Advanced Mathematics and Mechanics Applications Using Matlab
Howard B. Wilson, Louis H. Turcotte, David Halpern
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
- 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
- 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
- Concepts of Interpolation
- Interpolation, Differentiation, and Integration by Cubic Splines
- Numerical Differentiation Using Finite Differences
- 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
- Definitions and Computation of Fourier Coefficients
- Some Applications
- Solving the Structural Dynamics Equations for Periodic Applied Forces
- Direct Integration Methods
- 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
- 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
- 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
- Introduction
- 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
- 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
- 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 | 3eme 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 |
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