1st Edition

Numerical and Analytical Methods with MATLAB for Electrical Engineers

By William Bober, Andrew Stevens Copyright 2013
    388 Pages 168 B/W Illustrations
    by CRC Press

    Combining academic and practical approaches to this important topic, Numerical and Analytical Methods with MATLAB® for Electrical Engineers is the ideal resource for electrical and computer engineering students. Based on a previous edition that was geared toward mechanical engineering students, this book expands many of the concepts presented in that book and replaces the original projects with new ones intended specifically for electrical engineering students.

    This book includes:

    • An introduction to the MATLAB programming environment
    • Mathematical techniques for matrix algebra, root finding, integration, and differential equations
    • More advanced topics, including transform methods, signal processing, curve fitting, and optimization
    • An introduction to the MATLAB graphical design environment, Simulink

    Exploring the numerical methods that electrical engineers use for design analysis and testing, this book comprises standalone chapters outlining a course that also introduces students to computational methods and programming skills, using MATLAB as the programming environment. Helping engineering students to develop a feel for structural programming—not just button-pushing with a software program—the illustrative examples and extensive assignments in this resource enable them to develop the necessary skills and then apply them to practical electrical engineering problems and cases.

    Numerical Methods for Electrical Engineers

    Engineering Goals

    Programming Numerical Solutions

    Why MATLAB®?

    The MATLAB® Programming Language

    Conventions in This Book

    Example Programs

    MATLAB® Fundamentals

    The MATLAB® Windows

    Constructing a Program in MATLAB®

    MATLAB® Fundamentals

    MATLAB® Input/Output

    MATLAB® Program Flow

    MATLAB® Function Files

    Anonymous Functions

    MATLAB® Anonymous Functions

    MATLAB® Graphics

    Working with Matrices

    Working with Functions of a Vector

    Additional Examples Using Characters and Strings

    Interpolation and MATLAB®’s interp1 Function

    MATLAB®’s textscan Function

    Exporting MATLAB® Data to Excel

    Debugging a Program

    The Parallel RLC Circuit


    Matrix Operations

    System of Linear Equations

    Gauss Elimination

    The Gauss-Jordan Method

    Number of Solutions

    Inverse Matrix

    The Eigenvalue Problem

    Roots of Algebraic and Transcendental Equations

    The Search Method

    Bisection Method

    Newton-Raphson Method

    MATLAB®’s fzero and roots Functions

    Numerical Integration

    Numerical Integration and Simpson’s Rule

    Improper Integrals

    MATLAB®’s quad Function

    The Electric Field

    The quiver Plot

    MATLAB®’s dblquad Function

    Numerical Integration of Ordinary Differential Equations

    The Initial Value Problem

    The Euler Algorithm

    Modified Euler Method with Predictor-Corrector Algorithm

    Numerical Error for Euler Algorithms

    The Fourth-Order Runge-Kutta Method

    System of Two First-Order Differential Equations

    A Single Second-Order Equation

    MATLAB®’s ODE Function

    Boundary Value Problems

    Solution of a Tri-Diagonal System of Linear Equations

    Method Summary for m equations

    Difference Formulas

    One-Dimensional Plate Capacitor Problem

    Laplace Transforms

    Laplace Transform and Inverse Transform

    Transforms of Derivatives

    Ordinary Differential Equations, Initial Value Problem


    Laplace Transforms Applied to Circuits

    Impulse Response

    Fourier Transforms and Signal Processing

    Mathematical Description of Periodic Signals: Fourier Series

    Complex Exponential Fourier Series and Fourier Transforms

    Properties of Fourier Transforms


    Discrete-Time Representation of Continuous-Time Signals

    Fourier Transforms of Discrete-Time Signals

    A Simple Discrete-Time Filter

    Curve Fitting

    Method of Least Squares

    Curve Fitting with the Exponential Function

    MATLAB®’s polyfit Function

    Cubic Splines

    The Function interp1 for Cubic Spline Curve Fitting

    Curve Fitting with Fourier Series


    Unconstrained Optimization Problems

    Method of Steepest Descent

    MATLAB®’s fminunc Function

    Optimization with Constraints

    Lagrange Multipliers

    MATLAB®’s fmincon Function


    Creating a Model in Simulink

    Typical Building Blocks in Constructing a Model

    Tips for Constructing and Running Models

    Constructing a Subsystem

    Using the Mux and Fcn Blocks

    Using the Transfer Fcn Block

    Using the Relay and Switch Blocks

    Trigonometric Function Blocks

    Appendix A:
    RLC Circuits

    Appendix B: Special Characters in MATLAB® Plots

    MATLAB® Function Index


    Dr. William Bober received his B.S. degree in civil engineering from the City College of New York (CCNY), his M.S. degree in engineering science from Pratt Institute, and his Ph.D. degree in engineering science and aerospace engineering from Purdue University. At Purdue University, he was on a Ford Foundation Fellowship; he was assigned to teach one engineering course each semester. After receiving his Ph.D., he went to work as an associate engineering physicist in the Applied Mechanics Department at Cornell Aeronautical Laboratory in Buffalo, New York. After leaving Cornell Labs, he was employed as an associate professor in the Department of Mechanical Engineering at the Rochester Institute of Technology (RIT) for the following twelve years. After leaving RIT, he obtained employment at Florida Atlantic University (FAU) in the Department of Mechanical Engineering. More recently, he transferred to the Department of Civil Engineering at FAU.

    Dr. Andrew Stevens, P.E., received his bachelor’s degree from Massachusetts Institute of Technology, his master’s degree from the University of Pennsylvania, and his doctorate from Columbia University, all in electrical engineering. He did his Ph.D. thesis work at IBM Research in the area of integrated circuit design for high-speed optical networks. While at Columbia, he lectured a course in the core undergraduate curriculum and won the IEEE Solid-State Circuits Fellowship. He has held R&D positions at AT&T Bell Laboratories in the development of T-carrier multiplexer systems and at Argonne National Laboratory in the design of radiation-hardened integrated circuits for colliding beam detectors. Since 2001, he has been president of Electrical Science, an engineering consulting firm specializing in electrical hardware and software.

    "… I like the organization of the book and especially the early focus on matrix fundamentals … use of examples is excellent. …The end-of chapter problems are good … presents some excellent frameworks for computational methods— students should be able to build their programs more effectively by understanding the core components and following the directions…"

    —Michael R. Gustafson II, Duke University, Durham, North Carolina, USA

    "… covers MATLAB® first while providing gradual introduction first and progressing to advanced concepts. Numerical methods, algorithms, and implementations are well explained."

    — Gleb V. Tcheslavski, Lamar University, Beaumont, Texas, USA