Numerical and Analytical Methods with MATLAB for Electrical Engineers

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

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

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

Simulink

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 Inde