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1. TABLE OF CONTENTS

1. TABLE OF CONTENTS 1.1
2. ECONOMIC JUSTIFICATION 1.5
3. STATISTICS 1.8
3.1 DATA DISTRIBUTIONS 1.8
4. PROBABILITY 1.21
4.1 DISCRETE DISTRIBUTIONS 1.23
5. PETRI NETS 1.30
6. CURVES, SURFACES, VOLUMES AND SPLINES 1.44
6.1 INTRODUCTION 1.44
6.2 LINES/CURVES 1.45
6.3 SURFACE PATCHES 1.58
6.4 REFERENCES 1.62
6.5 PRACTICE PROBLEMS 1.62
7. DYNAMIC SYSTEM MODELLING AND CONTROL 1.64
7.1 INTRODUCTION 1.64
7.2 MODELING 1.64
8. TRANSLATION 1.65
8.1 MATHEMATICAL PROPERTIES 1.65
8.2 SYSTEM EXAMPLES 1.78
8.3 PRACTICE PROBLEMS 1.84
9. ROTATION 1.86
9.1 MATHEMATICAL ELEMENTS 1.86
9.2 SYSTEM EXAMPLES 1.93
9.3 PRACTICE PROBLEMS 1.96
10. ELECTRICAL COMPONENTS 1.99
10.1 MATHEMATICAL PROPERTIES 1.99
10.2 EXAMPLE SYSTEMS 1.108
10.3 PRACTICE PROBLEMS 1.110
11. ELECTROMECHANICAL SYSTEMS 1.115
11.1 MATHEMATICAL PROPERTIES 1.115
11.2 EXAMPLE SYSTEMS 1.116
11.3 PRACTICE PROBLEMS 1.122
12. THERMAL SYSTEMS 1.123
12.1 MATHEMATICAL PROPERTIES 1.123
12.2 EXAMPLE SYSTEMS 1.126
12.3 PRACTICE PROBLEMS 1.129
13. FLUID SYSTEMS 1.130
13.1 MATHEMATICAL PROPERTIES 1.130
13.2 EXAMPLE SYSTEMS 1.136
13.3 PRACTICE PROBLEMS 1.137
14. STANDARD MODEL FORMS 1.138
14.1 STATE VARIABLE EQUATIONS 1.138
14.2 INPUT-OUTPUT EQUATIONS 1.154
14.3 PRACTICE PROBLEMS 1.156
15. SYSTEM RESPONSES 1.163
15.1 FIRST ORDER STEP RESPONSE 1.163
15.2 SECOND ORDER STEP RESPONSE 1.166
15.3 OTHER RESPONSES 1.169
15.4 RESPONSE ANALYSIS 1.170
15.5 STEADY STATE - EQUILIBRIUM 1.170
15.6 PRACTICE PROBLEMS 1.171
16. LAPLACE TRANSFER FUNCTIONS 1.173
16.1 THE LAPLACE TRANSFORM 1.173
16.2 MODELING MECHANICAL SYSTEMS 1.179
16.3 MODELING ELECTRICAL SYSTEMS 1.180
16.4 USING LAPLACE TRANSFORMS 1.182
16.5 FOURIER TRANSFORMS FOR STEADY STATE ANALYSIS 1.200
16.6 BODE PLOTS 1.203
16.7 ROOT LOCUS ANALYSIS 1.209
16.8 A MAP OF TECHNIQUES FOR LAPLACE ANALYSIS 1.212
16.9 VIBRATIONS 1.213
16.10 SIGNAL SPECTRUMS 1.214
16.11 NON-LINEAR ELEMENTS 1.215
16.12 PRACTICE PROBLEMS 1.216
16.13 MORE PRACTICE PROBLEMS 1.222
16.14 LOG SCALE GRAPH PAPER 1.224
16.15 REFERENCES 1.227
17. DISCRETE CONTROL SYSTEMS 1.228
17.1 SAMPLES AS IMPULSE FUNCTION 1.228
17.2 INTRODUCTION TO Z-TRANSFORM 1.230
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