1st Edition
Numerical and Analytical Methods with MATLAB
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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
Introduction
Constructing a Program in MATLAB
The MATLAB Program
Program Examples
Debugging a Program
3-D and Contour Plots
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
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
Simulink
Introduction
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
Optimization
Introduction
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
Convolution
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
Introduction
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
Appendices
Index
Exercises, Projects, and References appear at the end of most chapters.
Biography
William Bober, Chi-Tay Tsai, and Oren Masory are all professors in the Department of Mechanical Engineering at Florida Atlantic University.
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