Advanced Mathematics and Mechanics Applications Using Matlab

Howard B. Wilson, Louis H. Turcotte, David Halpern

692 pages, parution le 07/01/2003 (3^eme édition)

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Résumé

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 applications
Makes extensive use of MATLAB graphics capabilities, including animation and the rotate and zoom features
Includes more than 12,000 lines of MATLAB code in a format with line numbers and comments that allow the programs to stand as separate entities
Provides a separate listing of programs by subject matter
Supplies source code for all programs on the Web at www.crcpress.com

Since its introduction in 1984, MATLAB's ever-growing popularity and functionality have secured its position as an industry-standard software package. The user-friendly, interactive environment of MATLAB 6.x, which includes a high-level programming language, versatile graphics capabilities, and abundance of intrinsic functions, helps users focus on their applications rather than on programming errors. MATLAB has now leapt far ahead of FORTRAN as the software of choice for engineering applications.

Contents

Introduction

MATLAB: A Tool for Engineering Analysis
MATLAB Commands and Related Reference Materials
Example Problem on Financial Analysis
Computer Code and Results

Elementary Aspects of MATLAB Graphics

Introduction
Overview of Graphics
Example Comparing Polynomial and Spline Interpolation
Conformal Mapping Example
Nonlinear Motion of a Damped Pendulum
A Linear Vibration Model
Example on Waves in an Elastic String
Properties of Curves and Surfaces

Summary of Concepts from Linear Algebra

Introduction
Vectors, Norms, Linear Independence, and Rank
Systems of Linear Equations, Consistency, and Least Square Approximation
Applications of Least Square Approximation
Eigenvalue Problems
Computing Natural Frequencies for a Rectangular Membrane
Column Space, Null Space, Orthonormal Bases, and SVD
Computation Time to Run a MATLAB Program

Methods for Interpolation and Numerical Differentiation

Concepts of Interpolation
Interpolation, Differentiation, and Integration by Cubic Splines
Numerical Differentiation Using Finite Differences

Gauss Integration with Geometric Property Applications

Fundamental Concepts and Intrinsic Integration Tools in MATLAB
Concepts of Gauss Integration
Comparing Results from Gauss Integration and Function QUADL
Geometrical Properties of Areas and Volumes
Computing Solid Properties Using Triangular Surface Elements and Using Symbolic Math
Numerical and Symbolic Results for the Example
Geometrical Properties of a Polyhedron
Evaluating Integrals Having Square Root Type Singularities
Gauss Integration of a Multiple Integral

Fourier Series and the Fast Fourier Transform

Definitions and Computation of Fourier Coefficients
Some Applications

Dynamic Response of Linear Second Order Systems

Solving the Structural Dynamics Equations for Periodic Applied Forces
Direct Integration Methods

Integration of Nonlinear Initial Value Problems

General Concepts on Numerical Integration of Nonlinear Matrix Differential Equations
Runge-Kutta Methods and the ODE Integrator Provided in MATLAB
Step-Size Limits Necessary to Maintain Numerical Stability
Discussion of Procedures to Maintain Accuracy by Varying Integration Step-size
Example on Forced Oscillations of an Inverted Pendulum
Dynamics of a Spinning Top
Motion of a Projectile
Example on Dynamics of a Chain with Specified End Motion
Dynamics of an Elastic Chain

Boundary VALUE Problems for Linear Partial Differential Equations

Several Important Partial Differential Equations
Solving the Laplace Equation Inside a Rectangular Region
The Vibrating String
Force Moving on an Elastic String
Waves in Rectangular or Circular Membranes
Wave Propagation in a Beam with an Impact Moment Applied to One End
Forced Vibration of a Pile Embedded in an Elastic Medium
Transient Heat Conduction in a One-Dimensional Slab
Transient Heat Conduction in a Circular Cylinder with Spatially Varying Boundary Temperature
Torsional Stresses in a Beam of Rectangular Cross Section

Eigenvalue Problems and Applications

Introduction
Approximation Accuracy in a Simple Eigenvalue Problem
Stress Transformation and Principal Coordinates
Vibration of Truss Structures
Buckling of Axially Loaded Columns
Accuracy Comparison for Euler Beam Natural Frequencies by Finite Element and Finite Difference Methods
Vibration Modes of an Elliptic Membrane

Bending Analysis of Beams of General Cross Section

Introduction

Applications of Analytic Functions

Properties of Analytic Functions
Definition of Analyticity
Series Expansions
Integral Properties
Physical Problems Leading to Analytic Functions
Branch Points and Multivalued Behavior
Conformal Mapping and Harmonic Functions
Mapping onto the Exterior or the Interior of an Ellipse
Linear Fractional Transformations
Schwarz-Christoffel Mapping onto a Square
Determining Harmonic Functions in a Circular Disk
Inviscid Fluid Flow around an Elliptic Cylinder
Torsional Stresses in a Beam Mapped onto a Unit Disk
Stress Analysis by the Kolosov-Muskhelishvili Method

Nonlinear Optimization Applications

Basic Concepts
Initial Angle for a Projectile
Fitting Nonlinear Equations to Data
Nonlinear Deflections of a Cable
Quickest Time Descent Curve (the Brachistochrone)
Determining the Closest Points on Two Surfaces

Appendices

A List of MATLAB Routines with Descriptions
B Selected Utility and Application Functions

L'auteur - Howard B. Wilson

University of Alabama, Northport, Alabama USA

L'auteur - Louis H. Turcotte

Rose-Hulman Institute of Technology, Indiana, USA

L'auteur - David Halpern

University of Alabama, Tuscaloosa, Alabama, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Howard B. Wilson, Louis H. Turcotte, David Halpern
Parution	07/01/2003
Édition	3^eme édition
Nb. de pages	692
Format	16 x 24
Couverture	Relié
Poids	1081g
Intérieur	Noir et Blanc
EAN13	9781584882626
ISBN13	978-1-58488-262-6