# Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB, Second Edition

CRC Press, Oct 20, 2006 - Technology & Engineering - 480 pages
Showing how MATLAB® can help solve computational problems in engineering, Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB®, Second Edition explores practical mathematical methods for students, covering numerical techniques of elementary calculus and linear algebra and detailed introductory material on difference equations, complex variables, transformation theory, and probability theory. This integrated approach strengthens students' analytical and computational abilities.

Updated to reflect the newest version of MATLAB, this edition features a new layout for enhanced readability. The book covers both linear and nonlinear difference equations, elementary functions, numerical differentiation, integration and ordinary differential equations solving techniques, optimization methods, complex numbers, vectors, matrix algebra and special matrices, geometric and Lorentz transformations, and probability theory.

New to the Second Edition:
• Updated MATLAB syntax that conforms to MATLAB 7.1
• Expanded introductory chapter that reduces the need to refer to MATLAB online help or user manuals
• Special advanced sections for students looking for more challenging material
• Appendix of symbolic capabilities of MATLAB

Smoothing the transition from elementary math, physics, and computer science sequences to more advanced engineering concepts, this book helps students master fundamental quantitative tools that allow them to progress to more complex electrical and computer engineering applications.
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### Contents

 Starting with MATLAB and Exploring Its Graphics Capabilities 5 12 Basic Algebraic Operations and Functions 5 13 Plotting Points 6 131 Axes Commands 8 132 Labeling a Graph 9 14 Mfiles 10 15 MATLAB Simple Programming 11 152 ifelseend Structures 12
 662 Total Phasor of Many Signals 214 67 Interference and Diffraction of Electromagnetic Waves 216 672 Addition of Two Electromagnetic Waves 217 673 Generalization to Nwaves 218 The Impedance Method 220 681 RLC Circuit Phasor Analysis 221 682 The Infinite LC Ladder 222 69 Transfer Function for a Difference Equation with Constant Coefficients 224

