This compendium of essential formulae, definitions, tables and general information provides the mathematical information required by engineering students, technicians, scientists and professionals in day-to-day engineering practice. A practical and versatile reference source, now in its fifth edition, the layout has been changed and streamlined to ensure the information is even more quickly and readily available - making it a handy companion on-site, in the office as well as for academic study. It also acts as a practical revision guide for those undertaking degree courses in engineering and science, and for BTEC Nationals, Higher Nationals and NVQs, where mathematics is an underpinning requirement of the course.
All the essentials of engineering mathematics - from algebra, geometry and trigonometry to logic circuits, differential equations and probability - are covered, with clear and succinct explanations and illustrated with over 300 line drawings and 500 worked examples based in real-world application. The emphasis throughout the book is on providing the practical tools needed to solve mathematical problems quickly and efficiently in engineering contexts. John Bird's presentation of this core material puts all the answers at your fingertips.
Author(s): John Bird
Edition: 5
Publisher: Routledge
Year: 2020
Language: English
Pages: xiv+556
Cover
Title Page
Copyright Page
Table of Contents
Preface
Section 1: Engineering conversions, constants and symbols
Chapter 1: General conversions and the Greek alphabet
Chapter 2: Basic SI units, derived units and common prefixes
Chapter 3: Some physical and mathematical constants
Chapter 4: Recommended mathematical symbols
Chapter 5: Symbols for physical quantities
Section 2: Some algebra topics
Chapter 6: Introduction to algebra
Chapter 7: Polynomial division
Chapter 8: The factor theorem
Chapter 9: The remainder theorem
Chapter 10: Continued fractions
Chapter 11: Solving simple equations
Chapter 12: Transposing formulae
Chapter 13: Solving simultaneous equations
Chapter 14: Solving quadratic equations by factorising
Chapter 15: Solving quadratic equations by completing the square
Chapter 16: Solving quadratic equations by formula
Chapter 17: Logarithms
Chapter 18: Exponential functions
Chapter 19: Napierian logarithms
Chapter 20: Hyperbolic functions
Chapter 21: Partial fractions
Section 3: Some number topics
Chapter 22: Simple number sequences
Chapter 23: Arithmetic progressions
Chapter 24: Geometric progressions
Chapter 25: Inequalities
Chapter 26: The binomial series
Chapter 27: Maclaurin’s theorem
Chapter 28: Limiting values – L’Hopital’s rule
Chapter 29: Solving equations by iterative methods (1) – the bisection method
Chapter 30: Solving equations by iterative methods (2) – an algebraic method of successive approximations
Chapter 31: Solving equations by iterative methods (3) – the Newton-Raphson method
Chapter 32: Computer numbering systems
Section 4: Areas and volumes
Chapter 33: Area of plane figures
Chapter 34: Circles
Chapter 35: Volumes and surface areas of regular solids
Chapter 36: Volumes and surface areas of frusta of pyramids and cones
Chapter 37: The frustum and zone of a sphere
Chapter 38: Areas and volumes of irregular figures and solids
Chapter 39: The mean or average value of a waveform
Section 5: Geometry and trigonometry
Chapter 40: Types and properties of angles
Chapter 41: Properties of triangles
Chapter 42: The theorem of Pythagoras
Chapter 43: Trigonometric ratios of acute angles
Chapter 44: Evaluating trigonometric ratios
Chapter 45: Fractional and surd forms of trigonometric ratios
Chapter 46: Solution of right-angled triangles
Chapter 47: Cartesian and polar co-ordinates
Chapter 48: Sine and cosine rules and areas of any triangle
Chapter 49: Graphs of trigonometric functions
Chapter 50: Angles of any magnitude
Chapter 51: Sine and cosine waveforms
Chapter 52: Trigonometric identities and equations
Chapter 53: The relationship between trigonometric and hyperbolic functions
Chapter 54: Compound angles
Section 6: Graphs
Chapter 55: The straight-line graph
Chapter 56: Determination of law
Chapter 57: Graphs with logarithmic scales
Chapter 58: Graphical solution of simultaneous equations
Chapter 59: Quadratic graphs
Chapter 60: Graphical solution of cubic equations
Chapter 61: Polar curves
Chapter 62: The ellipse and hyperbola
Chapter 63: Graphical functions
Section 7: Complex numbers
Chapter 64: General complex number formulae
Chapter 65: Cartesian form of a complex number
Chapter 66: Polar form of a complex number
Chapter 67: Applications of complex numbers
Chapter 68: De Moivre’s theorem
Chapter 69: Exponential form of a complex number
Section 8: Vectors
Chapter 70: Scalars and vectors
Chapter 71: Vector addition
Chapter 72: Resolution of vectors
Chapter 73: Vector subtraction
Chapter 74: Relative velocity
Chapter 75: i, j, k notation
Chapter 76: Combination of two periodic functions
Chapter 77: The scalar product of two vectors
Chapter 78: Vector products
Section 9: Matrices and determinants
Chapter 79: Addition, subtraction and multiplication of matrices
Chapter 80: The determinant and inverse of a 2 by 2 matrix
Chapter 81: The determinant of a 3 by 3 matrix
Chapter 82: The inverse of a 3 by 3 matrix
Chapter 83: Solution of simultaneous equations by matrices
Chapter 84: Solution of simultaneous equations by determinants
Chapter 85: Solution of simultaneous equations using Cramer’s rule
Chapter 86: Solution of simultaneous equations using Gaussian elimination
Chapter 87: Eigenvalues and eigenvectors
