Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB

Header......Page 1
Cover......Page 2
Title Page......Page 3
About the Author......Page 5
Introduction......Page 6
Contents......Page 9
1.1 - Getting Started......Page 15
1.2 - Basic Algebraic Operations and Functions......Page 16
1.3 - Plotting Points......Page 17
1.4 - M-files......Page 20
1.5 - MATLAB Simple Programming......Page 22
1.6 - Array Operations......Page 24
1.7 - Curve and Surface Plotting......Page 25
1.8 - Polar Plots......Page 34
1.9 - Animation......Page 36
1.10 - Histograms......Page 37
1.11 - Printing and Saving Work in MATLAB......Page 38
1.12 - MATLAB Commands Review......Page 39
2.1 - Simple Linear Forms......Page 41
2.2 - Amortization......Page 43
2.3 - An Interative Geometric Construct: The Koch Curve......Page 45
2.4 - Solution of Linear Constant Coefficients Difference Equations......Page 48
2.5 - Convolution-Summation of a First-Order System with Constant Coefficients......Page 54
2.6 - General First-Order Linear Difference Equations......Page 57
2.7 - Nonlinear Difference Equations......Page 59
2.8 - Fractals and Computer Art......Page 62
2.9 - Generation of Special Functions from Their Recursion Relations*......Page 67
3.1 - Function Files......Page 71
3.2 - Examples with Affine Functions......Page 72
3.3 - Examples with Quadratic Functions......Page 78
3.4 - Examples with Polynominal Functions......Page 79
3.5 - Examples with the Trigonometric Functions......Page 80
3.6 - Examples with the Logarithmic Function......Page 81
3.7 - Examples with the Exponential Function......Page 84
3.8 - Examples with the Hyberbolic Functions and Their Inverses......Page 86
3.9 - Commonly Used Signal Processing Functions......Page 87
3.10 - Animation of a Moving Rectangular Pulse......Page 94
3.11 - MATLAB Commands Review......Page 95
4.1 - Limits of Indeterminate Forms......Page 96
4.2 - Derivative of a Function......Page 98
4.3 - Infinite Sums......Page 100
4.4 - Numerical Integration......Page 102
4.5 - A Better Numerical Differentiator......Page 106
4.6 - A Better Numerical Integrator: Simpson's Rule......Page 110
4.7 - Numerical Solutions of Ordinary Differential Equations......Page 117
4.8 - MATLAB Commands Review......Page 135
5.1 - Finding the Real Roots of a Function......Page 136
5.2 - Roots of a Polynominal......Page 147
5.3 - Optimization Methods......Page 148
5.4 - MATLAB Commands Review......Page 157
6.2 - The Basics......Page 158
6.3 - Complex Conjugation and Division......Page 162
6.4 - Polar Form of Complex Numbers......Page 165
6.5 - Analytical Solutions of Constant Coefficients ODE......Page 172
6.6 - Phasors......Page 177
6.7 - Interference and Diffraction of Electromagnetic Waves......Page 181
6.8 - Solving ac Circuits with Phasors: The Impedance Method......Page 185
6.9 - Transfer Function for a Difference Equation with Constant Coefficients*......Page 190
6.10 - MATLAB Commands Review......Page 200
7.1 - Vectors in Two Dimensions (2-D)......Page 201
7.2 - Dot (or Scalar) Product......Page 205
7.3 - Components, Direction Cosines, and Projections......Page 209
7.4 - The Dirac Notation and Some General Theorems*......Page 210
7.5 - Cross Product and Scalar Triple Product*......Page 215
7.6 - Vector Valued Functions......Page 219
7.7 - Line Integral......Page 222
7.8 - Infinite Dimensional Vector Spaces*......Page 223
7.9 - MATLAB Commands Review......Page 234
8.1 - Setting up Matrices......Page 235
8.2 - Adding Matrices......Page 241
8.4 - Multiplying Matrices......Page 242
8.5 - Inverse of a Matrix......Page 244
8.6 - Solving a System of Linear Equations......Page 246
8.7 - Application of Matrix Methods......Page 250
8.8 - Eigenvalues and Eigenvectors*......Page 260
8.9 - The Cayley-Hamilton and Other Analytical Techniques*......Page 265
8.10 - Special Classes of Matrices*......Page 279
8.11 - MATLAB Commands Review......Page 289
9.1 - Two-Dimensional (2-D) Geometric Transforms......Page 291
9.2 - Homogeneous Coordinates......Page 296
9.3 - Geometrical Manipulation of Images......Page 299
9.4 - Lorentz Transformation*......Page 303
9.5 - MATLAB Commands Review......Page 307
10.1 - Introduction......Page 308
10.2 - Basics......Page 309
10.3 - Addition Laws for Probabilities......Page 314
10.4 - Conditional Probability......Page 318
10.5 - Repeated Trials......Page 323
10.6 - The Poisson and the Normal Distributions......Page 326
S.1 - Affine Functions......Page 332
S.2 - Quadratic Functions......Page 333
S.4 - Trigonometric Functions......Page 338
S.6 - The Natural Logarithmic Function......Page 340
S.7 - The Exponential Function......Page 341
S.8 - The Hyberbolic Functions......Page 342
S.9 - The Inverse Hyberbolic Functions......Page 344
Sum of Integers and Their Powers......Page 346
Taylor's Series......Page 347
Relation of Trigonometric and Hyberbolic Functions......Page 348
Expansion of Elementary Functions in Power Series......Page 349