Acheson D.J. From Calculus to Chaos: An Introduction to Dynamics
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Oxford University Press, 1997. 280 р. — ISBN:0198500777.
Рассмотрены базовые основы процессов динамики предметов и сред. Приведены примеры составления программ по динамическим процессам.What is calculus really for? This book is a highly readable introduction to applications of calculus, from Newton's time to the present day. These often involve questions of dynamics, i.e. of how - and why - things change with time. Problems of this kind lie at the heart of much of applied mathematics, physics, and engineering. From Calculus to Chaos takes a fresh approach to the subject as a whole, by moving from first steps to the frontiers, and by highlighting only the most important and interesting ideas, which can get lost amid a snowstorm of detail in conventional texts. The book is aimed at a wide readership, and assumes only some knowledge of elementary calculus. There are exercises (with full solutions) and simple but powerful computer programs which are suitable even for readers with no previous computing experience. David Acheson's book will inspire new students by providing a foretaste of more advanced mathematics and showing just how interesting the subject can be.Introduction A brief review of calculus Ordinary differential equations Computer solution methods Elementary oscillations Planetary motion Waves and diffusion The best of all possible worlds ? Fluid flow Instability and catastrophe Nonlinear oscillations and chaos The not-so-simple pendulum Further reading Appendix A: Elementary programming in QBasic Appendix B: Ten programs for exploring dynamics Solutions to the exercises Index
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Taylor & Francis, 1985. - 219 pages.
In creating mathematical models of real processes, scientists, engineers and students frequently encounter differential equations whose exact solutions are necessarily complicated and are normally solvable only by computer or through complex formal mathematics. This practical book demonstrates how approximate methods may be used to minimise...