Chemistry Maths Book

ISBN-10: 0199205353
ISBN-13: 9780199205356
Edition: 2nd 2007 (Reprint)
List price: $65.00
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Description: 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,  More...

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Book details

List price: $65.00
Edition: 2nd
Copyright year: 2007
Publisher: Oxford University Press, Incorporated
Publication date: 4/7/2008
Binding: Paperback
Pages: 576
Size: 6.75" wide x 9.75" long x 1.25" tall
Weight: 1.430
Language: English

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 the subject. 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 of examples 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. Online Resource Centre: The Online Resource Centre features the following resources for registered adopters of the text: - Figures from the book in electronic format, ready to download - Full worked solutions to all end of chapter exercises

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

Numbers, variables, and units
Concepts
Real numbers
Factorization, factors, and factorials
Decimal representation of numbers
Variables
The algebra of real numbers
Complex numbers
Units
Exercises
Algebraic functions
Concepts
Graphical representation of functions
Factorization and simplification of expressions
Inverse functions
Polynomials
Rational functions
Partial fractions
Solution of simultaneous equations
Exercises
Transcendental functions
Concepts
Trigonometric functions
Inverse trigonometric functions
Trigonometric relations
Polar coordinates
The exponential function
The logarithmic function
Values of exponential and logarithmic functions
Hyperbolic functions
Exercises
Differentiation
Concepts
The process of differentiation
Continuity
Limits
Differentiation from first principles
Differentiation by rule
Implicit functions
Logarithmic differentiation
Successive differentiation
Stationary points
Linear and angular motion
The differential
Exercises
Integration
Concepts
The indefinite integral
The definite integral
The integral calculus
Uses of the integral calculus
Static properties of matter
Dynamics
Pressure-volume work
Exercises
Methods of integration
Concepts
The use of trigonometric relations
The method of substitution
Integration by parts
Reduction formulas
Rational integrands. The method of partial fractions
Parametric differentiation of integrals
Exercises
Sequences and series
Concepts
Sequences
Finite series
Infinite series
Tests of convergence
MacLaurin and Taylor series
Approximate values and limits
Operations with power series
Exercises
Complex numbers
Concepts
Algebra of complex numbers
Graphical representation
Complex functions
Euler's formula
Periodicity
Evaluation of integrals
Exercises
Functions of several variables
Concepts
Graphical representation
Partial differentiation
Stationary points
The total differential
Some differential properties
Exact differentials
Line integrals
Multiple integrals
The double integral
Change of variables
Exercises
Functions in 3 dimensions
Concepts
Spherical polar coordinates
Functions of position
Volume integrals
The Laplacian operator
Other coordinate systems
Exercises
First-order differential equations
Concepts
Solution of a differential equation
Separable equations
Separable equations in chemical kinetics
First-order linear equations
An example of linear equations in chemical kinetics
Electric circuits
Exercises
Second-order differential equations. Constant coefficients
Concepts
Homogeneous linear equations
The general solution
Particular solutions
The harmonic oscillator
The particle in a one-dimensional box
The particle in a ring
Inhomogeneous linear equations
Forced oscillations
Exercises
Second-order differential equations. Some special functions
Concepts
The power-series method
The Frobenius method
The Legendre equation
The Hermite equation
The Laguerre equation
Bessel functions
Exercises
Partial differential equations
Concepts
General solutions
Separation of variables
The particle in a rectangular box
The particle in a circular box
The hydrogen atom
The vibrating string
Exercises
Orthogonal expansions. Fourier analysis
Concepts
Orthogonal expansions
Two expansions in Legendre polynomials
Fourier series
The vibrating string
Fourier transforms
Exercises
Vectors
Concepts
Vector algebra
Components of vectors
Scalar differentiation of a vector
The scalar (dot) product
The vector (cross) product
Scalar and vector fields
The gradient of a scalar field
Divergence and curl of a vector field
Vector spaces
Exercises
Determinants
Concepts
Determinants of order 3
The general case
The solution of linear equations
Properties of determinants
Reduction to triangular form
Alternating functions
Exercises
Matrices and linear transformations
Concepts
Some special matrices
Matrix algebra
The inverse matrix
Linear transformations
Orthogonal matrices and orthogonal transformations
Symmetry operations
Exercises
The matrix eigenvalue problem
Concepts
The eigenvalue problem
Properties of the eigenvectors
Matrix diagonalization
Quadratic forms
Complex matrices
Exercises
Numerical methods
Concepts
Errors
Solution of ordinary equations
Interpolation
Numerical integration
Methods in linear algebra
Gauss elimination for the solution of linear equations
Gauss-Jordan elimination for the inverse of a matrix
First-order differential equations
Systems of differential equations
Exercises
Probability and statistics
Concepts
Descriptive statistics
Frequency and probability
Combinations of probabilities
The binomial distribution
Permutations and combinations
Continuous distributions
The Gaussian distribution
More than one variable
Least squares
Sample statistics
Exercises
Standard integrals
Solutions to exercises
Index

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