The chemistry maths book

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The chemistry maths book / Erich Steiner

版:: 2nd ed
資料種別:: 図書
出版情報:: Oxford ; New York : Oxford University Press, 2008
形態:: xii, 668 p. ; 25 cm
著者名:: Steiner, Erich, 1937- <DA10429980>
ISBN:: 9780199205356 [0199205353] (: pbk)
書誌ID:: BB23261649

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注記:

Includes index
"First published 1996"--T.p. verso

主題:

Chemistry--Mathematics; Mathematics

言語:

英語

目次情報:

Numbers, variables, and units / 1：

Concepts / 1.1：

Real numbers / 1.2：

Factorization, factors, and factorials / 1.3：

Decimal representation of numbers / 1.4：

Variables / 1.5：

The algebra of real numbers / 1.6：

Complex numbers / 1.7：

Units / 1.8：

Exercises / 1.9：

Algebraic functions / 2：

Graphical representation of functions / 2.1：

Factorization and simplification of expressions / 2.3：

Inverse functions / 2.4：

Polynomials / 2.5：

Rational functions / 2.6：

Partial fractions / 2.7：

Solution of simultaneous equations / 2.8：

Transcendental functions / 2.9：

Trigonometric functions / 3.1：

Inverse trigonometric functions / 3.3：

Trigonometric relations / 3.4：

Polar coordinates / 3.5：

The exponential function / 3.6：

The logarithmic function / 3.7：

Values of exponential and logarithmic functions / 3.8：

Hyperbolic functions / 3.9：

Differentiation / 3.10：

The process of differentiation / 4.1：

Continuity / 4.3：

Limits / 4.4：

Differentiation from first principles / 4.5：

Differentiation by rule / 4.6：

Implicit functions / 4.7：

Logarithmic differentiation / 4.8：

Successive differentiation / 4.9：

Stationary points / 4.10：

Linear and angular motion / 4.11：

The differential / 4.12：

Integration / 4.13：

The indefinite integral / 5.1：

The definite integral / 5.3：

The integral calculus / 5.4：

Uses of the integral calculus / 5.5：

Static properties of matter / 5.6：

Dynamics / 5.7：

Pressure-volume work / 5.8：

Methods of integration / 5.9：

The use of trigonometric relations / 6.1：

The method of substitution / 6.3：

Integration by parts / 6.4：

Reduction formulas / 6.5：

Rational integrands. The method of partial fractions / 6.6：

Parametric differentiation of integrals / 6.7：

Sequences and series / 6.8：

Sequences / 7.1：

Finite series / 7.3：

Infinite series / 7.4：

Tests of convergence / 7.5：

MacLaurin and Taylor series / 7.6：

Approximate values and limits / 7.7：

Operations with power series / 7.8：

Algebra of complex numbers / 7.9：

Graphical representation / 8.3：

Complex functions / 8.4：

Euler's formula / 8.5：

Periodicity / 8.6：

Evaluation of integrals / 8.7：

Functions of several variables / 8.8：

Partial differentiation / 9.1：

The total differential / 9.4：

Some differential properties / 9.6：

Exact differentials / 9.7：

Line integrals / 9.8：

Multiple integrals / 9.9：

The double integral / 9.10：

Change of variables / 9.11：

Functions in 3 dimensions / 9.12：

Spherical polar coordinates / 10.1：

Functions of position / 10.3：

Volume integrals / 10.4：

The Laplacian operator / 10.5：

Other coordinate systems / 10.6：

First-order differential equations / 10.7：

Solution of a differential equation / 11.1：

Separable equations / 11.3：

Separable equations in chemical kinetics / 11.4：

First-order linear equations / 11.5：

An example of linear equations in chemical kinetics / 11.6：

Electric circuits / 11.7：

Second-order differential equations. Constant coefficients / 11.8：

Homogeneous linear equations / 12.1：

The general solution / 12.3：

Particular solutions / 12.4：

The harmonic oscillator / 12.5：

The particle in a one-dimensional box / 12.6：

The particle in a ring / 12.7：

Inhomogeneous linear equations / 12.8：

Forced oscillations / 12.9：

Second-order differential equations. Some special functions / 12.10：

The power-series method / 13.1：

The Frobenius method / 13.3：

The Legendre equation / 13.4：

The Hermite equation / 13.5：

The Laguerre equation / 13.6：

Bessel functions / 13.7：

Partial differential equations / 13.8：

General solutions / 14.1：

Separation of variables / 14.3：

The particle in a rectangular box / 14.4：

The particle in a circular box / 14.5：

The hydrogen atom / 14.6：

The vibrating string / 14.7：

Orthogonal expansions. Fourier analysis / 14.8：

Orthogonal expansions / 15.1：

Two expansions in Legendre polynomials / 15.3：

Fourier series / 15.4：

Fourier transforms / 15.5：

Vectors / 15.7：

Vector algebra / 16.1：

Components of vectors / 16.3：

Scalar differentiation of a vector / 16.4：

The scalar (dot) product / 16.5：

The vector (cross) product / 16.6：

Scalar and vector fields / 16.7：

The gradient of a scalar field / 16.8：

Divergence and curl of a vector field / 16.9：

Vector spaces / 16.10：

Determinants / 16.11：

Determinants of order 3 / 17.1：

The general case / 17.3：

The solution of linear equations / 17.4：

Properties of determinants / 17.5：

Reduction to triangular form / 17.6：

Alternating functions / 17.7：

Matrices and linear transformations / 17.8：

Some special matrices / 18.1：

Matrix algebra / 18.3：

The inverse matrix / 18.4：

Linear transformations / 18.5：

Orthogonal matrices and orthogonal transformations / 18.6：

Symmetry operations / 18.7：

The matrix eigenvalue problem / 18.8：

The eigenvalue problem / 19.1：

Properties of the eigenvectors / 19.3：

Matrix diagonalization / 19.4：

Quadratic forms / 19.5：

Complex matrices / 19.6：

Numerical methods / 19.7：

Errors / 20.1：

Solution of ordinary equations / 20.3：

Interpolation / 20.4：

Numerical integration / 20.5：

Methods in linear algebra / 20.6：

Gauss elimination for the solution of linear equations / 20.7：

Gauss-Jordan elimination for the inverse of a matrix / 20.8：

Systems of differential equations / 20.9：

Probability and statistics / 20.11：

Descriptive statistics / 21.1：

Frequency and probability / 21.3：

Combinations of probabilities / 21.4：

The binomial distribution / 21.5：

Permutations and combinations / 21.6：

Continuous distributions / 21.7：

The Gaussian distribution / 21.8：

More than one variable / 21.9：

Least squares / 21.10：

Sample statistics / 21.11：

Standard integrals / 21.12：

Solutions to exercises

Index

Numbers, variables, and units / 1：

Concepts / 1.1：

Real numbers / 1.2：

Factorization, factors, and factorials / 1.3：

Decimal representation of numbers / 1.4：

Variables / 1.5：

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