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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields
An application of the techniques of dynamical systems and bifurcation theories to the study of nonlinear oscillations. Taking their cue from Poincare, the authors stress the geometrical and topological properties of solutions of differential equations and iterated maps. Numerous exercises, some of which require nontrivial algebraic manipulations and computer work, convey the important analytical underpinnings of problems in dynamical systems and help readers develop an intuitive feel for the properties involved.
Dynamic Models in Biology
From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.
Regular Differential Forms
Suitable for students and researchers in commutative algebra, algebraic geometry, and neighboring disciplines, this book introduces various sheaves of differential forms for equidimensional morphisms of finite type between noetherian schemes, the most important being the sheaf of regular differential forms.
Control in an Information Rich World
The field of control provides the principles and methods used to design physical and information systems that maintain desirable performance by sensing and automatically adapting to changes in the environment. This report spells out some of the prospects for control in the current and future technological environment, describes the role the field will play in military, commercial, and scientific applications over the next decade, and recommends actions required to enable new breakthroughs in engineering and technology through the application of control research. This brief yet thorough report provides renewed vision, a detailed list of new application areas, and specific recommendations for future research directions in control, dynamics, and systems, compiled by experts in the field.
Inverse Scattering and Applications
This book presents papers given at a Conference on Inverse Scattering on the Line, held in June 1990 at the University of Massachusetts, Amherst. A wide variety of topics in inverse problems were covered: inverse scattering problems on the line; inverse problems in higher dimensions; inverse conductivity problems; and numerical methods. In addition, problems from statistical physics were covered, including monodromy problems, quantum inverse scattering, and the Bethe ansatz. One of the aims of the conference was to bring together researchers in a variety of areas of inverse problems which have seen intensive activity in recent years. scattering
The Legacy of Sonya Kovalevskaya
Sonya Kovalevskaya was a distinguished mathematician and considered by her contemporaries to be among the best of her generation. This work contains background material about Kovalevskaya's life and work, including a discussion of how she has been perceived by the mathematical community over the last century.
Azumaya Algebras, Actions, and Modules
This volume contains the proceedings of a conference in honor of Goro Azumaya's seventieth birthday, held at Indiana University of Bloomington in May 1990. Professor Azumaya, who has been on the faculty of Indiana University since 1968, has made many important contributions to modern abstract algebra. His introduction and investigation of what have come to be known as Azumaya algebras subsequently stimulated much research on such rings and algebras, as well as applications to geometry and number theory. In addition to honoring Professor Azumaya's contributions, the conference was intended to stimulate interaction among three areas of his research interests; Azumaya algebras, group and Hopf algebra actions, and module theory. Aimed at researchers in algebra, this volume contains contributions by some of the leaders in these areas.
Classical Groups and Related Topics
During his lifetime, L. K. Hua played a leading role in and exerted a great influence upon the development in China of modern mathematics, both pure and applied. His mathematical career began in 1931 at Tsinghua University where he continued as a professor for many years. Hua made many significant contributions to number theory, algebra, geometry, complex analysis, numerical analysis, and operations research. In particular, he initiated the study of classical groups in China and developed new matrix methods which, as applied by him as well as his followers, were instrumental in the successful attack of many problems. To honor his memory, a joint China-U.S. conference on Classical Groups and Related Topics was held at Tsinghua University in Beijing in May 1987. This volume represents the proceedings of that conference and contains both survey articles and research papers focusing on classical groups and closely related topics.
Geometry of Random Motion
In July 1987, an AMS-IMS-SIAM Joint Summer Research Conference on Geometry of Random Motion was held at Cornell University. The initial impetus for the meeting came from the desire to further explore the now-classical connection between diffusion processes and second-order (hypo)elliptic differential operators. To accomplish this goal, the conference brought together leading researchers with varied backgrounds and interests: probabilists who have proved results in geometry, geometers who have used probabilistic methods, and probabilists who have studied diffusion processes. Focusing on the interplay between probability and differential geometry, this volume examines diffusion processes on va...
