1st Edition
Introduction to Numerical and Analytical Methods with MATLAB® for Engineers and Scientists
Introduction to Numerical and Analytical Methods with MATLAB® for Engineers and Scientists provides the basic concepts of programming in MATLAB for engineering applications.
• Teaches engineering students how to write computer programs on the MATLAB platform
• Examines the selection and use of numerical and analytical methods through examples and case studies
• Demonstrates mathematical concepts that can be used to help solve engineering problems, including matrices, roots of equations, integration, ordinary differential equations, curve fitting, algebraic linear equations, and more
The text covers useful numerical methods, including interpolation, Simpson’s rule on integration, the Gauss elimination method for solving systems of linear algebraic equations, the Runge-Kutta method for solving ordinary differential equations, and the search method in combination with the bisection method for obtaining the roots of transcendental and polynomial equations. It also highlights MATLAB’s built-in functions. These include interp1 function, the quad and dblquad functions, the inv function, the ode45 function, the fzero function, and many others. The second half of the text covers more advanced topics, including the iteration method for solving pipe flow problems, the Hardy-Cross method for solving flow rates in a pipe network, separation of variables for solving partial differential equations, and the use of Laplace transforms to solve both ordinary and partial differential equations.
This book serves as a textbook for a first course in numerical methods using MATLAB to solve problems in mechanical, civil, aeronautical, and electrical engineering. It can also be used as a textbook or as a reference book in higher level courses.
Computer Programming with MATLAB® for Engineers
Introduction
Computer Usage in Engineering
Mathematical Model
Computer Programming
Why MATLAB®?
MATLAB® Programming Language
Building Blocks in Writing a Program
Conventions in This Book
MATLAB® Fundamentals
Introduction
MATLAB® Desktop
Constructing a Program in MATLAB®
MATLAB® Fundamentals
MATLAB® Input/Output
Loops
MATLAB® Graphics
Conditional Operators and Alternate Paths
Working with Built-In Functions with Vector Arguments
More on MATLAB® Graphics
Debugging a Program
Projects
References
Taylor Series, Self-Written Functions and MATLAB®’s interp1 Function
Introduction
Functions Expressed as a Series
Self-Written Functions
Anonymous Functions
MATLAB®’s interp1 Function
Working with Characters and Strings
Projects
References
Matrices
Introduction
Matrix Operations
System of Linear Equations
Statics Truss Problem
Resistive Circuit Problem
Gauss Elimination
Gauss–Jordan Method
Number of Solutions
Inverse Matrix
Eigenvalue Problem in Mechanical Vibrations
Eigenvalue Problem in Electrical Circuits
Projects
Reference
Roots of Algebraic and Transcendental Equations
Introduction
The Search Method
Bisection Method
Newton–Raphson Method
MATLAB®’s Root-finding Functions
Projects
Reference
Numerical Integration
Introduction
Numerical Integration with the Trapezoidal Rule
Numerical Integration and Simpson’s Rule
MATLAB®’s quad Function
MATLAB®’s dblquad Function
Projects
Numerical Integration of Ordinary Differential Equations
Introduction
Initial Value Problem
Euler Algorithm
Modified Euler Method with Predictor–Corrector Algorithm
Fourth-Order Runge–Kutta Method
System of Two First-Order Differential Equations
Single Second-Order Equation
MATLAB®’s ODE Function
Projects
Boundary Value Problems of Ordinary Differential Equations
Introduction
Difference Formulas
Solution of a Tri-Diagonal System of Linear Equations
Projects
Curve Fitting
Introduction
Method of Least Squares
Curve Fitting with the Exponential Function
MATLAB®’s Curve Fitting Functions
Cubic Splines
MATLAB®’s Cubic Spline Curve Fitting Function
Curve Fitting with Fourier Series
Projects
Simulink®
Introduction
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
To Workspace Block
Projects
Reference
Optimization
Introduction
Unconstrained Optimization Problems
Method of Steepest Descent
MATLAB®’s fminbnd and fminsearch Functions
Optimization with Constraints
Lagrange Multipliers
MATLAB®’s fmincon Function
Projects
Reference
Iteration Method
Introduction
Iteration in Pipe Flow Analysis
Hardy–Cross Method
Projects
References
Partial Differential Equations
Classification of Partial Differential Equations
Solution by Separation of Variables
Review of Finite-Difference Formulas
Finite-Difference Methods Applied to Partial Differential
Equations
The Gauss–Seidel Method
Projects
Laplace Transforms
Introduction
Laplace Transform and Inverse Transform
Transforms of Derivatives
Ordinary Differential Equations, Initial Value Problem
MATLAB®’s residue Function
Unit Step Function
Convolution
Laplace Transforms Applied to Circuits
Delta Function
Laplace Transforms Applied to Partial Differential Equations
Projects
References
Review Answers
Appendices
Index
Biography
William Bober, PhD, received his BS in civil engineering from the City College of New York (CCNY), his MS in engineering science from Pratt Institute, and his PhD in engineering science and aerospace engineering from Purdue University.
He worked as an associate engineering physicist in the Applied Mechanics Department at Cornell Aeronautical Laboratory in Buffalo, New York, was employed as an associate professor in the Department of Mechanical Engineering at the Rochester Institute of Technology, and is an associate professor at Florida Atlantic University (FAU), working in the Department of Mechanical Engineering and the Department of Civil Engineering at FAU.
"…provides in a very simple and clear way the first skills in computer programming under the MATLAB platform. The author uses various mathematical concepts (matrices, roots of equations, integration, ordinary differential equations, interpolation, etc.) in order to solve mathematical problems associated with engineering type problems. …the graphic of the work is fairly suggestive and assists a smooth learning."
—Zentralblatt MATH 1284