[PDF] Dynamics Numerical Explorations eBook

Author : Helena E. Nusse
Publisher : Springer
Page : 502 pages
File Size : 45,41 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1468402315

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Co-author J.A. Yorke developed an array of tools to help visualize the properties of dynamical systems, while Yorke found it useful to combine these various basic tools into one single package: Dynamics. The program together with this manual provides an introduction to and an overview of fundamental, sophisticated tools and numerical methods together with many simple examples. All numerical methods described in this handbook are implemented in the program, which is capable of, among others: iterating maps and solving differential equations; plotting trajectories; featuring an array of simple commands; printing a created picture in resolution higher than that of the screen. Requires a UNIX workstation running X11 graphics or a PC.

Author : Helena Engelina Nusse
Publisher : Springer
Page : 484 pages
File Size : 34,63 MB
Release : 1994-01-01
Category : Chaotic behavior in systems
ISBN : 9780387942544

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This book, together with the accompanying software program 'Dynamics' helps the novice to begin immediately exploring dynamical systems with a broad array of interactive techniques. Numerous examples in the book present a step-by-step approach to creating pictures of complex phenomena in simple systems.

Author : Thomas LoFaro
Publisher : CRC Press
Page : 216 pages
File Size : 14,47 MB
Release : 2021-03-22
Category : Mathematics
ISBN : 1000358933

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Discovering Dynamical Systems Through Experiment and Inquiry differs from most texts on dynamical systems by blending the use of computer simulations with inquiry-based learning (IBL). IBL is an excellent tool to move students from merely remembering the material to deeper understanding and analysis. This method relies on asking students questions first, rather than presenting the material in a lecture. Another unique feature of this book is the use of computer simulations. Students can discover examples and counterexamples through manipulations built into the software. These tools have long been used in the study of dynamical systems to visualize chaotic behavior. We refer to this unique approach to teaching mathematics as ECAP—Explore, Conjecture, Apply, and Prove. ECAP was developed to mimic the actual practice of mathematics in an effort to provide students with a more holistic mathematical experience. In general, each section begins with exercises guiding students through explorations of the featured concept and concludes with exercises that help the students formally prove the results. While symbolic dynamics is a standard topic in an undergraduate dynamics text, we have tried to emphasize it in a way that is more detailed and inclusive than is typically the case. Finally, we have chosen to include multiple sections on important ideas from analysis and topology independent from their application to dynamics.

Author : Claude P. Bruter
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 17,8 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 3662049090

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Recent progress in research, teaching and communication has arisen from the use of new tools in visualization. To be fruitful, visualization needs precision and beauty. This book is a source of mathematical illustrations by mathematicians as well as artists. It offers examples in many basic mathematical fields including polyhedra theory, group theory, solving polynomial equations, dynamical systems and differential topology. For a long time, arts, architecture, music and painting have been the source of new developments in mathematics. And vice versa, artists have often found new techniques, themes and inspiration within mathematics. Here, while mathematicians provide mathematical tools for the analysis of musical creations, the contributions from sculptors emphasize the role of mathematics in their work.