Advanced Mathematics and Mechanics Applications
Using MATLAB
Authors - Howard B. Wilson, Jr.
University of Alabama, Tuscaloosa
and Louis H. Turcotte
Mississippi State University
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Publication Information and Price
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.
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- Partial list of MATLAB 4.xx statements
- Descriptions of MATLAB routines
- Sample programs to solve applied problems
- Diskette containing all programs discussed in text
- 70 figures to help illustrate key points
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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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This book is a useful reference for research engineers, workers
dealing with physical applications, and senior-graduate students
taking courses in advanced engineering mechanics, numerical analysis,
and engineering mathematics.
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Catalog no. 2482
ISBN: 0-8493-2482-3
For orders, contact our order department
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