Advanced Mathematics and Mechanics Applications Using MATLAB, Third Edition,9781584882626

Advanced Mathematics and Mechanics Applications Using MATLAB, Third Edition

by ;
Edition: 3rd
ISBN13: 9781584882626
ISBN10: 158488262X
Format: Hardcover
Pub. Date: 2002-09-17
Publisher(s): Chapman & Hall/
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Summary

Incorporates full revisions that reflect the latest 6.x version of MATLAB. Focuses on the use of MATLAB as a programming environment for computational mathematics and engineering problems.

Table of Contents

Introduction
1(14)
MATLAB: A Tool for Engineering Analysis
1(1)
MATLAB Commands and Related Reference Materials
2(1)
Example Problem on Financial Analysis
3(2)
Computer Code and Results
5(10)
Computer Output
5(3)
Discussion of the MATLAB Code
8(1)
Code for Financial Problem
9(6)
Elementary Aspects of MATLAB Graphics
15(58)
Introduction
15(1)
Overview of Graphics
16(1)
Example Comparing Polynomial and Spline Interpolation
17(5)
Conformal Mapping Example
22(6)
Nonlinear Motion of a Damped Pendulum
28(9)
A Linear Vibration Model
37(6)
Example of Waves in an Elastic String
43(8)
Properties of Curves and Surfaces
51(22)
Curve Properties
51(9)
Surface Properties
60(5)
Program Output and Code
65(8)
Summary of Concepts from Linear Algebra
73(44)
Introduction
73(1)
Vectors, Norms, Linear Independence, and Rank
73(1)
Systems of Linear Equations, Consistency, and Least Squares Approximation
74(3)
Applications of Least Squares Approximation
77(15)
A Membrane Deflection Problem
77(5)
Mixed Boundary Value Problem for a Function Harmonic Inside a Circular Disk
82(5)
Using Rational Functions to Conformally Map a Circular Disk onto a Square
87(5)
Eigenvalue Problems
92(11)
Statement of the Problem
92(2)
Application to Solution of Matrix Differential Equations
94(1)
The Structural Dynamics Equation
95(8)
Computing Natural Frequencies for a Rectangular Membrane
103(4)
Column Space, Null Space, Orthonormal Bases, and SVD
107(2)
Computation Time to Run a MATLAB Program
109(8)
Methods for Interpolation and Numerical Differentiation
117(24)
Concepts of Interpolation
117(2)
Interpolation, Differentiation, and Integration by Cubic Splines
119(15)
Computing the Length and Area Bounded by a Curve
121(1)
Example: Length and Enclosed Area for a Spline Curve
121(5)
Generalizing the Intrinsic Spline Function in MATLAB
126(5)
Example: A Spline Curve with Several Parts and Corners
131(3)
Numerical Differentiation Using Finite Differences
134(7)
Example: Program to Derive Difference Formulas
136(5)
Gauss Integration with Geometric Property Applications
141(60)
Fundamental Concepts and Intrinsic Integration Tools in MATLAB
141(4)
Concepts of Gauss Integration
145(3)
Comparing Results from Gauss Integration and Function QUADL
148(5)
Geometrical Properties of Areas and Volumes
153(16)
Area Property Program
157(6)
Program Analyzing Volumes of Revolution
163(6)
Computing Solid Properties Using Triangular Surface Elements and Using Symbolic Math
169(3)
Numerical and Symbolic Results for the Example
172(8)
Geometrical Properties of a Polyhedron
180(10)
Evaluating Integrals Having Square Root Type Singularities
190(5)
Program Listing
190(5)
Gauss Integration of a Multiple Integral
195(6)
Example: Evaluating a Multiple Integral
197(4)
Fourier Series and the Fast Fourier Transform
201(32)
Definitions and Computation of Fourier Coefficients
201(4)
Trigonometric Interpolation and the Fast Fourier Transform
203(2)
Some Applications
205(28)
Using the FFT to Compute Integer Order Bessel Functions
205(3)
Dynamic Response of a Mass on an Oscillating Foundation
208(12)
General Program to Plot Fourier Expansions
220(13)
Dynamic Response of Linear Second Order Systems
233(26)
Solving the Structural Dynamics Equations for Periodic Forces
233(12)
Application to Oscillations of a Vertically Suspended Cable
235(10)
Direct Integration Methods
245(14)
Example on Cable Response by Direct Integration
247(12)
Integration of Nonlinear Initial Value Problems
259(50)
