basic_engineering_mathematics0

Contents
vii
13.3 Graphical solution of linear and quadratic equations simultaneously 99
13.4 Graphical solution of cubic equations 100
Assignment 6 102
14. Logarithms 103
14.1 Introduction to logarithms 103
14.2 Laws of logarithms 103
14.3 Indicial equations 105
14.4 Graphs of logarithmic functions 106
15. Exponential functions 107
15.1 The exponential function 107
15.2 Evaluating exponential functions 107
15.3 The power series for e x 108
15.4 Graphs of exponential functions 110
15.5 Napierian logarithms 111
15.6 Evaluating Napierian logarithms 111
15.7 Laws of growth and decay 113
Assignment 7 116
16. Reduction of non-linear laws to linear-form 117
16.1 Determination of law 117
16.2 Determination of law involving logarithms 119
17. Graphs with logarithmic scales 124
17.1 Logarithmic scales 124
17.2 Graphs of the form y = ax n 124
17.3 Graphs of the form y = ab x 127
17.4 Graphs of the form y = ae kx 128
18. Geometry and triangles 131
18.1 Angular measurement 131
18.2 Types and properties of angles 132
18.3 Properties of triangles 134
18.4 Congruent triangles 136
18.5 Similar triangles 137
18.6 Construction of triangles 139
Assignment 8 141
19. Introduction to trigonometry 142
19.1 Trigonometry 142
19.2 The theorem of Pythagoras 142
19.3 Trigonometric ratios of acute angles 143
19.4 Solution of right-angled triangles 145
19.5 Angles of elevation and depression 147
19.6 Evaluating trigonometric ratios of any angles 148
20. Trigonometric waveforms 151
20.1 Graphs of trigonometric functions 151
20.2 Angles of any magnitude 152
20.3 The production of a sine and cosine wave 154