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

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CRC Press, Oct 20, 2006 - Technology & Engineering - 480 pages
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Showing how MATLABŪ can help solve computational problems in engineering, Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLABŪ, 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
    1
    12 Basic Algebraic Operations and Functions
    2
    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

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