“Very inclusive and covers all the essentials for the study of Physical Chemistry I and II.” — Yirong Mo, Western Michigan University
“As a physical chemistry instructor, for years I have found this book to be very useful. Many times, other than teaching physical chemistry concepts I had to first teach math. Now with this book, students can get on board a little easier. It is also perfect for a math review at the beginning of the semester.” — Jiangyue Zhang, Immaculate University
“A well-written textbook. Its size is unintimidating and it reads like a novel. Students often complain that chemistry books are so big and heavy. This is a must-have book for chemistry majors and libraries.” — Allen Ahoparadze, College of St. Scholastica
248 pages, $49.95 list
1-4786-3247-X
978-1-4786-3247-4
© 2004
paperback
eBook availability
Applied Mathematics for Physical Chemistry
Third Edition
By the time chemistry students are ready to study physical chemistry, they’ve completed mathematics courses through calculus. But a strong background in mathematics doesn’t necessarily equate to knowledge of how to apply that mathematics to solving physicochemical problems. In addition, in-depth understanding of modern concepts in physical chemistry requires knowledge of mathematical concepts and techniques beyond introductory calculus, such as differential equations, Fourier series, and Fourier transforms. This results in many physical chemistry instructors spending valuable lecture time teaching mathematics rather than chemistry.
Barrante presents both basic and advanced mathematical techniques in the context of how they apply to physical chemistry. Many problems at the end of each chapter test students’ mathematical knowledge. Designed and priced to accompany traditional core textbooks in physical chemistry, Applied Mathematics for Physical Chemistry provides students with the tools essential for answering questions in thermodynamics, atomic/molecular structure, spectroscopy, and statistical mechanics.
Barrante presents both basic and advanced mathematical techniques in the context of how they apply to physical chemistry. Many problems at the end of each chapter test students’ mathematical knowledge. Designed and priced to accompany traditional core textbooks in physical chemistry, Applied Mathematics for Physical Chemistry provides students with the tools essential for answering questions in thermodynamics, atomic/molecular structure, spectroscopy, and statistical mechanics.
Reactions
1. Coordinate Systems
Introduction / Cartesian Coordinates / Plane Polar Coordinates / Spherical Polar Coordinates / Complex Numbers
2. Functions and Graphs
Functions / Graphical Representations of Functions / Roots of Polynomial Equations
3. Logarithms
Introduction / General Properties of Logarithms / Common Logarithms / Natural Logarithms
4. Differential Calculus
Introduction / Functions of Single Variables / Functions of Several Variables; Partial Derivatives / The Total Differential / Derivative as a Ratio of Infinitesimally Small Changes / Geometric Properties of Derivatives / Constrained Maxima and Minima
5. Integral Calculus
Introduction / Integral as an Antiderivative / General Methods of Integration / Special Methods of Integration / The Integral as a Summation of Infinitesimally Small Elements / Line Integrals / Double and Triple Integrals
6. Infinite Series
Introduction / Tests for Convergence and Divergence / Power Series Revisited / Maclaurin and Taylor Series / Fourier Series and Fourier Transforms
7. Differential Equations
Introduction / Linear Combinations / First-Order Differential Equations / Second-Order Differential Equations with Constant Coefficients / General Series Methods of Solution / Special Polynomial Solutions of Differential Equations / Exact and Inexact Differentials / Integrating Factors / Partial Differential Equations
8. Scalars and Vectors
Introduction / Addition of Vectors / Multiplication of Vectors / Applications
9. Matrices and Determinants
Introduction / Square Matrices and Determinants / Matrix Algebra / Solutions of Systems of Linear Equations / Characteristic Equation of a Matrix
10. Operators
Introduction / Vector Operators / Eigenvalue Equations Revisited / Hermitian Operators / Rotational Operators / Transformation of §2 to Plane Coordinates
11. Numerical Methods and the Use of the Computer
Introduction / Graphical Presentation / Numerical Integration / Roots of Equations / Fourier Transforms Revisited: Macros
12. Mathematical Methods in the Laboratory
Introduction / Probability / Experimental Errors / Propagation of Errors / Preparation of Graphs / Linear Regression / Tangents and Areas
Appendix I: Table of Physical Constants
Appendix II: Table of Integrals
Appendix III: Transformation of §2 to Spherical Polar Coordinates
Appendix IV: Stirling's Approximation
Appendix V: Solving a 3 × 3 Determinant
Appendix VI: Statistics
Answers
Introduction / Cartesian Coordinates / Plane Polar Coordinates / Spherical Polar Coordinates / Complex Numbers
2. Functions and Graphs
Functions / Graphical Representations of Functions / Roots of Polynomial Equations
3. Logarithms
Introduction / General Properties of Logarithms / Common Logarithms / Natural Logarithms
4. Differential Calculus
Introduction / Functions of Single Variables / Functions of Several Variables; Partial Derivatives / The Total Differential / Derivative as a Ratio of Infinitesimally Small Changes / Geometric Properties of Derivatives / Constrained Maxima and Minima
5. Integral Calculus
Introduction / Integral as an Antiderivative / General Methods of Integration / Special Methods of Integration / The Integral as a Summation of Infinitesimally Small Elements / Line Integrals / Double and Triple Integrals
6. Infinite Series
Introduction / Tests for Convergence and Divergence / Power Series Revisited / Maclaurin and Taylor Series / Fourier Series and Fourier Transforms
7. Differential Equations
Introduction / Linear Combinations / First-Order Differential Equations / Second-Order Differential Equations with Constant Coefficients / General Series Methods of Solution / Special Polynomial Solutions of Differential Equations / Exact and Inexact Differentials / Integrating Factors / Partial Differential Equations
8. Scalars and Vectors
Introduction / Addition of Vectors / Multiplication of Vectors / Applications
9. Matrices and Determinants
Introduction / Square Matrices and Determinants / Matrix Algebra / Solutions of Systems of Linear Equations / Characteristic Equation of a Matrix
10. Operators
Introduction / Vector Operators / Eigenvalue Equations Revisited / Hermitian Operators / Rotational Operators / Transformation of §2 to Plane Coordinates
11. Numerical Methods and the Use of the Computer
Introduction / Graphical Presentation / Numerical Integration / Roots of Equations / Fourier Transforms Revisited: Macros
12. Mathematical Methods in the Laboratory
Introduction / Probability / Experimental Errors / Propagation of Errors / Preparation of Graphs / Linear Regression / Tangents and Areas
Appendix I: Table of Physical Constants
Appendix II: Table of Integrals
Appendix III: Transformation of §2 to Spherical Polar Coordinates
Appendix IV: Stirling's Approximation
Appendix V: Solving a 3 × 3 Determinant
Appendix VI: Statistics
Answers