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

388 Pages
by CRC Press

Also available as eBook on:

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

Matrices

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

The Electric Field

The quiver Plot

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

Convolution

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

Filters

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

Optimization

Unconstrained Optimization Problems

Method of Steepest Descent

MATLAB®’s fminunc Function

Optimization with Constraints

Lagrange Multipliers

MATLAB®’s fmincon Function

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

### Biography

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