1st Edition

Introduction to Numerical and Analytical Methods with MATLAB® for Engineers and Scientists

By William Bober Copyright 2014
    556 Pages 208 B/W Illustrations
    by CRC Press

    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