Download or read book Sur les propri t s des fonctions d finies par les quations aux diff rences partielles written by Henri Poincaré and published by . This book was released on 1879 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations written by Marcelo Viana and published by American Mathematical Society. This book was released on 2021-12-30 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time—pure and applied alike—ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.
Download or read book Henri Poincar written by Jeremy Gray and published by Princeton University Press. This book was released on 2013 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive look at the mathematics, physics, and philosophy of Henri Poincaré Henri Poincaré (1854–1912) was not just one of the most inventive, versatile, and productive mathematicians of all time—he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later. The first in-depth and comprehensive look at his many accomplishments, Henri Poincaré explores all the fields that Poincaré touched, the debates sparked by his original investigations, and how his discoveries still contribute to society today. Math historian Jeremy Gray shows that Poincaré's influence was wide-ranging and permanent. His novel interpretation of non-Euclidean geometry challenged contemporary ideas about space, stirred heated discussion, and led to flourishing research. His work in topology began the modern study of the subject, recently highlighted by the successful resolution of the famous Poincaré conjecture. And Poincaré's reformulation of celestial mechanics and discovery of chaotic motion started the modern theory of dynamical systems. In physics, his insights on the Lorentz group preceded Einstein's, and he was the first to indicate that space and time might be fundamentally atomic. Poincaré the public intellectual did not shy away from scientific controversy, and he defended mathematics against the attacks of logicians such as Bertrand Russell, opposed the views of Catholic apologists, and served as an expert witness in probability for the notorious Dreyfus case that polarized France. Richly informed by letters and documents, Henri Poincaré demonstrates how one man's work revolutionized math, science, and the greater world.
Download or read book The Logarithmic Potential and Other Monographs written by Griffith Conrad Evans and published by American Mathematical Soc.. This book was released on 1980 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume contains the following monographs: The Logarithmic Potential by Evans Fundamental Existence Theorems by Bliss Differential-Geometric Aspects of Dynamics by Kasner All three monographs were originally published by the AMS and are now available in this single volume from AMS Chelsea Publishing.
Download or read book Fundamental Existence Theorems written by Gilbert Ames Bliss and published by . This book was released on 1913 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Colloquium Lectures written by and published by . This book was released on 1913 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Approaches for Emerging and Reemerging Infectious Diseases An Introduction written by Carlos Castillo-Chavez and published by Springer Science & Business Media. This book was released on 2002-05-02 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book grew out of the discussions and presentations that began during the Workshop on Emerging and Reemerging Diseases (May 17-21, 1999) sponsored by the Institute for Mathematics and its Application (IMA) at the University of Minnesota with the support of NIH and NSF. The workshop started with a two-day tutorial session directed at ecologists, epidemiologists, immunologists, mathematicians, and scientists interested in the study of disease dynamics. The core of this first volume, Volume 125, covers tutorial and research contributions on the use of dynamical systems (deterministic discrete, delay, PDEs, and ODEs models) and stochastic models in disease dynamics. The volume includes the study of cancer, HIV, pertussis, and tuberculosis. Beginning graduate students in applied mathematics, scientists in the natural, social, or health sciences or mathematicians who want to enter the fields of mathematical and theoretical epidemiology will find this book useful.
Download or read book Mathematics of the 19th Century written by A.N. Kolmogorov and published by Springer Science & Business Media. This book was released on 1998-03-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: The editors of the present series had originally intended to publish an integrated work on the history of mathematics in the nineteenth century, passing systemati cally from one discipline to another in some natural order. Circumstances beyond their control, mainly difficulties in choosing authors, led to the abandonment of this plan by the time the second volume appeared. Instead of a unified mono graph we now present to the reader a series of books intended to encompass all the mathematics of the nineteenth century, but not in the order of the accepted classification of the component disciplines. In contrast to the first two books of The Mathematics of the Nineteenth Century, which were divided into chapters, this third volume consists of four parts, more in keeping with the nature of the publication. 1 We recall that the first book contained essays on the history of mathemati 2 cal logic, algebra, number theory, and probability, while the second covered the history of geometry and analytic function theory. In the present third volume the reader will find: 1. An essay on the development of Chebyshev's theory of approximation of functions, later called "constructive function theory" by S. N. Bernshtein. This highly original essay is due to the late N. I. Akhiezer (1901-1980), the author of fundamental discoveries in this area. Akhiezer's text will no doubt attract attention not only from historians of mathematics, but also from many specialists in constructive function theory.
