Advanced Mathematics and Mechanics Applications Using MATLAB, Third Edition

by Halpern; David

• ISBN13: 9781584882626
• ISBN10: 158488262X
• Edition: 3rd
• Format: Hardcover
• Copyright: 2002-09-17
• Publisher: Chapman & Hall/

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