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 ELEMENTARY MATHEMATICAL and COMPUTATIONAL TOOLS for ELECTRICAL and COMPUTER ENGINEERS USING MATLAB
 Jamal T. Manassah
 
 1. Introduction to MATLAB® and Its Graphics Capabilities
 1.1 Getting Started
 1.2 Basic Algebraic Operations and Functions
 1.3 Plotting Points
 1.3.1 Axes Commands
 1.3.2 Labeling a Graph
 1.3.3 Plotting a Point in 3-D
 1.4 M-files
 1.5 MATLAB Simple Programming
 1.5.1 Iterative Loops
 1.5.2 If-Else-End Structures
 1.6 Array Operations
 1.7 Curve and Surface Plotting
 1.7.1 x-y Parametric Plot
 1.7.2 More Parametric Plots in 2-D
 1.7.3 Plotting a 3-D Curve
 1.7.4 Plotting a 3-D Surface
 1.8 Polar Plots
 1.9 Animation
 1.10 Histograms
 1.11 Printing and Saving Work in MATLAB
 1.12 MATLAB Commands Review
 2. Difference Equations
 2.1 Simple Linear Forms
 2.2 Amortization
 2.3 An Iterative Geometric Construct: The Koch Curve
 2.4 Solution of Linear Constant Coefficients Difference
 Equations
 2.4.1 Homogeneous Solution
 2.4.2 Particular Solution
 2.4.3 General Solution
 2.5 Convolution-Summation of a First-Order System with
 Constant Coefficients
 2.6 General First-Order Linear Difference Equations*
 2.7 Nonlinear Difference Equations
 2.7.1 Computing Irrational Numbers
 2.7.2 The Logistic Equation
 © 2001 by CRC Press LLC
 2.8 Fractals and Computer Art
 2.8.1 Mira’s Model
 2.8.2 Hénon’s Model
 2.9 Generation of Special Functions from Their Recursion
 Relations*
 3. Elementary Functions and Some of Their Uses
 3.1 Function Files
 3.2 Examples with Affine Functions
 3.3 Examples with Quadratic Functions
 3.4 Examples with Polynomial Functions
 3.5 Examples with Trigonometric Functions
 3.6 Examples with the Logarithmic Function
 3.6.1 Ideal Coaxial Capacitor
 3.6.2 The Decibel Scale
 3.6.3 Entropy
 3.7 Examples with the Exponential Function
 3.8 Examples with the Hyperbolic Functions and Their
 Inverses
 3.8.1 Capacitance of Two Parallel Wires
 3.9 Commonly Used Signal Processing Functions
 3.10 Animation of a Moving Rectangular Pulse
 3.11 MATLAB Commands Review
 4. Numerical Differentiation, Integration, and Solutions of
 Ordinary Differential Equations
 4.1 Limits of Indeterminate Forms
 4.2 Derivative of a Function
 4.3 Infinite Sums
 4.4 Numerical Integration
 4.5 A Better Numerical Differentiator
 4.6 A Better Numerical Integrator: Simpson’s Rule
 4.7 Numerical Solutions of Ordinary Differential Equations
 4.7.1 First-Order Iterator
 4.7.2 Higher-Order Iterators: The Runge-Kutta
 Method*
 4.7.3 MATLAB ODE Solvers
 4.8 MATLAB Commands Review
 5. Root Solving and Optimization Methods
 5.1 Finding the Real Roots of a Function
 5.1.1 Graphical Method
 5.1.2 Numerical Methods
 5.1.3 MATLAB fsolve and fzero Built-in Functions
 5.2 Roots of a Polynomial
 © 2001 by CRC Press LLC
 5.3 Optimization Methods
 5.3.1 Graphical Method
 5.3.2 Numerical Methods
 5.3.3 MATLAB fmin and fmins Built-in Function
 5.4 MATLAB Commands Review
 6. Complex Numbers
 6.1 Introduction
 6.2 The Basics
 6.2.1 Addition
 6.2.2 Multiplication by a Real or Imaginary Number
 6.2.3 Multiplication of Two Complex Numbers
 6.3 Complex Conjugation and Division
 6.3.1 Division
 6.4 Polar Form of Complex Numbers
 6.4.1 New Insights into Multiplication and Division
 of Complex Numbers
 6.5 Analytical Solutions of Constant Coefficients ODE
 6.5.1 Transient Solutions
 6.5.2 Steady-State Solutions
 6.5.3 Applications to Circuit Analysis
 6.6 Phasors
 6.6.1 Phasor of Two Added Signals
 6.7 Interference and Diffraction of ElectromagneticWaves
