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

Published:
October 20, 2006 by CRC Press - 480 Pages
Author(s):
Jamal T. Manassah, City College of New York, USA
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ISBN 9780849374258
Cat# 7425
 

Features

  • Introduces the computational and graphics capabilities of MATLAB
  • Discusses simple algorithms to numerically implement the basic operations of calculus and linear alegbra
  • Contains additional mathematical material necessary to understand intermediate electrical engineering courses
  • Provides scientists and professional engineers with a quick reference to use MATLAB as a problem-solving tool
  • Includes numerous exercises and examples that offer a glimpse into fascinating problems encountered in engineering practice as well as end-of-chapter MATLAB definitions

    • Summary

    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.

    • Table of Contents

    PREFACE TO FIRST EDITION
    PREFACE TO SECOND EDITION

    STARTING WITH MATLAB AND EXPLORING ITS GRAPHICS CAPABILITIES
    First Steps
    Basic Algebraic Operations and Functions
    Plotting Points
    M-Files
    MATLAB Simple Programming
    Arrays
    Data Analysis
    Parametric Equations
    Polar Plots
    3-D Plotting
    Animation
    Specialized Plots: Velocity, Gradient, etc.
    Printing and Saving Work in MATLAB
    MATLAB Commands Review

    DIFFERENCE EQUATIONS
    Simple Linear Forms
    Amortization
    An Iterative Geometric Construct: The Koch Curve
    Solution of Linear Constant Coefficients Difference Equations
    Convolution-Summation of a First-Order System with Constant Coefficients
    General First-Order Linear Difference Equations
    Nonlinear Difference Equations
    Fractals and Computer Art
    Generation of Special Functions from Their Recursion Relations
    ELEMENTARY FUNCTIONS AND SOME OF THEIR USES
    Function Files
    Examples with Affine Functions
    Examples with Quadratic Functions
    Examples with Polynomial Functions
    Examples with the Trigonometric Functions
    Examples with the Logarithmic Function
    Examples with the Exponential Function
    Examples with the Hyperbolic Functions and Their Inverses
    Commonly Used Signal Processing Functions
    Animation of a Moving Rectangular Pulse
    Use of the Function Handle
    MATLAB Commands Review

    DIFFERENTIATION, INTEGRATION, AND SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS
    Limits of Indeterminate Forms
    Derivative of a Function
    Infinite Sums
    Numerical Integration
    A Better Numerical Differentiator
    A Better Numerical Integrator: Simpson's Rule
    Numerical Solutions of Ordinary Differential Equations
    Integral Equations
    MATLAB Commands Review

    ROOT SOLVING AND OPTIMIZATION METHODS
    Finding the Real Roots of a Function of One Variable
    Roots of a Polynomial
    Optimization Methods for Functions of One Variable
    The Zeros and the Minima of Functions in Two Variables
    Finding the Minima of Functions with Constraints Present
    MATLAB Commands Review
    COMPLEX NUMBERS
    Introduction
    The Basics
    Complex Conjugation and Division
    Polar Form of Complex Numbers
    Analytical Solutions of Constant Coefficients ODE
    Phasors
    Interference and Diffraction of Electromagnetic Waves
    Solving ac Circuits with Phasors: The Impedance Method
    Transfer Function for a Difference Equation with Constant Coefficients
    MATLAB Commands Review

    VECTORS
    Vectors in Two Dimensions
    Dot (or Scalar) Product
    Components, Direction Cosines, and Projections
    The Dirac Notation and Some General Theorems
    Cross Product and Scalar Triple Product
    Tangent, Normal, and Curvature
    Velocity and Acceleration Vectors in Polar Coordinates
    Line Integral
    Infinite-Dimensional Vector Spaces
    MATLAB Commands Review

    MATRICES
    Setting up Matrices
    Adding Matrices
    Multiplying a Matrix by a Scalar
    Multiplying Matrices
    Inverse of a Matrix
    Solving a System of Linear Equations
    Application of Matrix Methods
    Eigenvalues and Eigenvectors
    The Cayley-Hamilton and Other Analytical Techniques
    Special Classes of Matrices
    Transfer Matrices
    Covariance Matrices
    MATLAB Commands Review

    TRANSFORMATIONS
    Two-Dimensional Geometric Transformations
    Homogeneous Coordinates
    Manipulation of 2-D Images
    Lorentz Transformation
    Iterative Constructs
    MATLAB Commands Review

    A TASTE OF PROBABILITY THEORY
    Introduction
    Basics
    Addition Laws for Probabilities
    Conditional Probability
    Repeated Trials
    Generalization of Bernoulli Trials
    The Poisson and the Normal Distributions

    APPENDIX A: REVIEW OF ELEMENTARY FUNCTIONS
    APPENDIX B: DETERMINANTS
    APPENDIX C: SYMBOLIC CALCULATIONS WITH MATLAB®
    APPENDIX D: SOME USEFUL FORMULAE
    APPENDIX E: TEXT FORMATTING

    SELECTED REFERENCES
    INDEX

    Editorial Reviews

    "Clear presentation of computational methods, graphics and symbolic calculus in MATLAB with updated syntax in this 2nd edition . . . a nice book to help the students to perform their programming capability."

    – Jacek Gilewicz, in Zentralblatt Math, 2007, Vol. 1105, No. 7

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