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I Euler's Method<br> II Runge-Kutta Methods<br> III The Method of Taylor Expansions<br> IV Large Second Order Systems with Application to Nano Systems<br> V Completely Conservative, Covariant Numerical Methodology<br> VI Instability<br> VII Numerical Solution of Tridiagonal Linear Algebraic Systems and Related Nonlinear Systems<br> VIII Approximate Solution of Boundary Value Problems<br> IX Special Relativistic Motion<br> X Special Topics<br> Appendix -<br> Basic Matrix Operations<br> Bibliography<br>

Donald Greenspan is Professor of Mathematics at the University of Texas, where he received the Distinguished Research Award in 1983. An experienced lecturer, he has authored 200 papers and 14 books, many of them textbooks on computational mathematics. His assignments included positions at Harvard, Stanford, Berkeley and Princeton.<br>

An up-to-date survey on numerical solutions with intuitive presentation of computer algorithms.<br> Ordinary differential equations (ODE) play a significant role in mathematics, physics and engineering sciences, and thus are part of relevant college and university courses.<br> Many problems, however, both traditional and modern, do not possess exact solutions, and must be treated numerically. Usually this is done with software packages, but for this to be efficient requires a sound understanding of the mathematics involved.<br> This work meets the need for an affordable textbook that helps in understanding numerical solutions of ODE. Carefully structured by an experienced textbook author, it provides a survey of ODE for various applications, both classical and modern, including such special applications as relativistic systems. The examples are carefully explained and compiled into an algorithm, each of which is presented independent of a specific programming language, while each chapter is rounded off with exercises.<br> The text meets the demands of MA2600 courses as well as the newly created Numerical Solution of Differential Equations courses, making it ideal for both students and lecturers in physics, mathematics, mechanical engineering, electrical engineering, a well as physicists, mathematicians, engineers, and electrical engineers.

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