Sinopsis
This book presents variousMATLAB applications in mechanics and applied mathematics. Our objective is to employ numerical methods in examples emphasizing the appeal of MATLAB as a programming tool. The programs are intended for study as a primary component of the text. The numerical methods used include interpolation, numerical integration, Þnite differences, linear algebra, Fourier analysis, roots of nonlinear equations, linear differential equations, nonlinear differential equations, linear partial differential equations, analytic functions, and optimization methods. Many intrinsic MATLAB functions are used along with some utility functions developed by the authors. The physical applications vary widely from solution of linear and nonlinear differential equations in mechanical system dynamics to geometrical property calculations for areas and volumes.
For many years FORTRAN has been the favorite programming language for solving mathematical and engineering problems on digital computers. An attractive alternative is MATLAB which facilitates program development with excellent error diagnostics and code tracing capabilities. Matrices are handled efÞciently with many intrinsic functions performing familiar linear algebra tasks. Advanced software features such as dynamic memory allocation and interactive error tracing reduce the time to get solutions. The versatile but simple graphics commands in MATLAB also allow easy preparation of publication quality graphs and surface plots for technical papers and books. The authors have found that MATLAB programs are often signifantly shorter than corresponding FORTRAN versions. Consequently, more time is available for the primary purpose of computing, namely, to better understand physical system behavior.
The mathematical foundation needed to grasp most topics presented here is covered in an undergraduate engineering curriculum. This should include a grounding in calculus, differential equations, and knowledge of a procedure oriented programming language like FORTRAN. An additional course on advanced engineering mathematics covering linear algebra, matrix differential equations, and eigenfunction solutions of partial differential equations will also be valuable. The MATLAB programs were written primarily to serve as instructional examples in classes traditionally referred to as advanced engineering mathematics and applied numerical methods. The greatest beneÞt to the reader will probably be derived through study of the programs relating mainly to physics and engineering applications. Furthermore, we believe that several of the MATLAB functions are useful as general utilities. Typical examples include routines for spline interpolation, differentiation, and integration; area and inertial moments for general plane shapes; and volume and inertial properties of arbitrary polyhedra. We have also included examples demonstrating natural frequency analysis and wave propagation in strings and membranes.
MATLAB is now employed in more than two thousand universities and the user community throughout the world numbers in the thousands. Continued growth will be fueled by decreasing hardware costs and more people familiar with advanced analytical methods. The authors hope that our problem solutions will motivate analysts already comfortable with languages like FORTRAN to learnMATLAB. The rewards of such efforts can be considerable.
Content
- Introduction
- Elementary Aspects of MATLAB Graphics
- Summary of Concepts fromLinear Algebra
- Methods for Interpolation and Numerical Differentiation
- Gauss Integration with Geometric Property Applications
- Fourier Series and the Fast Fourier Transform
- Dynamic Response of Linear Second Order Systems
- Integration of Nonlinear Initial Value Problems
- Boundary Value Problems for Partial Differential Equations
- Eigenvalue Problems and Applications
- Bending Analysis of Beams of General Cross Section
- Applications of Analytic Functions
- Nonlinear Optimization Applications
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