Synopses & Reviews
Applied Mathematics for Physical Chemistry is the perfect resource for students who need to refresh themselves on the algebra and calculus required to understand thermodynamics, atomic and molecular structure, spectroscopy, and statistical mechanics. Designed to supplement all textbooks of physical chemistry, this book will help today's physical chemistry students succeed in their course.
This book features: - Introductory chapters that deal with coordinate systems, functions and graphs, and the use of logarithms.
- Chapters on differential and integral calculus.
- A chapter of mathematical methods in the laboratory, including error analysis, propagation of errors, linear regression calculations, and preparing graphs.
- An introduction to differential equations.
- A chapter illustrating the use of Fourier series and Fourier transforms.
- Problems at the end of each chapter, with answers to all problems in an appendix.
New to this edition: - A completely revised chapter on Numerical Methods and the Use of the Computer that illustrates how to complete calculations using Microsoft Excel^{}.
Synopsis
A how to do it review and learn book on advanced mathematics necessary to physical chemistry. Coordinate systems, functions and graphs, logarithms, differential calculus, integral calculus, infinite series, differential equations, scalars and vectors, matrices and determinants, operators, numerical methods and the use of the computer, and mathematical methods in the laboratory. Educators, Technicians, and other professionals using mathematics in physical chemistry.
Table of Contents
1. Coordinate Systems.
Cartesian Coordinates. Plane Polar Coordinates. Spherical Polar Coordinates. Complex Numbers.
2. Functions and Graphs.
Functions. Graphical Representation of Functions. Roots to Polynomial Equations.
3. Logarithms.
General Properties of Logarithms. Common Logarithms. Natural Logarithms.
4. Differential Calculus.
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.
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.
Tests for Convergence and Divergence. Power Series Revisited. Maclaurin and Taylor Series. Fourier Series and Fourier Transforms.
7. Differential Equations.
Linear Combinations. First-Order Differential Equations. Second-Order Differential Equations. with Constant Coefficients. General Series Methods of Solution. Special Polynomial Solutions to Differential Equations. Exact and Inexact Differentials. Integrating Factors. Partial Differential Equations.
8. Scalars and Vectors.
Addition of Vectors. Multiplication of Vectors. Applications.
9. Matrices and Determinants.
Square Matrices and Determinants. Matrix Algebra.
10. Operators.
Vector Operators. Eigenvalue Equations Revisited. Hermitian Operators. Rotational Operators. Transformation of ∇^{2} to Plane Polar Coordinates.
11. Numerical Methods and the Use of the Computer.
Graphical Presentation. Numerical Integration. Roots to Equations. Fourier Transforms Revisited-Macros.
12. Mathematical Methods in the Laboratory.
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} Spherical Polar Coordinate.
Appendix IV. Stirling's Approximation.
Appendix V. Solving a 3x3 Determinant.
Appendix VI. Statistics.
Answers.
Index.