Advanced mathematics and mechanics applications using MATLAB
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書誌事項
Advanced mathematics and mechanics applications using MATLAB
CRC Press, c1994
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注記
With disk (3.5 inch)
Includes bibliographical references (p. [365]-373) and index
内容説明・目次
内容説明
Advanced Mathematics and Mechanics Applications Using MATLAB illustrates the problem-solving capabilities of MATLAB in advanced engineering and the physical sciences. The book covers a wide range of numerical topics and discusses the algorithmic methods that can be used for their solution. The applications emphasize solutions of linear and nonlinear differential equations. Linear partial differential equations and linear matrix differential equations are analyzed using eigenfunctions and series solutions. Several other diverse topics, such as conformal mapping, heat conduction, and inertial property calculation for areas, are also included.
The text has numerous sample programs that can be used to solve complicated applied problems. The programs have extensive comments and are intended for separate study without additional reference. Many of the programs presented in the text treat applications not presented in traditional texts, e.g., spline computation of inertia properties of arbitrary areas. Additionally, all the programs are contained on a diskette accompanying the book. This diskette is organized with directories corresponding to different chapters, and a group of frequently used functions-such as those for spline interpolation and interactive data input-comprises a separate utility library.
目次
Introduction
Software Tools for Engineering Analysis
Use of MATLAB Commands and Related Reference Materials
Description of MATLAB Commands and Related Reference Materials
Graphics Commands
Plotting Functions
Polynomial Interpolation Example
Conformal Mapping Example
String Vibration Example
Example on Animation of a Rotating Cube
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
Column Space, Null Space, Orthonormal Bases, and SVD
Program Comparing FLOP Counts for Various Matrix Operations
Methods for Interpolation and Numerical Differentiation
Concepts of Interpolation
Interpolation, Differentiation, and Integration by Cubic Splines
Numerical Differentiation Using Finite Differences
Gaussian Integration with Applications to Geometric Properties
Fundamental Concepts and Intrinsic Integration Tools Provided in MATLAB
Concepts of Gauss Integration
Examples Comparing Different Integration Methods
Line Integrals for Geometric Properties of Plane Areas
Spline Approximation of General Boundary Shapes
Fourier Series and the FFT
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 ODE23 and ODE45 Integrators 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
Example on Dynamics of a Chain with Specified End Motion
Boundary Value Problems for Linear Partial Differential Equations
Several Important Partial Differential Equations
Solving the Laplace Equation Inside a Rectangular Region
Transient Heat Conduction in a One-Dimensional Slab
Wave Propagation in a Beam with an Impact Moment Applied to One End
Torsional Stresses in a Beam of Rectangular Cross Section
Accuracy Comparison for Euler Beam Natural Frequencies Obtained by Finite Element and Finite Difference Methods
References
List of MATLAB Routines with Descriptions
MATLAB Utility Functions
Index
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