 153 The while Loop 15 16 Arrays 16 161 Array Relational Operations 17 162 Array Algebraic Operations 18 Alternative Syntax to the if Statement 19 164 Plotting Arrays 20 17 Data Analysis 22 172 Displaying Data 24 173 Normal Distribution 25 18 Parametric Equations 27 182 More Examples 28 183 Oscilloscope Graphics 30 19 Polar Plots 32 110 3D Plotting 34 1102 Parametric Equations for a 3D Curve 38 1103 Plotting a 3D Surface 40 A Powerful Tool for Exploring 2D Geometries 43 111 Animation 48 Velocity Gradient etc 49 1122 Gradient of a Potential 50 113 Printing and Saving Work in MATLAB 52 1132 Printing a Program File Script Mfile 54 114 MATLAB Commands Review 55 Difference Equations 59 22 Amortization 61 The Koch Curve 64 24 Solution of Linear Constant Coefficients Difference Equations 67 241 Homogeneous Solution 68 242 Particular Solution 70 25 ConvolutionSummation of a FirstOrder System with Constant Coefficients 74 26 General FirstOrder Linear Difference Equations 76 27 Nonlinear Difference Equations 78 272 The Logistic Equation 79 28 Fractals and Computer Art 81 282 Henons Model 84 29 Generation of Special Functions from Their Recursion Relations 86 Elementary Functions and Some of Their Uses 89 32 Examples with Affine Functions 91 322 Further Consideration of Figure 31 94 33 Examples with Quadratic Functions 95 34 Examples with Polynomial Functions 96 35 Examples with the Trigonometric Functions 99 36 Examples with the Logarithmic Function 100 362 The Decibel Scale 101 37 Examples with the Exponential Function 103 38 Examples with the Hyperbolic Functions and Their Inverses 105 310 Animation of a Moving Rectangular Pulse 111 311 Use of the Function Handle 112 312 MATLAB Commands Review 114 Differentiation Integration and Solutions of Ordinary Differential Equations 115 42 Derivative of a Function 117 43 Infinite Sums 119 44 Numerical Integration 121 45 A Better Numerical Differentiator 124 451 Application 127 Simpsons Rule 128 47 Numerical Solutions of Ordinary Differential Equations 135 471 FirstOrder Iterator 137 The RungeKutta Method 142 473 MATLAB ODE Solvers 146 48 Integral Equations 152 49 MATLAB Commands Review 158 Root Solving and Optimization Methods 159 512 Numerical Methods 160 513 MATLAB fzero Builtin Function 167 Zeros of the ZeroOrder Bessel Function 168 52 Roots of a Polynomial 170 53 Optimization Methods for Functions of One Variable 171 531 Graphical Method 172 The Golden Section Method 173 533 MATLAB fminbnd Builtin Function 175 54 The Zeros and the Minima of Functions in Two Variables 178 542 The MATLAB fminsearch Builtin Command 181 55 Finding the Minima of Functions with Constraints Present 185 551 Lagrange Multipliers 186 552 MATLAB fmincon Builtin Function 187 56 MATLAB Commands Review 189 Complex Numbers 191 621 Addition 192 622 Multiplication by a Real or Imaginary Number 193 63 Complex Conjugation and Division 195 631 Application to Division 196 64 Polar Form of Complex Numbers 197 641 New Insights into Multiplication and Division of Complex Numbers 198 642 Roots of Complex Numbers 200 643 The Function y ejϴ 201 65 Analytical Solutions of Constant Coefficients ODE 204 651 Transient Solutions 205 Green Function Technique 207 653 SteadyState Solutions 210 654 Applications to Circuit Analysis 211 66 Phasors 213
 610 MATLAB Commands Review 234 Vectors 235 713 Cartesian Representation 236 714 MATLAB Representation of Vectors 238 72 Dot or Scalar Product 239 721 MATLAB Representation of the Dot Product 241 73 Components Direction Cosines and Projections 243 733 Projections 244 741 CauchySchwartz Inequality 246 742 Triangle Inequality 248 75 Cross Product and Scalar Triple Product 249 752 Geometric Interpretation of the Cross Product 250 76 Tangent Normal and Curvature 253 77 Velocity and Acceleration Vectors in Polar Coordinates 255 78 Line Integral 261 79 InfiniteDimensional Vector Spaces 263 710 MATLAB Commands Review 272 Matrices 273 812 Retrieving Special Matrices from the MATLAB Library 275 813 Functional Construction of Matrices 277 82 Adding Matrices 280 84 Multiplying Matrices 281 85 Inverse of a Matrix 282 86 Solving a System of Linear Equations 285 87 Application of Matrix Methods 288 872 dc Circuit Design 289 873 ac Circuit Analysis 290 874 Accuracy of a Truncated Taylor Series 291 875 Reconstructing a Function from Its Fourier Components 294 876 Interpolating the Coefficients of an n 1 Degree Polynomial from n Points 296 877 LeastSquares Fit of Data 297 878 Numerical Solution of Fredholm Equations 298 88 Eigenvalues and Eigenvectors 299 882 Finding the Eigenvalues and Eigenvectors Using MATLAB 302 89 The CayleyHamilton and Other Analytical Techniques 305 892 Solution of Equations of the Form dXdt AX 306 dt 308 894 Pauli Spinors 312 810 Special Classes of Matrices 319 8102 Unitary Matrices 323 8103 Unimodular Matrices 324 811 Transfer Matrices 330 812 Covariance Matrices 334 8121 Parametric Estimation 336 8122 KarhunenLoeve Transform 339 813 MATLAB Commands Review 341 Transformations 343 912 Inversion about the Origin and Reflection about the Coordinate Axes 344 913 Rotation around the Origin 345 914 Scaling 346 915 Translation 347 93 Manipulation of 2D Images 351 932 Digital Image Processing 352 933 Encrypting an Image 353 94 Lorentz Transformation 355 942 Addition Theorem for Velocities 357 95 Iterative Constructs 358 952 The Serpenski Curve 361 96 MATLAB Commands Review 363 A Taste of Probability Theory 365 102 Basics 366 103 Addition Laws for Probabilities 371 104 Conditional Probability 375 1041 Total Probability Theorem 377 105 Repeated Trials 380 106 Generalization of Bernoulli Trials 382 1071 The Poisson Distribution 383 1072 The Normal Distribution 385 Review of Elementary Functions 389 A2 Quadratic Functions 390 A3 Polynomial Functions 395 A5 Inverse Trigonometric Functions 397 A7 The Exponential Function 398 A8 The Hyperbolic Functions 399 A9 The Inverse Hyperbolic Functions 401 Determinants 403 Symbolic Calculations with MATLAB 407 C1 Symbolic Manipulation 408 C12 Algebraic Manipulation 411 C13 Plotting Symbolic Expressions 414 C2 Symbolic Solution of Algebraic and Transcendental Equations 417 C3 Symbolic Calculus 418 C4 Symbolic Linear Algebra 423 C5 zTransform and Laplace Transform 428 C52 Solving Constant Coefficients Linear Difference Equations Using zTransform 431 C53 Laplace Transform 432 C54 Solving Constant Coefficients Linear ODE Using Laplace Transform 436 Some Useful Formulae 439 Text Formatting 443 Selected References 445 Index 447 Copyright