Understand Electrical and Electronics Maths (eBook)

Front Cover 1
Understand Electrical and Electronics Maths 4
Copyright Page 5
Contents 6
Preface 8
Symbols for mathematical operators 10
Symbols for equality and inequality 12
Part One - Basic Maths 14
Chapter 1. About numbers 16
Types of numbers 16
Factors 18
Highest common factor 19
Lowest common multiple 20
Factors of polynomials 21
Chapter 2. Quotients 25
Handling fractions 26
Algebraic fractions 29
Partial fractions 31
Chapter 3. Logs and other topics 36
Indices 36
Logarithms 38
Vectors 41
Chapter 4. Making sense of equations 46
Types of equations 47
Balancing equations 47
Changing the subject 50
Quadratic equations 52
Simultaneous equations 54
Expressing results 59
Chapter 5. Looking at graphs 61
Graph variables 62
Coordinates 63
Straight-line graphs 64
Gradient/intercept equation 65
Steepness 66
Testing a point 68
Distance between two points 68
Recognizing graphs 69
Graphs with log scales 74
Trig ratios 78
Other graphs 82
Important points 83
Functions 85
Chapter 6. From theory to practice 88
P.d. across a resistor 88
Resistance 89
Current through a resistor 89
Resistors in parallel 90
Currents in a resistor network 91
Potential divider 92
Flux density 94
Decibels 95
Induced emf 96
Alternating current 97
Phasors 98
Inductive impedance 98
Capacitative impedance 99
RLC series resonant circuit 100
Phase angle in RLC series circuit 101
Charging a capacitor 102
Part Two - Maths Topics 104
Chapter 7. Distance and direction 106
Types of coordinate 106
Polar coordinates 106
Circular motion 108
Vectors 109
Circular motion, vectors and sine waves 110
From sine waves to vectors 111
Rectangular to polar 113
Polar to rectangular 114
Chapter 8. Limits 116
Limits at zero 120
Limits at infinity 120
Using a calculator 121
Chapter 9. Rates of change 124
Pin-pointing the gradient 125
Simplifying the symbols 127
Finding dy/dx 128
A function from a function 130
Looking for tlie rules 130
Other symbols 131
Using the rules 132
Useful derivatives 134
Maximums and mínimums 137
The Chain Rule 140
Differentiation of a product 143
Differentiating a quotient 144
Partial differentials 145
Percentage changes 147
Rates of change 148
Chapter 10. Summing it up 151
Tidying up 153
Working in reverse 154
Standard integrals 155
Dealing with the constant of integration 156
Integrating ratios 160
Integration by substitution 160
More examples of substitution 162
Integrating by parts 163
Integration and averages 165
Integrating sine waves 167
Modified sine waves 168
Root mean square (rms) values 168
Chapter 11. Equations for actions 171
A simple model 171
Growth and decay 173
Solving the decay equation 174
First-order equations 176
More modelling 180
Second-order equations 183
Solving with positive discriminant 184
Solving with zero discriminant 185
Solving with negative discriminant 186
A second-order model 187
Chapter 12. Practical differentials 193
Euler's method 193
Operator D 198
Solving a differential equation 202
Imaginary roots 205
Higher-order equations 206
The Laplace transformation 208
Transforming differential equations 209
Inverse transformation 212
More transforming routines 218
Transforming integrals 219
Initial value 221
Final value 222
Chapter 13. Systematic solutions 225
Elimination in theory 225
Evaluating determinants 226
Solving equations by using determinants 227
Solving for three variables 229
Evaluating a determinant of third (or higher) order 231
Making it easier 234
Data tables 238
Describing a matrix 238
Working with matrices 239
Matrix multiplication 240
Order of multiplication 242
Identity matrix 243
The LED display problem again 244
The inverse of a 2 x 2 matrix 245
Finding the inverse of a 3x3 matrix 246
Testing the inverse 247
Another problem 248
Row equivalents 249
Chapter 14. Beyond the number line 253
Using the imagination 253
Working with j 254
The imaginary number line 255
Another approach 257
The algebra of complex numbers 258
Conjugate complex numbers 259
Division of complex numbers 260
Complex numbers and quadratic equations 261
Complex numbers and vectors 261
Polar form 262
Negative angles 264
Adding complex numbers in polar form 265
Multiplying in polar form 265
Dividing in polar form 266
Powers of complex numbers 266
Roots of complex numbers 267
Exponential form 268
Impedances in equations 272
Imaginary numbers solve real problems 275
Chapter 15. Analysing waveforms 281
Sine waves 282
Building the series 283
Converting the sines 284
Conditions 285
Finding the first term 286
Finding the cosine terms 288
Finding the sine terms 290
The final analysis 291
Fourier coefficients 291
Calculating coefficients 296
Symmetry 297
Rectified ac 300
Answers 305
Chapter 1 305
Chapter 2 306
Chapter 3 307
Chapter 4 309
Chapter 5 310
Chapter 7 313
Chapter 8 314
Chapter 9 314
Chapter 11 317
Chapter 13 320
Chapter 14 322
Chapter 15 323
Index 326