Download or read book Fractal Physiology written by James B Bassingthwaighte and published by Springer. This book was released on 2013-05-27 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: I know that most men, including those at ease with the problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives. Joseph Ford quoting Tolstoy (Gleick, 1987) We are used to thinking that natural objects have a certain form and that this form is determined by a characteristic scale. If we magnify the object beyond this scale, no new features are revealed. To correctly measure the properties of the object, such as length, area, or volume, we measure it at a resolution finer than the characteristic scale of the object. We expect that the value we measure has a unique value for the object. This simple idea is the basis of the calculus, Euclidean geometry, and the theory of measurement. However, Mandelbrot (1977, 1983) brought to the world's attention that many natural objects simply do not have this preconceived form. Many of the structures in space and processes in time of living things have a very different form. Living things have structures in space and fluctuations in time that cannot be characterized by one spatial or temporal scale. They extend over many spatial or temporal scales.
Download or read book Theoretical and Applied Mechanics written by P. Germain and published by Elsevier. This book was released on 2012-12-02 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contained in this volume are the full texts of the invited general and sectional lectures presented at this conference. The entire field of mechanics is covered, including analytical, solid and fluid mechanics and their applications. Invited papers on the following topics are also presented: Mechanics of large deformation and damage; The dynamics of two-phase flows; Mechanics of the earth's crust.The papers are written by leading experts and provide a valuable key to the latest and most important developments in various sub-fields of mechanics.
Download or read book Regular and Chaotic Motions in Dynamic Systems written by A. S. Wightman and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifth International School ~ Mathematical Physics was held at the Ettore Majorana Centro della Culture Scientifica, Erice, Sicily, 2 to 14 July 1983. The present volume collects lecture notes on the session which was devoted to'Regular and Chaotic Motions in Dynamlcal Systems. The School was a NATO Advanced Study Institute sponsored by the Italian Ministry of Public Education, the Italian Ministry of Scientific and Technological Research and the Regional Sicilian Government. Many of the fundamental problems of this subject go back to Poincare and have been recognized in recent years as being of basic importance in a variety of physical contexts: stability of orbits in accelerators, and in plasma and galactic dynamics, occurrence of chaotic motions in the excitations of solids, etc. This period of intense interest on the part of physicists followed nearly a half a century of neglect in which research in the subject was almost entirely carried out by mathematicians. It is an in dication of the difficulty of some of the problems involved that even after a century we do not have anything like a satisfactory solution.
Download or read book Thirteen papers on differential equations written by V. M. Alekseev and published by American Mathematical Soc.. This book was released on 1970-12-31 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Dynamical Systems V written by V.I. Arnold and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
Download or read book Vladimir I Arnold Collected Works written by Vladimir I. Arnold and published by Springer Science & Business Media. This book was released on 2009-10-22 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vladimir Arnold is one of the greatest mathematical scientists of our time, as well as one of the finest, most prolific mathematical authors. This first volume of his Collected Works focuses on representations of functions, celestial mechanics and KAM theory.
Download or read book The Three Body Problem and the Equations of Dynamics written by Henri Poincaré and published by Springer. This book was released on 2017-05-11 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating.
Download or read book Introduction to Applied Nonlinear Dynamical Systems and Chaos written by Stephen Wiggins and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 685 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction to applied nonlinear dynamics and chaos. The emphasis is on teaching the techniques and ideas that will enable students to take specific dynamical systems and obtain some quantitative information about their behavior. The new edition has been updated and extended throughout, and contains an extensive bibliography and a detailed glossary of terms.
Download or read book Elements of Applied Bifurcation Theory written by Yuri A. Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: A solid basis for anyone studying the dynamical systems theory, providing the necessary understanding of the approaches, methods, results and terminology used in the modern applied-mathematics literature. Covering the basic topics in the field, the text can be used in a course on nonlinear dynamical systems or system theory. Special attention is given to efficient numerical implementations of the developed techniques, illustrated by several examples from recent research papers. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used, making this book suitable for advanced undergraduate or graduate students in applied mathematics, as well as for researchers in other disciplines who use dynamical systems as model tools in their studies.
