FM-H8152.tex 19/7/2006 18: 59 Page vi
vi CONTENTS9 Solving equations by iterative methods 769.1 Introduction to iterative methods 76
9.2 The bisection method 76
9.3 An algebraic method of successive
approximations 80
9.4 The Newton-Raphson method 8310 Computer numbering systems 8610.1 Binary numbers 86
10.2 Conversion of binary to denary 86
10.3 Conversion of denary to binary 87
10.4 Conversion of denary to binary
via octal 88
10.5 Hexadecimal numbers 9011 Boolean algebra and logic circuits 9411.1 Boolean algebra and switching
circuits 94
11.2 Simplifying Boolean expressions 99
11.3 Laws and rules of Boolean algebra 99
11.4 De Morgan’s laws 101
11.5 Karnaugh maps 102
11.6 Logic circuits 106
11.7 Universal logic gates 110Assignment 3 114Section B: Geometry and
trigonometry 11512 Introduction to trigonometry 11512.1 Trigonometry 115
12.2 The theorem of Pythagoras 115
12.3 Trigonometric ratios of acute
angles 116
12.4 Solution of right-angled triangles 118
12.5 Angles of elevation and depression 119
12.6 Evaluating trigonometric ratios 121
12.7 Sine and cosine rules 124
12.8 Area of any triangle 125
12.9 Worked problems on the solution
of triangles and finding their areas 125
12.10 Further worked problems on
solving triangles and finding
their areas 126
12.11 Practical situations involving
trigonometry 128
12.12 Further practical situations
involving trigonometry 13013 Cartesian and polar co-ordinates 13313.1 Introduction 133
13.2 Changing from Cartesian into polar
co-ordinates 133
13.3 Changing from polar into Cartesian
co-ordinates 135
13.4 Use ofR→PandP→Rfunctions
on calculators 13614 The circle and its properties 13714.1 Introduction 137
14.2 Properties of circles 137
14.3 Arc length and area of a sector 138
14.4 Worked problems on arc length and
sector of a circle 139
14.5 The equation of a circle 140
14.6 Linear and angular velocity 142
14.7 Centripetal force 144Assignment 4 14615 Trigonometric waveforms 14815.1 Graphs of trigonometric functions 148
15.2 Angles of any magnitude 148
15.3 The production of a sine and
cosine wave 151
15.4 Sine and cosine curves 152
15.5 Sinusoidal formAsin (ωt±α) 157
15.6 Harmonic synthesis with complex
waveforms 16016 Trigonometric identities and equations 16616.1 Trigonometric identities 166
16.2 Worked problems on trigonometric
identities 166
16.3 Trigonometric equations 167
16.4 Worked problems (i) on
trigonometric equations 168
16.5 Worked problems (ii) on
trigonometric equations 169
16.6 Worked problems (iii) on
trigonometric equations 170
16.7 Worked problems (iv) on
trigonometric equations 17117 The relationship between trigonometric and
hyperbolic functions 17317.1 The relationship between
trigonometric and hyperbolic
functions 173
17.2 Hyperbolic identities 174