Section 10: Boolean algebra and logic circuits
Chapter 88: Boolean algebra and switching circuits
Chapter 89: Simplifying Boolean expressions
Chapter 90: Laws and rules of Boolean algebra
Chapter 91: De Morgan’s laws
Chapter 92: Karnaugh maps
Chapter 93: Logic circuits and gates
Chapter 94: Universal logic gates
Section 11: Differential calculus and its applications
Chapter 95: Common standard derivatives
Chapter 96: Products and quotients
Chapter 97: Function of a function
Chapter 98: Successive differentiation
Chapter 99: Differentiation of hyperbolic functions
Chapter 100: Rates of change using differentiation
Chapter 101: Velocity and acceleration
Chapter 102: Turning points
Chapter 103: Tangents and normals
Chapter 104: Small changes using differentiation
Chapter 105: Parametric equations
Chapter 106: Differentiating implicit functions
Chapter 107: Differentiation of logarithmic functions
Chapter 108: Differentiation of inverse trigonometric functions
Chapter 109: Differentiation of inverse hyperbolic functions
Chapter 110: Partial differentiation
Chapter 111: Total differential
Chapter 112: Rates of change using partial differentiation
Chapter 113: Small changes using partial differentiation
Chapter 114: Maxima, minima and saddle points of functions of two variables
Section 12: Integral calculus and its applications
Chapter 115: Standard integrals
Chapter 116: Non-standard integrals
Chapter 117: Integration using algebraic substitutions
Chapter 118: Integration using trigonometric and hyperbolic substitutions
Chapter 119: Integration using partial fractions
Chapter 120: The t = tan θ/2 substitution
Chapter 121: Integration by parts
Chapter 122: Reduction formulae
Chapter 123: Double and triple integrals
Chapter 124: Numerical integration
Chapter 125: Area under and between curves
Chapter 126: Mean or average values
Chapter 127: Root mean square values
Chapter 128: Volumes of solids of revolution
Chapter 129: Centroids
Chapter 130: Theorem of Pappus
Chapter 131: Second moments of area
Section 13: Differential equations
Chapter 132: The solution of equations of the form dy/dx = f(x)
Chapter 133: The solution of equations of the form dy/dx = f(y)
Chapter 134: The solution of equations of the form dy/dx = f(x).f(y)
Chapter 135: Homogeneous first order differential equations
Chapter 136: Linear first order differential equations
Chapter 137: Numerical methods for first order differential equations (1) – Euler’s method
Chapter 138: Numerical methods for first order differential equations (2) – Euler-Cauchy method
Chapter 139: Numerical methods for first order differential equations (3) – Runge-Kutta method
Chapter 140: Second order differential equations of the form ad2y/dx2 + bdy/dx + cy = 0
Chapter 141: Second order differential equations of the form a ad2y/dx2 + bdy/dx + cy = f(x)
Chapter 142: Power series methods of solving ordinary differential equations (1) – Leibniz theorem
Chapter 143: Power series methods of solving ordinary differential equations (2) – Leibniz-Maclaurin method
Chapter 144: Power series methods of solving ordinary differential equations (3) – Frobenius method
Chapter 145: Power series methods of solving ordinary differential equations (4) – Bessel’s equation
Chapter 146: Power series methods of solving ordinary differential equations (5) – Legendre’s equation and Legendre’s polynomials
Chapter 147: Power series methods of solving ordinary differential equations (6) – Rodrigue’s formula
Chapter 148: Solution of partial differential equations (1) – by direct integration
Chapter 149: Solution of partial differential equations (2) – the wave equation
Chapter 150: Solution of partial differential equations (3) – the heat conduction equation
Chapter 151: Solution of partial differential equations (4) – Laplace’s equation
Section 14: Laplace transforms
Chapter 152: Standard Laplace transforms
Chapter 153: The initial and final value theorems
Chapter 154: Inverse Laplace transforms
Chapter 155: Poles and zeros
Chapter 156: The Laplace transform of the Heaviside function
Chapter 157: Solving differential equations using Laplace transforms
Chapter 158: Solving simultaneous differential equations using Laplace transforms
Section 15: Z-transforms
Chapter 159: Sequences
Chapter 160: Properties of z-transforms
Chapter 161: Inverse z-transforms
Chapter 162: Using z-transforms to solve difference equations
Section 16: Fourier series
Chapter 163: Fourier series for periodic functions of period 2π
Chapter 164: Fourier series for a non-periodic function over period 2π
Chapter 165: Even and odd functions
Chapter 166: Half range Fourier series
Chapter 167: Expansion of a periodic function of period L
Chapter 168: Half-range Fourier series for functions defined over range L
Chapter 169: The complex or exponential form of a Fourier series
Chapter 170: A numerical method of harmonic analysis
Chapter 171: Complex waveform considerations
Section 17: Statistics and probability
Chapter 172: Presentation of ungrouped data
Chapter 173: Presentation of grouped data
Chapter 174: Measures of central tendency
Chapter 175: Quartiles, deciles and percentiles
Chapter 176: Probability
Chapter 177: Permutations and combinations
Chapter 178: Bayes’ theorem
Chapter 179: The binomial distribution
Chapter 180: The Poisson distribution
Chapter 181: The normal distribution
Chapter 182: Linear correlation
Chapter 183: Linear regression
Chapter 184: Sampling and estimation theories
Chapter 185: Chi-square values
Chapter 186: The sign test
Chapter 187: Wilcoxon signed-rank test
Chapter 188: The Mann-Whitney test
Index