 6.7.1 The ElectromagneticWave
 6.7.2 Addition of ElectromagneticWaves
 6.7.3 Generalization to N-waves
 6.8 Solving ac Circuits with Phasors: The Impedance
 Method
 6.8.1 RLC Circuit Phasor Analysis
 6.8.2 The Infinite LC Ladder
 6.9 Transfer Function for a Difference Equation with
 Constant Coefficients*
 6.10 MATLAB Commands Review
 7. Vectors
 7.1 Vectors in Two Dimensions (2-D)
 7.1.1 Addition
 7.1.2 Multiplication of a Vector by a Real Number
 7.1.3 Cartesian Representation
 7.1.4 MATLAB Representation of the Above Results
 7.2 Dot (or Scalar) Product
 7.2.1 MATLAB Representation of the Dot Product
 7.3 Components, Direction Cosines, and Projections
 7.3.1 Components
 © 2001 by CRC Press LLC
 7.3.2 Direction Cosines
 7.3.3 Projections
 7.4 The Dirac Notation and Some General Theorems*
 7.4.1 Cauchy-Schwartz Inequality
 7.4.2 Triangle Inequality
 7.5 Cross Product and Scalar Triple Product*
 7.5.1 Cross Product
 7.5.2 Geometric Interpretation of the Cross Product
 7.5.3 Scalar Triple Product
 7.6 Vector Valued Functions
 7.7 Line Integral
 7.8 Infinite Dimensional Vector Spaces*
 7.9 MATLAB Commands Review
 8. Matrices
 8.1 Setting up Matrices
 8.1.1 Creating Matrices in MATLAB
 8.2 Adding Matrices
 8.3 Multiplying a Matrix by a Scalar
 8.4 Multiplying Matrices
 8.5 Inverse of a Matrix
 8.6 Solving a System of Linear Equations
 8.7 Application of Matrix Methods
 8.7.1 dc Circuit Analysis
 8.7.2 dc Circuit Design
 8.7.3 ac Circuit Analysis
 8.7.4 Accuracy of a Truncated Taylor Series
 8.7.5 Reconstructing a Function from Its Fourier
 Components
 8.7.6 Interpolating the Coefficients of an (n – 1)-degree
 Polynomial from n Points
 8.7.7 Least-Square Fit of Data
 8.8 Eigenvalues and Eigenvectors*
 8.8.1 Finding the Eigenvalues of a Matrix
 8.8.2 Finding the Eigenvalues and Eigenvectors Using
 MATLAB
 8.9 The Cayley-Hamilton and Other Analytical Techniques*
 8.9.1 Cayley-Hamilton Theorem
 8.9.2 Solution of Equations of the Form
 8.9.3 Solution of Equations of the Form
 8.9.4 Pauli Spinors
 8.10 Special Classes of Matrices*
 8.10.1 Hermitian Matrices
 dX
 dt
 = AX
 dX
 dt
 =AX+B(t)
 © 2001 by CRC Press LLC
 8.10.2 Unitary Matrices
 8.10.3 Unimodular Matrices
 8.11 MATLAB Commands Review
 9. Transformations
 9.1 Two-dimensional (2-D) Geometric Transformations
 9.1.1 Polygonal Figures Construction
 9.1.2 Inversion about the Origin and Reflection about the
 Coordinate Axes
 9.1.3 Rotation around the Origin
 9.1.4 Scaling
 9.1.5 Translation
 9.2 Homogeneous Coordinates
 9.3 Manipulation of 2-D Images
 9.3.1 Geometrical Manipulation of Images
 9.3.2 Digital Image Processing
 9.3.3 Encrypting an Image
 9.4 Lorentz Transformation*
 9.4.1 Space-Time Coordinates
 9.4.2 Addition Theorem for Velocities
 9.5 MATLAB Commands Review
 10. A Taste of Probability Theory*
 10.1 Introduction
 10.2 Basics
 10.3 Addition Laws for Probabilities
 10.4 Conditional Probability
 10.4.1 Total Probability and Bayes Theorems
 10.5 Repeated Trials
 10.5.1 Generalization of Bernoulli Trials
 10.6 The Poisson and the Normal Distributions
 10.6.1 The Poisson Distribution
 10.6.2 The Normal Distribution
 Supplement: Review of Elementary Functions
 S.1 Affine Functions
 S.2 Quadratic Functions
 S.3 Polynomial Functions
 S.4 Trigonometric Functions
 S.5 Inverse Trigonometric Functions
 S.6 The Natural Logarithmic Function
 S.7 The Exponential Function
 S.8 The Hyperbolic Functions
 S.9 The Inverse Hyperbolic Functions
 Appendix: Some Useful Formulae
 
 
 
 
 
 
 
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