Mathematics Pocket Book for Engineers and Scientists

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