This treatment presents most of the methods for solving ordinary differential equations and systematic arrangements of more than 2,000 equations and their solutions. The material is organized so that standard equations can be easily found. Plus, the substantial number and variety of equations promises an exact equation or a sufficiently similar one. 1960 edition.
This collection of nearly forty essays in honor of the noted physicist and cosmologist Engelbert Schucking spans the gamut of research in Einsteins theory of general relativity and presents a lively and personal account of current work in the field. Indispensable for physicists involved in research in the field, the book includes important chapters by noted theorists such as A. Ashtekar, P.G. Bergmann, J. Ehlers, E.T. Newman, J.V. Narlikar, R. Penrose, D.W. Sciama, J. Stachel, and W. Rindler.
This book constitutes the proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing, CASC 2015, held in Aachen, Germany, in September 2015. The 35 full papers presented in this volume were carefully reviewed and selected from 42 submissions. They deal with the ongoing progress both in theoretical computer algebra and its expanding applications. New and closer interactions are fostered by combining the area of computer algebra methods and systems and the application of the tools of computer algebra for the solution of problems in scientific computing.
Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space. This approach relies on ideas and methods of modem functional analysis, general topology, the theory of multi-valued mappings and continuous selectors. Although the basic content of the previous monograph has been remained the same this monograph has been partly re-organized and the author's recent results have been added. The contents of the present book are divided into five Chapters and an Appendix. The first Chapter of the J>ook has been left without changes and deals with multi-valued differential equations generated by a differential inclusion. The second Chapter has been significantly revised and extended. Here the au thor's recent results concerning extreme continuous selectors of multi-functions with decomposable values, multi-valued selectors ofmulti-functions generated by a differential inclusion, the existence of solutions of a differential inclusion, whose right hand side has different properties of semicontinuity at different points, have been included. Some of these results made it possible to simplify schemes for proofs concerning the existence of solutions of differential inclu sions with semicontinuous right hand side a.nd to obtain new results. In this Chapter the existence of solutions of different types are considered.
This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016. This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.
Fluid Dynamics Transactions, Volume 1 is a compilation of papers presented at the Fifth Symposium on Fluid Dynamics held in Poland from August 26 to September 2, 1961. The symposium provided a forum for discussing developments in fluid dynamics based on the following topics: mathematical methods, hypersonic flow, rarefied gas dynamics, and magnetohydrodynamics. This volume is comprised of 26 chapters and begins by presenting equations for gas dynamics and highlighting some of applications of the general results. The discussion then turns to Cauchy's problem for the compressible flow of the simple wave type; the use of exact numerical methods for the solution of boundary layer problems; and the effect of surface catalytic efficiency on stagnation point heat transfer. A geometric method of classifying solutions of gas dynamics using certain space and the time-space Lie transformation groups is described. Subsequent chapters explore supersonic flow past blunt bodies; application of the Monte Carlo method to the analysis of rarefied gas flows; and fluid-fluid displacement in a porous medium. This book will be a useful resource for engineers and other scientists interested in fluid dynamics.
Maintaining the substance that has made Introduction to the Thermodynamics of Materials a perennial bestseller for decades, the Seventh Edition is updated to reflect the broadening field of materials science and engineering. Chapters are updated and revised throughout to be more useful and logical for students. Features more than 60 new homework problems for the students, a listing of terms and concepts introduced, and a summary section Includes more on mathematical and graphical analysis of the various state functions utilized in classical thermodynamics Includes a more extensive discussion of the third law of thermodynamics Features a new appendix on exact differential equations and mathematical relationships, including all mathematical relations among differentials of homogeneous functions utilized in the text Written as the definitive introduction to the thermodynamic behavior of materials systems, this text presents the underlying thermodynamic principles of materials and their applications and continues to be the best undergraduate textbook in thermodynamics for materials science students. An updated solutions manual is also available for qualifying adopting professors.
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