Mathematics for Engineers

Front Cover
Half Title Page
Title Page
Copyright Page
Dedication Page
Brief contents
Contents
Publisher’s acknowledgements
Preface
Using mathematical software packages
1 Arithmetic
	Block 1 Operations on numbers
	Block 2 Prime numbers and prime factorisation
	End of chapter exercises
2 Fractions
	Block 1 Introducing fractions
	Block 2 Operations on fractions
	End of chapter exercises
3 Decimal numbers
	Block 1 Introduction to decimal numbers
	Block 2 Significant figures
	End of chapter exercises
4 Percentage and ratio
	Block 1 Percentage
	Block 2 Ratio
	End of chapter exercises
5 Basic algebra
	Block 1 Mathematical notation and symbols
	Block 2 Indices
	Block 3 Simplification by collecting like terms
	Block 4 Removing brackets
	Block 5 Factorisation
	Block 6 Arithmetic of algebraic fractions
	Block 7 Formulae and transposition
	End of chapter exercises
6 Functions and mathematical models
	Block 1 Basic concepts of functions
	Block 2 The graph of a function
	Block 3 Composition of functions
	Block 4 One-to-one functions and inverse functions
	Block 5 Parametric representation of a function
	Block 6 Describing functions
	Block 7 The straight line
	Block 8 Common engineering functions
	Block 9 The equation of a circle
	End of chapter exercises
7 Polynomial equations, inequalities, partial fractions and proportionality
	Block 1 Solving linear equations
	Block 2 Solving quadratic equations
	Block 3 Factorising polynomial expressions and solving polynomial equations
	Block 4 Solving simultaneous equations
	Block 5 Solution of inequalities
	Block 6 Partial fractions
	Block 7 Proportionality
	End of chapter exercises
8 Logarithms and exponentials
	Block 1 The exponential function
	Block 2 Logarithms and their laws
	Block 3 Solving equations involving logarithms and exponentials
	Block 4 Applications of logarithms
	End of chapter exercises
9 Trigonometry
	Block 1 Angles
	Block 2 The trigonometrical ratios
	Block 3 The trigonometrical ratios in all quadrants
	Block 4 Trigonometrical functions and their graphs
	Block 5 Trigonometrical identities
	Block 6 Trigonometrical equations
	Block 7 Engineering waves
	End of chapter exercises
10 Further trigonometry
	Block 1 Pythagoras’s theorem and the solution of right-angled triangles
	Block 2 Solving triangles using the sine rule
	Block 3 Solving triangles using the cosine rule
	Block 4 Surveying
	Block 5 Resolution and resultant of forces
	End of chapter exercises
11 Complex numbers
	Block 1 Arithmetic of complex numbers
	Block 2 The Argand diagram and polar form of a complex number
	Block 3 The exponential form of a complex number
	Block 4 De Moivre’s theorem
	Block 5 Solving equations and finding roots of complex numbers
	Block 6 Phasors
	End of chapter exercises
12 Matrices and determinants
	Block 1 Introduction to matrices
	Block 2 Multiplication of matrices
	Block 3 Determinants
	Block 4 The inverse of a matrix
	Block 5 Computer graphics
	End of chapter exercises
13 Using matrices and determinants to solve equations
	Block 1 Cramer’s rule
	Block 2 Using the inverse matrix to solve simultaneous equations
	Block 3 Gaussian elimination
	Block 4 Eigenvalues and eigenvectors
	Block 5 Iterative techniques
	Block 6 Electrical networks
	End of chapter exercises
14 Vectors
	Block 1 Basic concepts of vectors
	Block 2 Cartesian components of vectors
	Block 3 The scalar product, or dot product
	Block 4 The vector product, or cross product
	Block 5 The vector equation of a line and a plane
	End of chapter exercises
15 Differentiation
	Block 1 Interpretation of a derivative
	Block 2 Using a table of derivatives
	Block 3 Higher derivatives
	End of chapter exercises
16 Techniques and applications of differentiation
	Block 1 The product rule and the quotient rule
	Block 2 The chain rule
	Block 3 Implicit differentiation
	Block 4 Parametric differentiation
	Block 5 Logarithmic differentiation
	Block 6 Tangents and normals
	Block 7 Maximum and minimum values of a function
	End of chapter exercises
17 Integration
	Block 1 Integration as differentiation in reverse
	Block 2 Definite integrals
	Block 3 The area bounded by a curve
	Block 4 Computational approaches to integration
	Block 5 Integration by parts
	Block 6 Integration by substitution
	Block 7 Integration using partial fractions
	Block 8 Integration of trigonometrical functions
	End of chapter exercises
18 Applications of integration
	Block 1 Integration as the limit of a sum
	Block 2 Volumes of revolution
	Block 3 Calculating centres of mass
	Block 4 Moment of inertia
	Block 5 The length of a curve and the area of a surface of revolution
	Block 6 The mean value and root-mean-square value of a function
	End of chapter exercises
19 Sequences and series
	Block 1 Sequences and series
	Block 2 Sums of whole numbers, their squares and cubes
	Block 3 Pascal’s triangle and the binomial theorem
	Block 4 Taylor, Maclaurin and other series
	End of chapter exercises
20 Differential equations
	Block 1 Basic concepts of differential equations
	Block 2 Separation of variables
	Block 3 Solving first-order linear equations using an integrating factor
	Block 4 Computational approaches to differential equations
	Block 5 Second-order linear constant-coefficient equations I
	Block 6 Second-order linear constant-coefficient equations II
	End of chapter exercises
21 Functions of more than one variable and partial differentiation
	Block 1 Functions of two independent variables, and their graphs
	Block 2 Partial differentiation
	Block 3 Higher-order derivatives
	Block 4 Partial differential equations
	Block 5 Stationary values of a function of two variables
	End of chapter exercises
22 The Laplace transform
	Block 1 The Laplace transform
	Block 2 The inverse Laplace transform
	Block 3 Solving differential equations using the Laplace transform
	End of chapter exercises
23 Statistics and probability
	Block 1 Data
	Block 2 Data averages
	Block 3 Variation of data
	Block 4 Elementary probability
	Block 5 Laws of probability
	Block 6 Probability distributions
	Block 7 The binomial distribution
	Block 8 The Poisson distribution
	Block 9 The normal distribution
	End of chapter exercises
24 An introduction to Fourier series and the Fourier transform
	Block 1 Periodic waveforms and their Fourier representation
	Block 2 Introducing the Fourier transform
	End of chapter exercises
Typical examination papers
Appendix 1: SI units and prefixes
Index
Back Cover