The Discovery of Dynamics


Book Description

"Originally published as Absolute or relative motion? volume 1, The discovery of dynamics, Cambridge University Press, 1989".







Philosophy and the Foundations of Dynamics


Book Description

Examines the main theories of dynamics, their original inception and their evolution over time into contemporary foundational theories.




Mach's Principle


Book Description

This volume is a collection of scholarly articles on the Mach Principle, the impact that this theory has had since the end of the 19th century, and its role in helping Einstein formulate the doctrine of general relativity. 20th-century physics is concerned with the concepts of time, space, motion, inertia and gravity. The documentation on all of these makes this book a reference for those who are interested in the history of science and the theory of general relativity




Dynamics Of Complex Systems


Book Description

This book aims to develop models and modeling techniques that are useful when applied to all complex systems. It adopts both analytic tools and computer simulation. The book is intended for students and researchers with a variety of backgrounds.




Discovering Discrete Dynamical Systems


Book Description

Discovering Discrete Dynamical Systems is a mathematics textbook designed for use in a student-led, inquiry-based course for advanced mathematics majors. Fourteen modules each with an opening exploration, a short exposition and related exercises, and a concluding project guide students to self-discovery on topics such as fixed points and their classifications, chaos and fractals, Julia and Mandelbrot sets in the complex plane, and symbolic dynamics. Topics have been carefully chosen as a means for developing student persistence and skill in exploration, conjecture, and generalization while at the same time providing a coherent introduction to the fundamentals of discrete dynamical systems. This book is written for undergraduate students with the prerequisites for a first analysis course, and it can easily be used by any faculty member in a mathematics department, regardless of area of expertise. Each module starts with an exploration in which the students are asked an open-ended question. This allows the students to make discoveries which lead them to formulate the questions that will be addressed in the exposition and exercises of the module. The exposition is brief and has been written with the intent that a student who has taken, or is ready to take, a course in analysis can read the material independently. The exposition concludes with exercises which have been designed to both illustrate and explore in more depth the ideas covered in the exposition. Each module concludes with a project in which students bring the ideas from the module to bear on a more challenging or in-depth problem. A section entitled "To the Instructor" includes suggestions on how to structure a course in order to realize the inquiry-based intent of the book. The book has also been used successfully as the basis for an independent study course and as a supplementary text for an analysis course with traditional content.




Shape Dynamics


Book Description

Shape Dynamics is a radical yet soundly based reinterpretation of Einstein's theory of gravity that has opened up new approaches to gravity research. This text offers both a brief introduction and a detailed walk-through of the motivations for the theory, its development from first principles and an in-depth look at its present status.




Observed Brain Dynamics


Book Description

The biomedical sciences have recently undergone revolutionary change, due to the ability to digitize and store large data sets. In neuroscience, the data sources include measurements of neural activity measured using electrode arrays, EEG and MEG, brain imaging data from PET, fMRI, and optical imaging methods. Analysis, visualization, and management of these time series data sets is a growing field of research that has become increasingly important both for experimentalists and theorists interested in brain function. Written by investigators who have played an important role in developing the subject and in its pedagogical exposition, the current volume addresses the need for a textbook in this interdisciplinary area. The book is written for a broad spectrum of readers ranging from physical scientists, mathematicians, and statisticians wishing to educate themselves about neuroscience, to biologists who would like to learn time series analysis methods in particular and refresh their mathematical and statistical knowledge in general, through self-pedagogy. It may also be used as a supplement for a quantitative course in neurobiology or as a textbook for instruction on neural signal processing. The first part of the book contains a set of essays meant to provide conceptual background which are not technical and shall be generally accessible. Salient features include the adoption of an active perspective of the nervous system, an emphasis on function, and a brief survey of different theoretical accounts in neuroscience. The second part is the longest in the book, and contains a refresher course in mathematics and statistics leading up to time series analysis techniques. The third part contains applications of data analysis techniques to the range of data sources indicated above (also available as part of the Chronux data analysis platform from http://chronux.org), and the fourth part contains special topics.




Data-Driven Science and Engineering


Book Description

A textbook covering data-science and machine learning methods for modelling and control in engineering and science, with Python and MATLAB®.




Geometric Dynamics


Book Description

The theme of this text is the philosophy that any particle flow generates a particle dynamics, in a suitable geometrical framework. It covers topics that include: geometrical and physical vector fields; field lines; flows; stability of equilibrium points; potential systems and catastrophe geometry; field hypersurfaces; bifurcations; distribution orthogonal to a vector field; extrema with nonholonomic constraints; thermodynamic systems; energies; geometric dynamics induced by a vector field; magnetic fields around piecewise rectilinear electric circuits; geometric magnetic dynamics; and granular materials and their mechanical behaviour. The text should be useful for first-year graduate students in mathematics, mechanics, physics, engineering, biology, chemistry, and economics. It can also be addressed to professors and researchers whose work involves mathematics, mechanics, physics, engineering, biology, chemistry, and economics.