Mathematics for Physical Chemistry
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Table of contents
- Cover
- Contentsvii
- Prefacexi
- 1 Numbers, Measurements, and Numerical Mathematics1
- Numbers and Measurements2
- Numerical Mathematical Operations5
- Units of Measurement11
- Numerical Calculations14
- 2 Symbolic Mathematics and Mathematical Functions21
- Algebraic Operations on Real Scalar Variables22
- Trigonometric Functions24
- Inverse Trigonometric Functions29
- Vectors and Coordinate Systems31
- Imaginary and Complex Numbers44
- Problem Solving and Symbolic Mathematics52
- 3 The Solution of Algebraic Equations57
- Algebraic Methods for Solving One Equation with One Unknown58
- Graphical Solution of Equations64
- Numerical Solution of Algebraic Equations70
- Simultaneous Equations: Two Equations with Two Unknowns79
- 4 Mathematical Functions and Differential Calculus89
- Mathematical Functions90
- The Tangent Line and the Derivative of a Function98
- Differentials102
- Some Useful Facts About Derivatives104
- Higher-Order Derivatives108
- Maximum-Minimum Problems110
- Limiting Values of Functions: L’Hôpital’s Rule113
- 5 Integral Calculus121
- The Antiderivative of a Function122
- The Process of Integration124
- Indefinite Integrals: Tables of Integrals132
- Improper Integrals134
- Methods of Integration136
- Numerical Integration141
- Probability Distributions and Mean Values145
- 6 Mathematical Series and Transforms158
- Constant Series159
- Functional Series165
- Fourier Series172
- Mathematical Operations on Series178
- Integral Transforms180
- 7 Calculus With Several Independent Variables189
- Functions of Several Independent Variables190
- Change of Variables196
- Additional Useful Relations Between Partial Derivatives198
- Exact and Inexact Differentials202
- Line Integrals205
- Multiple Integrals210
- Vector Derivative Operators217
- Maximum and Minimum Values of Functions of Several Variables224
- 8 Differential Equations234
- Differential Equations and Newton’s Laws of Motion235
- The Harmonic Oscillator: Linear Differential Equations with Constant Coefficients238
- Differential Equations with Separable Variables249
- Exact Differential Equations251
- Solution of Inexact Differential Equations by the Use of Integrating Factors252
- Partial Differential Equations: Waves in a String253
- Solution of Differential Equations with Laplace Transforms258
- Numerical Solutions of Differential Equations260
- 9 Operators, Matrices, and Group Theory268
- Operators and Operator Algebra269
- Symmetry Operators275
- Matrix Algebra282
- Matrix Algebra with Mathematica292
- An Elementary Introduction to Group Theory294
- 10 The Solution of Simultaneous Algebraic Equations305
- Simultaneous Equations with More than Two Unknowns306
- Cramer’s Rule306
- Solution by Matrix Inversion309
- The Use of Mathematica to Solve Simultaneous Equations313
- 11 The Treatment of Experimental Data318
- Experimental Errors in Measured Quantities319
- Statistical Treatment of Random Errors322
- Data Reduction and the Propagation of Errors329
- Graphical and Numerical Data Reduction333
- Numerical Curve Fitting: The Method of Least Squares (Regression)339
- Appendixes364
- A Values of Physical Constants1365
- B Some Mathematical Formulas and Identities367
- C Infinite Series370
- Series with Constant Terms370
- Power Series370
- D A Short Table of Derivatives373
- E A Short Table of Indefinite Integrals375
- F A Short Table of Definite Integrals379
- G Some Integrals with Exponentials in the Integrands: The Error Function383
- Index387
Mathematics for Physical Chemistry, Third Edition, is the ideal text for students and physical chemists who want to sharpen their mathematics skills. It can help prepare the reader for an undergraduate course, serve as a supplementary text for use during a course, or serve as a reference for graduate students and practicing chemists. The text concentrates on applications instead of theory, and, although the emphasis is on physical chemistry, it can also be useful in general chemistry courses.
The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.
* Numerous examples and problems interspersed throughout the presentations
* Each extensive chapter contains a preview, objectives, and summary
* Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory
* Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics
The Third Edition includes new exercises in each chapter that provide practice in a technique immediately after discussion or example and encourage self-study. The first ten chapters are constructed around a sequence of mathematical topics, with a gradual progression into more advanced material. The final chapter discusses mathematical topics needed in the analysis of experimental data.
* Numerous examples and problems interspersed throughout the presentations
* Each extensive chapter contains a preview, objectives, and summary
* Includes topics not found in similar books, such as a review of general algebra and an introduction to group theory
* Provides chemistry specific instruction without the distraction of abstract concepts or theoretical issues in pure mathematics