The chemistry maths book

The Chemistry Maths Book provides a complete course companion suitable for students at all levels. All the most useful and important topics are covered, with numerous examples of applications in chemistry and the physical sciences. Taking a clear, straightforward approach, the book develops ideas in a logical, coherent way, allowing students progressively to build a thorough working understanding of thesubject.Topics are organized into three parts: algebra, calculus, differential equations, and expansions in series; vectors, determinants and matrices; and numerical analysis and statistics. The extensive use ofexamples illustrates every important concept and method in the text, and are used to demonstrate applications of the mathematics in chemistry and several basic concepts in physics. The exercises at the end of each chapter, are an essential element of the development of the subject, and have been designed to give students a working understanding of the material in the text.

Author Notes

Dr Erich Steiner is a former senior lecturer at the University of Exeter, UK.

Reviews (1)

Choice Review

Steiner's small volume is an excellent quick reference to any math concept from number theory to matrix algebra, with emphasis on applications to chemistry. It contains exercises at the end of each chapter and answers to these exercises in a solutions section at the end of the book. Unlike most quick references of its kind, it also contains historical footnotes that add depth to its overall educational value. It is clearly written with excellent diagrams and treats subjects, such as the section 9.17 treatment of conversion from Cartesian to polar coordinates, in more detail than the student will usually find in chemistry textbooks. All levels. P. R. Douville emeritus, Central Connecticut State University

