1st Edition

Numerical and Analytical Methods with MATLAB

By William Bober, Chi-Tay Tsai, Oren Masory Copyright 2009
    486 Pages 267 B/W Illustrations
    by CRC Press

    Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated.

    This classroom-tested text first reviews the essentials involved in writing computer programs as well as fundamental aspects of MATLAB. It next explains how matrices can solve problems of linear equations, how to obtain the roots of algebraic and transcendental equations, how to evaluate integrals, and how to solve various ODEs. After exploring the features of Simulink, the book discusses curve fitting, optimization problems, and PDE problems, such as the vibrating string, unsteady heat conduction, and sound waves. The focus then shifts to the solution of engineering problems via iteration procedures, differential equations via Laplace transforms, and stress analysis problems via the finite element method. The final chapter examines control systems theory, including the design of single-input single-output (SISO) systems.

    Two Courses in One Textbook
    The first six chapters are appropriate for a lower level course at the sophomore level. The remaining chapters are ideal for a course at the senior undergraduate or first-year graduate level. Most of the chapters contain projects that require students to write a computer program in MATLAB that produces tables, graphs, or both. Many sample MATLAB programs (scripts) in the text provide guidance on completing these projects.

    Numerical Modeling for Engineering

    Computer Usage in Engineering

    The Mathematical Model

    Computer Programming

    Preparing a Computer Program

    Recommended Procedures for Writing a Program

    Building Blocks in Writing a Program

    MATLAB Fundamentals


    Constructing a Program in MATLAB

    The MATLAB Program

    Program Examples

    Debugging a Program

    3-D and Contour Plots


    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

    The fzero Function

    Numerical Integration

    Numerical Integration and Simpson’s Rule

    Improper Integrals

    MATLAB’s Quad Function

    MATLAB’s DBLQUAD Function

    Numerical Integration of Ordinary Differential Equations

    The Initial Value Problem

    The Fourth-Order Runge–Kutta Method

    System of Two First-Order Equations

    A Single Second-Order Equation

    MATLAB’s ODE Function

    Ordinary Differential Equations That Are Not Initial Value Problems

    Solution of a Tri-Diagonal System of Linear Equations

    Difference Formulas

    Deflection of a Beam



    Creating a Model in Simulink

    Typical Building Blocks in Constructing a Model

    Constructing and Running the Model

    Constructing a Subsystem

    Using the mux and fcn Blocks

    The Relay Block

    The Switch Block

    Trigonometric Function Blocks

    Curve Fitting

    Curve-Fitting Objective

    Method of Least Squares

    Curve Fitting with the Exponential Function

    MATLAB’s Curve-Fitting Function

    Cubic Splines

    The Function Interp1 for Cubic Spline Curve Fitting

    Curve Fitting with Fourier Series



    Unconstrained Optimization Problems

    Method of Steepest Descent

    Optimization with Constraints

    MATLAB’s Optimization Function

    Partial Differential Equations

    The Classification of Partial Differential Equations

    Solution by Separation of Variables

    Unsteady Heat Transfer in 2-D

    Perturbation Theory and Sound Waves

    Review of Finite Difference Formulas

    Example of Applying Finite Difference Methods to Partial Differential Equations

    Iteration Method

    Iteration in Pipe Flow Analysis

    The Gauss–Seidel Method

    The Hardy–Cross Method

    Laplace Transforms

    Laplace Transform and Inverse Transform

    Transforms of Derivatives

    Ordinary Differential Equations, Initial Value Problem

    A Shifting Theorem

    The Unit Step Function

    Laplace Transform of the Unit Step Function


    Laplace Transforms Applied to Partial Differential Equations

    Laplace Transforms and Complex Variables

    An Introduction to the Finite Element Method

    Finite Element Method for Stress Analysis

    Structural Mechanics Plane Stress Analysis

    The Shape Function for a Linear Triangle Element

    Finite Element Analysis Using MATLAB’s PDE Toolbox

    Structural Mechanics Plane Strain Analysis

    Model Analysis of 2-D Structures

    Finite Element Analysis for Heat Transfer

    Control Systems


    Representation of Systems in MATLAB

    Closed-Loop Systems

    MATLAB Tools for the Performance Analysis of Closed-Loop Systems

    MATLAB’s SISOtool

    Application of Simulink in Controls and Dynamic Systems

    Simulink’s Data Acquisition Toolbox



    Exercises, Projects, and References appear at the end of most chapters.


    William Bober, Chi-Tay Tsai, and Oren Masory are all professors in the Department of Mechanical Engineering at Florida Atlantic University.