It features numerous problems, many multi-part, that use the symbolism found in standard physical chemistry books or involve actual physical chemistry equations. It offers full-chapter coverage of many important topics relegated to appendices in other books. It also provides a full chapter on numerical methods and computer programming showing step-by-step how to write programs to do numerical integration, and covers areas of advanced mathematics — e.g., differential equations and operator mechanics.

**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 1. Table of Physical Constants.

Appendix 2. Table of Integrals.

Appendix 3. Transformation of ∇2 Spherical Polar Coordinate.

Appendix 4. Stirling’s Approximation.

Appendix 5. Solving a 3×3 Determinant.

Appendix 6. Statistics.

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