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For undergraduate level physical chemistry courses.
The textbook was written as a supplement to help students learn and apply the advanced mathematics necessary to understand physical chemistry. The first half of the book should act as a review of subject matter normally covered in prerequisite courses. The latter half of the book covers important material normally not covered in prerequisite mathematics courses, but is essential to physical chemistry study.
Features
Author Bio
Barrante, James R. : Southern Connecticut State University
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
For undergraduate level physical chemistry courses.
The textbook was written as a supplement to help students learn and apply the advanced mathematics necessary to understand physical chemistry. The first half of the book should act as a review of subject matter normally covered in prerequisite courses. The latter half of the book covers important material normally not covered in prerequisite mathematics courses, but is essential to physical chemistry study.
Features
Author Bio
Barrante, James R. : Southern Connecticut State University
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