General Concepts on Numerical Integration of Nonlinear Matrix Differential Equations
259(2)
Runge-Kutta Methods and the ODE45 Integrator Provided in MATLAB
261(1)
Step-size Limits Necessary to Maintain Numerical Stability
262(5)
Discussion of Procedures to Maintain Accuracy by Varying Integration Step-size
267(1)
Example on Forced Oscillations of an Inverted Pendulum
268(9)
Dynamics of a Spinning Top
277(7)
Motion of a Projectile
284(4)
Example on Dynamics of a Chain with Specified End Motion
288(12)
Dynamics of an Elastic Chain
300(9)
Boundary Value Problems for Partial Differential Equations
309(88)
Several Important Partial Differential Equations
309(1)
Solving the Laplace Equation inside a Rectangular Region
310(11)
The Vibrating String
321(10)
Force Moving on an Elastic String
331(5)
Computer Analysis
332(4)
Waves in Rectangular or Circular Membranes
336(14)
Computer Formulation
339(1)
Input Data for Program membwave
339(11)
Wave Propagation in a Beam with an Impact Moment Applied to One End
350(14)
Forced Vibration of a Pile Embedded in an Elastic Medium
364(9)
Transient Heat Conduction in a One-Dimensional Slab
373(4)
Transient Heat Conduction in a Circular Cylinder with Spatially Varying Boundary Temperature
377(11)
Problem Formulation
377(2)
Computer Formulation
379(9)
Torsional Stresses in a Beam of Rectangular Cross Section
388(9)
Eigenvalue Problems and Applications
397(70)
Introduction
397(1)
Approximation Accuracy in a Simple Eigenvalue Problem
397(5)
Stress Transformation and Principal Coordinates
402(2)
Principal Stress Program
402(1)
Principal Axes of the Inertia Tensor
403(1)
Vibration of Truss Structures
404(12)
Truss Vibration Program
410(6)
Buckling of Axially Loaded Columns
416(15)
Example for a Linearly Tapered Circular Cross Section
421(3)
Numerical Results
424(7)
Accuracy Comparison for Euler Beam Natural Frequencies by Finite Element and Finite Difference Methods
431(19)
Mathematical Formulation
431(4)
Discussion of the Code
435(1)
Numerical Results
436(14)
Vibration Modes of an Elliptic Membrane
450(17)
Analytical Formulation
450(2)
Computer Formulation
452(15)
Bending Analysis of Beams of General Cross Section
467(22)
Introduction
467(22)
Analytical Formulation
468(4)
Program to Analyze Beams of General Cross Section
472(1)
Program Output and Code
472(17)
Applications of Analytic Functions
489(74)
Properties of Analytic Functions
489(1)
Definition of Analyticity
489(2)
Series Expansions
491(1)
Integral Properties
491(2)
Cauchy Integral Formula
492(1)
Residue Theorem
492(1)
Physical Problems Leading to Analytic Functions
493(2)
Steady-State Heat Conduction
493(1)
Incompressible Inviscid Fluid Flow
494(1)
Torsion and Flexure of Elastic Beams
494(1)
Plane Elastostatics
494(1)
Electric Field Intensity
495(1)
Branch Points and Multivalued Behavior
495(2)
Conformal Mapping and Harmonic Functions
497(2)
Mapping onto the Exterior or the Interior of an Ellipse
499(9)
Program Output and Code
503(5)
Linear Fractional Transformations
508(7)
Program Output and Code
511(4)
Schwarz-Christoffel Mapping onto a Square
515(6)
Program Output and Code
518(3)
Determining Harmonic Functions in a Circular Disk
521(13)
Numerical Results
523(4)
Program Output and Code
527(7)
Inviscid Fluid Flow around an Elliptic Cylinder
534(5)
Program Output and Code
537(2)
Torsional Stresses in a Beam Mapped onto a Unit Disk
539(6)
Program Output and Code
541(4)
Stress Analysis by the Kolosov-Muskhelishvili Method
545(18)
Program Output and Code
550(6)
Stressed Plate with an Elliptic Hole
556(4)
Program Output and Code
560(3)
Nonlinear Optimization Applications
563(44)
Basic Concepts
563(2)
Initial Angle for a Projectile
565(6)
Fitting Nonlinear Equations to Data
571(5)
Nonlinear Deflections of a Cable
576(5)
Quickest Time Descent Curve (the Brachistochrone)
581(7)
Determining the Closest Points on Two Surfaces
588(19)
Discussion of the Computer Code
591(16)
List of MATLAB Routings with Descriptions 607(10)
Selected Utility and Application Functions 617(38)
References 655(8)
Index 663

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