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Many of today's students find themselves poorly prepared mathematically for their physical chemistry courses. This unique text is for them. This text helps students to recall the math they have learned, to apply mathematics to solve chemical problems, and to acquire a fuller set of mathematical skills necessary for such applications. Using an abundance of fully-worked examples, it shows step-by-step how to directly apply mathematics to physical chemistry problems. It offers full-chapter coverage of many important topics relegated to appendices in other texts, provides a full chapter on numerical methods and computer programming, and covers key areas of advanced mathematics.
Offers a basic review of differential and integral calculus with less emphasis on mathematical proofs and more emphasis on how to use the mathematics as a tool.
Covers mathematical methods used in the laboratory -- with an emphasis on error theory, presentation of graphical material, and numerical methods.
Features fully-worked examples throughout showing the application of the mathematics to physical chemistry.
Includes numerous problems, many with multiple parts, at the end of each chapter.
The problems are mathematical in nature but are generally presented within a physical chemistry framework, either using the symbolism found in standard physical chemistry texts or involving actual physical chemistry equations. Gives all answers at the end of the text.
Covers areas of advanced mathematics -- e.g., differential equations and operator mechanics -- which students may not generally be exposed to in their undergraduate curriculum.
Includes full chapters (not just appendices) on differential equations, infinite series (Fourier transforms), vector analysis, matrix and operator mechanics -- topics normally not covered in prerequisite math courses taken by chemistry majors, but important in the study of quantum chemistry and spectroscopy.
Provides a complete Table of Integrals (in an appendix).
NEW--Features detailed coverage of Fourier transforms and Fourier series -- used in much of the instrumentation found in today's chemistry laboratories.
NEW--Features a chapter on numerical methods and computer programming.
Shows how to write programs to do numerical integration -- e.g., by the Monte Carlo method -- or to solve for the roots of polynomial functions.
NEW--Explains how to solve the roots (or zeros) to polynomial equations by both graphical and numerical methods, using spread sheets or by programming personal computers.
NEW--Expands coverage of series method of solving differential equations to include Hermite, Legendre, and Laguerre polynomials -- important in quantum chemistry.
NEW--Covers the characteristic equation of a matrix along with diagonalizing matrices.
NEW--Explains a step-by-step method for the transformation of the Laplacian operator <177>2 from Cartesian to spherical polar coordinates.
1. Coordinate Systems.
2. Functions and Graphs.
3. Logarithms.
4. Differential Calculus.
5. Integral Calculus.
6. Differential Equations.
7. Infinite Series.
8. Scalars and Vectors.
9. Matrices and Determinants.
10. Operators.
11. Numerical Methods and the Use of the Computer.
12. Mathematical Methods in the Laboratory.
Appendices.
Answers.
Index.
Many of today's students find themselves poorly prepared mathematically for their physical chemistry courses. This unique text is for them. This text helps students to recall the math they have learned, to apply mathematics to solve chemical problems, and to acquire a fuller set of mathematical skills necessary for such applications. Using an abundance of fully-worked examples, it shows step-by-step how to directly apply mathematics to physical chemistry problems. It offers full-chapter coverage of many important topics relegated to appendices in other texts, provides a full chapter on numerical methods and computer programming, and covers key areas of advanced mathematics.
Offers a basic review of differential and integral calculus with less emphasis on mathematical proofs and more emphasis on how to use the mathematics as a tool.
Covers mathematical methods used in the laboratory -- with an emphasis on error theory, presentation of graphical material, and numerical methods.
Features fully-worked examples throughout showing the application of the mathematics to physical chemistry.
Includes numerous problems, many with multiple parts, at the end of each chapter.
The problems are mathematical in nature but are generally presented within a physical chemistry framework, either using the symbolism found in standard physical chemistry texts or involving actual physical chemistry equations. Gives all answers at the end of the text.
Covers areas of advanced mathematics -- e.g., differential equations and operator mechanics -- which students may not generally be exposed to in their undergraduate curriculum.
Includes full chapters (not just appendices) on differential equations, infinite series (Fourier transforms), vector analysis, matrix and operator mechanics -- topics normally not covered in prerequisite math courses taken by chemistry majors, but important in the study of quantum chemistry and spectroscopy.
Provides a complete Table of Integrals (in an appendix).
NEW--Features detailed coverage of Fourier transforms and Fourier series -- used in much of the instrumentation found in today's chemistry laboratories.
NEW--Features a chapter on numerical methods and computer programming.
Shows how to write programs to do numerical integration -- e.g., by the Monte Carlo method -- or to solve for the roots of polynomial functions.
NEW--Explains how to solve the roots (or zeros) to polynomial equations by both graphical and numerical methods, using spread sheets or by programming personal computers.
NEW--Expands coverage of series method of solving differential equations to include Hermite, Legendre, and Laguerre polynomials -- important in quantum chemistry.
NEW--Covers the characteristic equation of a matrix along with diagonalizing matrices.
NEW--Explains a step-by-step method for the transformation of the Laplacian operator <177>2 from Cartesian to spherical polar coordinates.
Table of Contents
1. Coordinate Systems.
2. Functions and Graphs.
3. Logarithms.
4. Differential Calculus.
5. Integral Calculus.
6. Differential Equations.
7. Infinite Series.
8. Scalars and Vectors.
9. Matrices and Determinants.
10. Operators.
11. Numerical Methods and the Use of the Computer.
12. Mathematical Methods in the Laboratory.
Appendices.
Answers.
Index.