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Taylor & Francis
Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB / Edition 2

Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB / Edition 2

by Jamal T. Manassah
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  • Product Details

    ISBN-13: 2900849374257
    Publisher: Taylor & Francis
    Publication date: 08/11/2006
    Edition description: REV
    Pages: 368
    Product dimensions: 6.00(w) x 1.25(h) x 9.00(d)

    Table of Contents

    1.Introduction to MATLAB and Its Graphics Capabilities1
    1.1Getting Started1
    1.2Basic Algebraic Operations and Functions2
    1.3Plotting Points3
    1.3.1Axes Commands5
    1.3.2Labeling a Graph6
    1.3.3Plotting a Point in 3-D6
    1.5MATLAB Simple Programming8
    1.5.1Iterative Loops8
    1.5.2If-Else-End Structures8
    1.6Array Operations10
    1.7Curve and Surface Plotting11
    1.7.1x-y Parametric Plot12
    1.7.2More Parametric Plots in 2-D13
    1.7.3Plotting a 3-D Curve17
    1.7.4Plotting a 3-D Surface18
    1.8Polar Plots20
    1.11Printing and Saving Work in MATLAB24
    1.12MATLAB Commands Review25
    2.Difference Equations27
    2.1Simple Linear Forms27
    2.3An Iterative Geometric Construct: The Koch Curve31
    2.4Solution of Linear Constant Coefficients Difference Equations34
    2.4.1Homogeneous Solution34
    2.4.2Particular Solution36
    2.4.3General Solution37
    2.5Convolution-Summation of a First-Order System with Constant Coefficients40
    2.6General First-Order Linear Difference Equations43
    2.7Nonlinear Difference Equations45
    2.7.1Computing Irrational Numbers45
    2.7.2The Logistic Equation46
    2.8Fractals and Computer Art48
    2.8.1Mira's Model49
    2.8.2Henon's Model51
    2.9Generation of Special Functions from Their Recursion Relations53
    3.Elementary Functions and Some of Their Uses57
    3.1Function Files57
    3.2Examples with Affine Functions58
    3.3Examples with Quadratic Functions64
    3.4Examples with Polynomial Functions65
    3.5Examples with Trigonometric Functions66
    3.6Examples with the Logarithmic Function67
    3.6.1Ideal Coaxial Capacitor67
    3.6.2The Decibel Scale68
    3.7Examples with the Exponential Function70
    3.8Examples with the Hyperbolic Functions and Their Inverses72
    3.8.1Capacitance of Two Parallel Wires72
    3.9Commonly Used Signal Processing Functions73
    3.10Animation of a Moving Rectangular Pulse80
    3.11MATLAB Commands Review81
    4.Numerical Differentiation, Integration, and Solutions of Ordinary Differential Equations83
    4.1Limits of Indeterminate Forms83
    4.2Derivative of a Function85
    4.3Infinite Sums87
    4.4Numerical Integration89
    4.5A Better Numerical Differentiator93
    4.6A Better Numerical Integrator: Simpson's Rule97
    4.7Numerical Solutions of Ordinary Differential Equations104
    4.7.1First-Order Iterator106
    4.7.2Higher-Order Iterators: The Runge-Kutta Method112
    4.7.3MATLAB ODE Solvers116
    4.8MATLAB Commands Review122
    5.Root Solving and Optimization Methods123
    5.1Finding the Real Roots of a Function123
    5.1.1Graphical Method123
    5.1.2Numerical Methods124
    5.1.3MATLAB fsolve and fzero Built-in Functions130
    5.2Roots of a Polynomial134
    5.3Optimization Methods135
    5.3.1Graphical Method136
    5.3.2Numerical Methods137
    5.3.3MATLAB fmin and fmins Built-in Function140
    5.4MATLAB Commands Review144
    6.Complex Numbers145
    6.2The Basics145
    6.2.2Multiplication by a Real or Imaginary Number147
    6.2.3Multiplication of Two Complex Numbers148
    6.3Complex Conjugation and Division149
    6.4Polar Form of Complex Numbers152
    6.4.1New Insights into Multiplication and Division of Complex Numbers153
    6.5Analytical Solutions of Constant Coefficients ODE159
    6.5.1Transient Solutions159
    6.5.2Steady-State Solutions161
    6.5.3Applications to Circuit Analysis163
