Mathematics for Engineers, 5th Edition By Anthony Croft, Robert Davison ( )

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 Pr ...

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