Download or read book Differential Equations with Discontinuous Righthand Sides written by A.F. Filippov and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Download or read book Differential Equations with Impulse Effects written by Nikolai A. Perestyuk and published by Walter de Gruyter. This book was released on 2011-07-27 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems. Impulsive systems are also encountered in numerous problems of natural sciences described by mathematical models with conditions reflecting the impulsive action of external forces with pulses whose duration can be neglected. Differential equations with set-valued right-hand side arise in the investigation of evolution processes in the case of measurement errors, inaccuracy or incompleteness of information, action of bounded perturbations, violation of unique solvability conditions, etc. Differential inclusions also allow one to describe the dynamics of controlled processes and are widely used in the theory of optimal control. This monograph is devoted to the investigation of impulsive differential equations with set-valued and discontinuous right-hand sides. It is intended for researchers, lecturers, postgraduate students, and students of higher schools specialized in the field of the theory of differential equations, the theory of optimal control, and their applications.

Download or read book Differential Equations with Discontinuous Coefficients written by Ward Conrad Sangren and published by . This book was released on 1953 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multivalued Differential Equations written by Klaus Deimling and published by Walter de Gruyter. This book was released on 2011-07-22 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome. Please submit book proposals to Jürgen Appell.

Download or read book Principles of Partial Differential Equations written by Alexander Komech and published by Springer. This book was released on 2009-09-23 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques. The theoretical part is rigorous and with important details presented with care. Hints are provided to help the reader restore the arguments to their full rigor. Many examples from physics are intended to keep the book intuitive and to illustrate the applied nature of the subject. The book is useful for a higher-level undergraduate course and for self-study.

Download or read book Differential Equations written by David Lomen and published by Prentice Hall. This book was released on 1988 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Download or read book Introduction to the Theory of Differential Inclusions written by Georgi V. Smirnov and published by American Mathematical Soc.. This book was released on 2002 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential inclusions play an important role as a tool in the study of various dynamical processes described by equations with a discontinuous or multivalued right-hand side. This text acts as an introduction to the subject.

Download or read book Monotone Iterative Techniques for Discontinuous Nonlinear Differential Equations written by V. Lakshmikantham and published by Routledge. This book was released on 2017-09-29 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""Providing the theoretical framework to model phenomena with discontinuous changes, this unique reference presents a generalized monotone iterative method in terms of upper and lower solutions appropriate for the study of discontinuous nonlinear differential equations and applies this method to derive suitable fixed point theorems in ordered abstract spaces.

Download or read book Differential Equations written by Harry Hochstadt and published by Courier Corporation. This book was released on 2014-05-05 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVModern approach presents subject in terms of ideas and concepts rather than special cases and tricks. 134 problems. Preface. Index. /div

Download or read book Partial Differential Equations written by Bitsadze A V and published by World Scientific. This book was released on 1993-12-27 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook in partial differential equations has been adopted as course material by the Moscow State University. The theoretical foundations of PDE are explained rigorously and clearly in such a way that their importance on applications is also taken into account. The presentation of materials has been arranged to be conducive to promoting students' interest in mathematical experiments.

Download or read book Differential Equations and Their Applications written by Martin Braun and published by Springer. This book was released on 2012 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1 First-order differential equations.- 1.1 Introduction.- 1.2 First-order linear differential equations.- 1.3 The van Meegeren art forgeries.- 1.4 Separable equations.- 1.5 Population models.- 1.6 An atomic waste disposal problem.- 1.7 The dynamics of tumor growth, mixing problems, and orthogonal trajectories.- 1.8 Exact equations, and why we cannot solve very many differential equations.- 1.9 The existence-uniqueness theorem; Picard iteration.- 1.10 Difference equations, and how to compute the interest due on your student loans.- 2 Second-order linear differential equations.- 2.1 Algebraic properties of solutions.- 2.2 Linear equations with constant coefficients.- 2.2.1 Complex roots.- 2.2.2 Equal roots; reduction of order.- 2.3 The nonhomogeneous equation.- 2.4 The method of variation of parameters.- 2.5 The method of judicious guessing.- 2.6 Mechanical vibrations.- 2.6.1 The Tacoma Bridge disaster.- 2.6.2 Electrical networks.- 2.7 A model for the detection of diabetes.- 2.8 Series solutions.- 2.8.1 Singular points; the method of Frobenius.- 2.9 The method of Laplace transforms.- 2.10 Some useful properties of Laplace transforms.- 2.11 Differential equations with discontinuous right-hand sides.- 2.12 The Dirac delta function.- 2.13 The convolution integral.- 2.14 The method of elimination for systems.- 2.15 A few words about higher-order equations.- 3 Systems of differential equations.- 3.1 Algebraic properties of solutions of linear systems.- 3.2 Vector spaces.- 3.3 Dimension of a vector space.- 3.4 Applications of linear algebra to differential equations.- 3.5 The theory of determinants.- 3.6 The eigenvalue-eigenvector method of finding solutions.- 3.7 Complex roots.- 3.8 Equal roots.- 3.9 Fundamental matrix solutions; eAt.- 3.10 The nonhomogeneous equation; variation of parameters.- 3.11 Solving systems by Laplace transforms.- 4 Qualitative theory of differential equations.- 4.1 Introduction.- 4.2 The phase-plane.- 4.3 Lanchester's combat models and the battle of Iwo Jima.- Appendix A.- Some simple facts concerning functions of several variables.- Appendix B.- Sequences and series.- Answers to odd-numbered exercises.

Download or read book Bifurcation in Autonomous and Nonautonomous Differential Equations with Discontinuities written by Marat Akhmet and published by Springer. This book was released on 2017-01-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.

Download or read book Differential Equations with Applications written by Paul D. Ritger and published by Courier Corporation. This book was released on 2000-01-01 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coherent, balanced introductory text focuses on initial- and boundary-value problems, general properties of linear equations, and the differences between linear and nonlinear systems. Includes large number of illustrative examples worked out in detail and extensive sets of problems. Answers or hints to most problems appear at end.

Download or read book Ordinary Differential Equations written by George F. Carrier and published by SIAM. This book was released on 1968-01-01 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers an alternative to the "rote" approach of presenting standard categories of differential equations accompanied by routine problem sets. The exercises presented amplify and provide perspective for the material, often giving readers opportunity for ingenuity. Little or no previous acquaintance with the subject is required to learn usage of techniques for constructing solutions of differential equations in this reprint volume.

Download or read book Partial Differential Equations written by William Elwyn Williams and published by Oxford University Press, USA. This book was released on 1980 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Ordinary Differential Equations written by W. Cox and published by Butterworth-Heinemann. This book was released on 1996-01-05 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts are worked through in detail and the student is encouraged to develop much of the routine material themselves.