This book uses MATLABR to analyze various applications in mathematics and mechanics. The authors hope to encourage engineers and scientists to consider this modern programming environment as an excellent alternative to languages such as FORTRAN or C++. MATLAB1 embodies an interactive environment with a high level programming language supporting both numerical and graphical commands for two- and three-dimensional data analysis and presentation. The wealth of intrinsic mathematical commands to handle matrix algebra, Fourier series, differential equations, and complex-valued functions makes simple calculator operations of many tasks previously requiring subroutine libraries with cumbersome argument lists.
We analyze problems, drawn from our teaching and research interests, emphasizing linear and nonlinear differential equation methods. Linear partial differential equations and linear matrix differential equations are analyzed using eigenfunctions and series solutions. Several types of physical problems are considered. Among these are heat conduction, harmonic response of strings, membranes, beams, and trusses, geometrical properties of areas and volumes, ßexure and buckling of indeterminate beams, elastostatic stress analysis, and multi-dimensional optimization.
Numerical integration of matrix differential equations is used in several examples illustrating the utility of such methods as well as essential aspects of numerical approximation. Attention is restricted to the Runge-Kutta method which is adequate to handle most situations. Space limitation led us to omit some interesting MATLAB features concerning predictor-corrector methods, stiff systems, and event locations.
This book is not an introductory numerical analysis text. It is most useful as a reference or a supplementary text in computationally oriented courses emphasizing applications. The authors have previously solved many of the examples in FORTRAN. Our MATLAB solutions consume over three hundred pages (over twelve thousand lines). Although few books published recently present this much code, comparable FORTRAN versions would probably be signifcantly longer. In fact, the conciseness of MATLAB was a primary motivation for writing the book.