1 Numbers, variables, and units	p. 1
1.1 Concepts	p. 1
1.2 Real numbers	p. 3
1.3 Factorization, factors, and factorials	p. 7
1.4 Decimal representation of numbers	p. 9
1.5 Variables	p. 13
1.6 The algebra of real numbers	p. 14
1.7 Complex numbers	p. 19
1.8 Units	p. 19
1.9 Exercises	p. 29
2 Algebraic functions	p. 31
2.1 Concepts	p. 31
2.2 Graphical representation of functions	p. 32
2.3 Factorization and simplification of expressions	p. 34
2.4 Inverse functions	p. 37
2.5 Polynomials	p. 40
2.6 Rational functions	p. 50
2.7 Partial fractions	p. 52
2.8 Solution of simultaneous equations	p. 55
2.9 Exercises	p. 58
3 Transcendental functions	p. 62
3.1 Concepts	p. 62
3.2 Trigonometric functions	p. 63
3.3 Inverse trigonometric functions	p. 72
3.4 Trigonometric relations	p. 73
3.5 Polar coordinates	p. 77
3.6 The exponential function	p. 80
3.7 The logarithmic function	p. 83
3.8 Values of exponential and logarithmic functions	p. 86
3.9 Hyperbolic functions	p. 87
3.10 Exercises	p. 89
4 Differentiation	p. 93
4.1 Concepts	p. 93
4.2 The process of differentiation	p. 94
4.3 Continuity	p. 97
4.4 Limits	p. 98
4.5 Differentiation from first principles	p. 100
4.6 Differentiation by rule	p. 102
4.7 Implicit functions	p. 110
4.8 Logarithmic differentiation	p. 111
4.9 Successive differentiation	p. 113
4.10 Stationary points	p. 114
4.11 Linear and angular motion	p. 118
4.12 The differential	p. 119
4.13 Exercises	p. 122
5 Integration	p. 126
5.1 Concepts	p. 126
5.2 The indefinite integral	p. 127
5.3 The definite integral	p. 132
5.4 The integral calculus	p. 142
5.5 Uses of the integral calculus	p. 147
5.6 Static properties of matter	p. 148
5.7 Dynamics	p. 152
5.8 Pressure-volume work	p. 157
5.9 Exercises	p. 160
6 Methods of integration	p. 163
6.1 Concepts	p. 163
6.2 The use of trigonometric relations	p. 163
6.3 The method of substitution	p. 165
6.4 Integration by parts	p. 173
6.5 Reduction formulas	p. 176
6.6 Rational integrands. The method of partial fractions	p. 179
6.7 Parametric differentiation of integrals	p. 184
6.8 Exercises	p. 187
7 Sequences and series	p. 191
7.1 Concepts	p. 191
7.2 Sequences	p. 191
7.3 Finite series	p. 196
7.4 Infinite series	p. 203
7.5 Tests of convergence	p. 204
7.6 MacLaurin and Taylor series	p. 208
7.7 Approximate values and limits	p. 214
7.8 Operations with power series	p. 219
7.9 Exercises	p. 221
8 Complex numbers	p. 225
8.1 Concepts	p. 225
8.2 Algebra of complex numbers	p. 226
8.3 Graphical representation	p. 228
8.4 Complex functions	p. 235
8.5 Euler's formula	p. 236
8.6 Periodicity	p. 240
8.7 Evaluation of integrals	p. 244
8.8 Exercises	p. 245
9 Functions of several variables	p. 247
9.1 Concepts	p. 247
9.2 Graphical representation	p. 248
9.3 Partial differentiation	p. 249
9.4 Stationary points	p. 253
9.5 The total differential	p. 258
9.6 Some differential properties	p. 262
9.7 Exact differentials	p. 272
9.8 Line integrals	p. 275
9.9 Multiple integrals	p. 281
9.10 The double integral	p. 283
9.11 Change of variables	p. 285
9.12 Exercises	p. 289
10 Functions in 3 dimensions	p. 294
10.1 Concepts	p. 294
10.2 Spherical polar coordinates	p. 294
10.3 Functions of position	p. 296
10.4 Volume integrals	p. 299
10.5 The Laplacian operator	p. 304
10.6 Other coordinate systems	p. 307
10.7 Exercises	p. 312
11 First-order differential equations	p. 314
11.1 Concepts	p. 314
11.2 Solution of a differential equation	p. 315
11.3 Separable equations	p. 318
11.4 Separable equations in chemical kinetics	p. 322
11.5 First-order linear equations	p. 328
11.6 An example of linear equations in chemical kinetics	p. 330
11.7 Electric circuits	p. 332
11.8 Exercises	p. 334
12 Second-order differential equations. Constant coefficients	p. 337
12.1 Concepts	p. 337
12.2 Homogeneous linear equations	p. 337
12.3 The general solution	p. 340
12.4 Particular solutions	p. 344
12.5 The harmonic oscillator	p. 348
12.6 The particle in a one-dimensional box	p. 352
12.7 The particle in a ring	p. 356
12.8 Inhomogeneous linear equations	p. 359
12.9 Forced oscillations	p. 363
12.10 Exercises	p. 365
13 Second-order differential equations. Some special functions	p. 368
13.1 Concepts	p. 368
13.2 The power-series method	p. 369
13.3 The Frobenius method	p. 371
13.4 The Legendre equation	p. 375
13.5 The Hermite equation	p. 381
13.6 The Laguerre equation	p. 384
13.7 Bessel functions	p. 385
13.8 Exercises	p. 389
14 Partial differential equations	p. 391
14.1 Concepts	p. 391
14.2 General solutions	p. 392
14.3 Separation of variables	p. 393
14.4 The particle in a rectangular box	p. 395
14.5 The particle in a circular box	p. 398
14.6 The hydrogen atom	p. 401
14.7 The vibrating string	p. 410
14.8 Exercises	p. 413
15 Orthogonal expansions. Fourier analysis	p. 416
15.1 Concepts	p. 416
15.2 Orthogonal expansions	p. 416
15.3 Two expansions in Legendre polynomials	p. 421
15.4 Fourier series	p. 425
15.5 The vibrating string	p. 432
15.6 Fourier transforms	p. 433
15.7 Exercises	p. 441
16 Vectors	p. 444
16.1 Concepts	p. 444
16.2 Vector algebra	p. 445
16.3 Components of vectors	p. 448
16.4 Scalar differentiation of a vector	p. 453
16.5 The scalar (dot) product	p. 456
16.6 The vector (cross) product	p. 462
16.7 Scalar and vector fields	p. 466
16.8 The gradient of a scalar field	p. 467
16.9 Divergence and curl of a vector field	p. 469
16.10 Vector spaces	p. 471
16.11 Exercises	p. 471
17 Determinants	p. 474
17.1 Concepts	p. 474
17.2 Determinants of order 3	p. 476
17.3 The general case	p. 481
17.4 The solution of linear equations	p. 483
17.5 Properties of determinants	p. 488
17.6 Reduction to triangular form	p. 493
17.7 Alternating functions	p. 494
17.8 Exercises	p. 496
18 Matrices and linear transformations	p. 499
18.1 Concepts	p. 499
18.2 Some special matrices	p. 502
18.3 Matrix algebra	p. 505
18.4 The inverse matrix	p. 513
18.5 Linear transformations	p. 516
18.6 Orthogonal matrices and orthogonal transformations	p. 521
18.7 Symmetry operations	p. 524
18.8 Exercises	p. 529
19 The matrix eigenvalue problem	p. 532
19.1 Concepts	p. 532
19.2 The eigenvalue problem	p. 534
19.3 Properties of the eigenvectors	p. 537
19.4 Matrix diagonalization	p. 543
19.5 Quadratic forms	p. 546
19.6 Complex matrices	p. 551
19.7 Exercises	p. 555
20 Numerical methods	p. 558
20.1 Concepts	p. 558
20.2 Errors	p. 558
20.3 Solution of ordinary equations	p. 562
20.4 Interpolation	p. 566
20.5 Numerical integration	p. 573
20.6 Methods in linear algebra	p. 581
20.7 Gauss elimination for the solution of linear equations	p. 581
20.8 Gauss-Jordan elimination for the inverse of a matrix	p. 584
20.9 First-order differential equations	p. 585
20.10 Systems of differential equations	p. 590
20.11 Exercises	p. 592
21 Probability and statistics	p. 595
21.1 Concepts	p. 595
21.2 Descriptive statistics	p. 595
21.3 Frequency and probability	p. 601
21.4 Combinations of probabilities	p. 603
21.5 The binomial distribution	p. 604
21.6 Permutations and combinations	p. 607
21.7 Continuous distributions	p. 613
21.8 The Gaussian distribution	p. 615
21.9 More than one variable	p. 618
21.10 Least squares	p. 619
21.11 Sample statistics	p. 623
21.12 Exercises	p. 624
Appendix Standard integrals	p. 627
Solutions to exercises	p. 631
Index	p. 653

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