Mathematics for Physical Chemistry, 4th, Third Edition

Cover Page......Page 1
Mathematics for Physical Chemistry......Page 3
Title Page......Page 5
ISBN 0125083475......Page 6
Contents......Page 9
Preface......Page 13
1 Numbers, Measurements, and Numerical Mathematics......Page 15
Numbers and Measurements......Page 16
Numerical Mathematical Operations......Page 19
Units of Measurement......Page 25
Numerical Calculations......Page 28
2 Symbolic Mathematics and Mathematical Functions......Page 35
Algebraic Operations on Real Scalar Variables......Page 36
Trigonometric Functions......Page 38
Inverse Trigonometric Functions......Page 43
Vectors and Coordinate Systems......Page 45
Imaginary and Complex Numbers......Page 58
Problem Solving and Symbolic Mathematics......Page 66
PROBLEMS......Page 68
3 The Solution of Algebraic Equations......Page 71
Algebraic Methods for Solving One Equation with One Unknown......Page 72
Graphical Solution of Equations......Page 78
Numerical Solution of Algebraic Equations......Page 84
Simultaneous Equations: Two Equations with Two Unknowns......Page 93
PROBLEMS......Page 99
4 Mathematical Functions and Differential Calculus......Page 103
Mathematical Functions......Page 104
The Tangent Line and the Derivative of a Function......Page 112
Differentials......Page 116
Some Useful Facts About Derivatives......Page 118
Higher-Order Derivatives......Page 122
Maximum-Minimum Problems......Page 124
Limiting Values of Functions: L’Hôpital’s Rule......Page 127
PROBLEMS......Page 130
5 Integral Calculus......Page 135
The Antiderivative of a Function......Page 136
The Process of Integration......Page 138
Indefinite Integrals: Tables of Integrals......Page 146
Improper Integrals......Page 148
Methods of Integration......Page 150
Numerical Integration......Page 155
Probability Distributions and Mean Values......Page 159
6 Mathematical Series and Transforms......Page 172
Constant Series......Page 173
Functional Series......Page 179
Fourier Series......Page 186
Mathematical Operations on Series......Page 192
Integral Transforms......Page 194
PROBLEMS......Page 199
7 Calculus With Several Independent Variables......Page 203
Functions of Several Independent Variables......Page 204
Change of Variables......Page 210
Additional Useful Relations Between Partial Derivatives......Page 212
Exact and Inexact Differentials......Page 216
Line Integrals......Page 219
Multiple Integrals......Page 224
Vector Derivative Operators......Page 231
Maximum and Minimum Values of Functions of Several Variables......Page 238
PROBLEMS......Page 244
8 Differential Equations......Page 248
Differential Equations and Newton’s Laws of Motion......Page 249
The Harmonic Oscillator: Linear Differential Equations with Constant Coefficients......Page 252
Differential Equations with Separable Variables......Page 263
Exact Differential Equations......Page 265
Solution of Inexact Differential Equations by the Use of Integrating Factors......Page 266
Partial Differential Equations: Waves in a String......Page 267
Solution of Differential Equations with Laplace Transforms......Page 272
Numerical Solutions of Differential Equations......Page 274
PROBLEMS......Page 278
9 Operators, Matrices, and Group Theory......Page 282
Operators and Operator Algebra......Page 283
Symmetry Operators......Page 289
Matrix Algebra......Page 296
Matrix Algebra with Mathematica......Page 306
An Elementary Introduction to Group Theory......Page 308
PROBLEMS......Page 315
10 The Solution of Simultaneous Algebraic Equations......Page 319
Cramer’s Rule......Page 320
Solution by Matrix Inversion......Page 323
The Use of Mathematica to Solve Simultaneous Equations......Page 327
PROBLEMS......Page 329
11 The Treatment of Experimental Data......Page 332
Experimental Errors in Measured Quantities......Page 333
Statistical Treatment of Random Errors......Page 336
Data Reduction and the Propagation of Errors......Page 343
Graphical and Numerical Data Reduction......Page 347
Numerical Curve Fitting: The Method of Least Squares (Regression)......Page 353
PROBLEMS......Page 368
Additional Reading......Page 374
Appendixes......Page 378
A Values of Physical Constants......Page 379
B Some Mathematical Formulas and Identities......Page 381
Power Series......Page 384
D A Short Table of Derivatives......Page 387
E A Short Table of Indefinite Integrals......Page 389
F A Short Table of Definite Integrals......Page 393
G Some Integrals with Exponentials in the Integrands: The Error Function......Page 397
Index......Page 401