Advanced Mathematics and Mechanics Applications Using MATLAB

ISBN-13: 9781584882626 / Angielski / Twarda / 2002 / 696 str.

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

Opis

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.

Recenzje

"Material [in this book] can serve as a valuable resource for the AEM course that provides a brief exposure to numerics. It can also supplement the more heavily numerical course."
- SIAM Review, Vol. 46, No. 3

Spis treści

INTRODUCTION
MATLAB: A Tool for Engineering Analysis
Use of 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
Computing the Length and Area Bounded by a Curve
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
Analytical Formulation
Program to Analyze Beams of General Cross Section
Program Output and Code
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
Potential 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
List of MATLAB Routines with Descriptions
Selected Utility and Application Functions

O autorze

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