NUMERICAL AND ANALYTICAL METHODS WITH MATLAB®
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Synopsis
Alleviating the mystery behind the black boxes of MATLAB � functions, this classroom-tested text shows how the built-in functions of MATLAB can numerically solve systems of linear equations, ordinary differential equations, roots of transcendental equations, integrals, statistical problems, optimization problems, control systems problems, and stress analysis problems using the finite element method. It discusses topics often not covered in similar books, including the finite element method and mechanical controls. Incorporating basic numerical and analytical methods, the text contains many sample MATLAB programs (scripts) that provide guidance on completing the projects given at the end of each chapter.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 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 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.
Product Identifiers
ISBN-10
1420093568
ISBN-13
9781420093568
Key Details
Author
Chi-Tay Tsai, Oren Masory, William Bober
Number Of Pages
472 pages
Series
Computational Mechanics and Applied Analysis
Format
EBOOK
Publication Date
2009-08-11
Language
English
Publisher
CRC Press LLC
Publication Year
2009
Additional Details
Copyright Date
2009
Illustrated
Yes
Dimensions
Weight
28 Oz
Height
1.4 In.
Width
6.2 In.
Length
9.2 In.
Target Audience
Group
College Audience
Classification Method
LCCN
2009-018493
LC Classification Number
QA297.B565 2009
Dewey Decimal
518.0285
Dewey Edition
22
Table Of Content
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.
Synopsis
Alleviating the mystery behind the black boxes of MATLAB � functions, this classroom-tested text shows how the built-in functions of MATLAB can numerically solve systems of linear equations, ordinary differential equations, roots of transcendental equations, integrals, statistical problems, optimization problems, control systems problems, and stress analysis problems using the finite element method. It discusses topics often not covered in similar books, including the finite element method and mechanical controls. Incorporating basic numerical and analytical methods, the text contains many sample MATLAB programs (scripts) that provide guidance on completing the projects given at the end of each chapter.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 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 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.
Product Identifiers
ISBN-10
1420093568
ISBN-13
9781420093568
Key Details
Author
Chi-Tay Tsai, Oren Masory, William Bober
Number Of Pages
472 pages
Series
Computational Mechanics and Applied Analysis
Format
EBOOK
Publication Date
2009-08-11
Language
English
Publisher
CRC Press LLC
Publication Year
2009
Additional Details
Copyright Date
2009
Illustrated
Yes
Dimensions
Weight
28 Oz
Height
1.4 In.
Width
6.2 In.
Length
9.2 In.
Target Audience
Group
College Audience
Classification Method
LCCN
2009-018493
LC Classification Number
QA297.B565 2009
Dewey Decimal
518.0285
Dewey Edition
22
Table Of Content
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.