction and the Propagation of Errors
- Abstract
- 17.1. The Combination of Errors
- 17.2. Curve Fitting
- 17.3. Data Reduction With a Derivative
- Chapter 18: Mathematica: Advanced Applications
- Abstract
- The Basic Math Assistant
- Symbolic Mathematics
- Functions and Plots
- Other Types of Plots
- 2D Graphics
- Plain English Instructions
- External Data
- 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 Odd-Numbered Problems
- 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
- Index
- Edition: 5
- Published: February 20, 2023
- Imprint: Elsevier
- No. of pages: 274
- Language: English
- Paperback ISBN: 9780443189456
- eBook ISBN: 9780443189463
RM
Robert G. Mortimer
Robert G. Mortimer is a Professor Emeritus of Chemistry at Rhodes College in Memphis, Tennessee. He has taught physical chemistry at Indiana University and Rhodes College for over 40 years. He has carried out both experimental and theoretical research in the area of nonequilibrium processes in fluid systems.
Affiliations and expertise
Professor Emeritus of Chemistry, Rhodes College, Memphis, TN, USASB
S.M. Blinder
S.M. Blinder is a Professor Emeritus of Chemistry and Physics at the University of Michigan, Ann Arbor, and a telecommuting senior scientist with Wolfram Research in Champaign, Illinois. His research interests within the fields of theoretical chemistry and mathematical physics have included applications of quantum mechanics to atomic and molecular structure, theory and applications of Coulomb Propagators, structure and self-energy of the electron, supersymmetric quantum mechanics, and quantum computers. He is the author of four books and over 200 journal articles in theoretical chemistry and mathematical physics.
Affiliations and expertise
Professor Emeritus, Chemistry and Physics, University of Michigan, Ann Arbor, MI, USARead Mathematics for Physical Chemistry on ScienceDirect