    6.6.1Phasor of Two Added Signals165
    6.7Interference and Diffraction of Electromagnetic Waves168
    6.7.1The Electromagnetic Wave168
    6.7.2Addition of Electromagnetic Waves170
    6.7.3Generalization to N-waves170
    6.8Solving ac Circuits with Phasors: The Impedance Method172
    6.8.1RLC Circuit Phasor Analysis173
    6.8.2The Infinite LC Ladder175
    6.9Transfer Function for a Difference Equation with Constant Coefficients177
    6.10MATLAB Commands Review187
    7.1Vectors in Two Dimensions (2-D)189
    7.1.2Multiplication of a Vector by a Real Number189
    7.1.3Cartesian Representation189
    7.1.4MATLAB Representation of the Above Results192
    7.2Dot (or Scalar) Product193
    7.2.1MATLAB Representation of the Dot Product195
    7.3Components, Direction Cosines, and Projections197
    7.3.2Direction Cosines197
    7.4The Dirac Notation and Some General Theorems198
    7.4.1Cauchy-Schwartz Inequality200
    7.4.2Triangle Inequality202
    7.5Cross Product and Scalar Triple Product203
    7.5.1Cross Product203
    7.5.2Geometric Interpretation of the Cross Product204
    7.5.3Scalar Triple Product204
    7.6Vector Valued Functions207
    7.7Line Integral210
    7.8Infinite Dimensional Vector Spaces211
    7.9MATLAB Commands Review222
    8.1Setting up Matrices223
    8.1.1Creating Matrices in MATLAB223
    8.2Adding Matrices229
    8.3Multiplying a Matrix by a Scalar230
    8.4Multiplying Matrices230
    8.5Inverse of a Matrix232
    8.6Solving a System of Linear Equations234
    8.7Application of Matrix Methods238
    8.7.1dc Circuit Analysis238
    8.7.2dc Circuit Design239
    8.7.3ac Circuit Analysis240
    8.7.4Accuracy of a Truncated Taylor Series242
    8.7.5Reconstructing a Function from Its Fourier Components244
    8.7.6Interpolating the Coefficients of an (n - 1)-degree Polynomial from n Points246
    8.7.7Least-Square Fit of Data247
    8.8Eigenvalues and Eigenvectors248
    8.8.1Finding the Eigenvalues of a Matrix249
    8.8.2Finding the Eigenvalues and Eigenvectors Using MATLAB250
    8.9The Cayley-Hamilton and Other Analytical Techniques253
    8.9.1Cayley-Hamilton Theorem253
    8.9.2Solution of Equations of the Form dX/dt = AX254
    8.9.3Solution of Equations of the Form dX/dt = AX + B(t)256
    8.9.4Pauli Spinors260
    8.10Special Classes of Matrices267
    8.10.1Hermitian Matrices267
    8.10.2Unitary Matrices270
    8.10.3Unimodular Matrices272
    8.11MATLAB Commands Review277
    9.1Two-dimensional (2-D) Geometric Transformations279
    9.1.1Polygonal Figures Construction279
    9.1.2Inversion about the Origin and Reflection about the Coordinate Axes280
    9.1.3Rotation around the Origin281
    9.2Homogeneous Coordinates284
    9.3Manipulation of 2-D Images287
    9.3.1Geometrical Manipulation of Images287
    9.3.2Digital Image Processing288
    9.3.3Encrypting an Image290
    9.4Lorentz Transformation291
    9.4.1Space-Time Coordinates291
    9.4.2Addition Theorem for Velocities293
    9.5MATLAB Commands Review295
    10.A Taste of Probability Theory297
    10.3Addition Laws for Probabilities303
    10.4Conditional Probability307
    10.4.1Total Probability and Bayes Theorems309
    10.5Repeated Trials312
    10.5.1Generalization of Bernoulli Trials314
    10.6The Poisson and the Normal Distributions315
    10.6.1The Poisson Distribution315
    10.6.2The Normal Distribution317
    Supplement: Review of Elementary Functions321
    S.1Affine Functions321
    S.2Quadratic Functions322
    S.3Polynomial Functions327
    S.4Trigonometric Functions327
    S.5Inverse Trigonometric Functions329
    S.6The Natural Logarithmic Function329
    S.7The Exponential Function330
    S.8The Hyperbolic Functions331
    S.9The Inverse Hyperbolic Functions333
    AppendixSome Useful Formulae335
    Addendum: MATLAB 6339
    Selected References343

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