Principles Of Differential Equations
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| Author | : Nelson G. Markley |
| Publisher | : John Wiley & Sons |
| Total Pages | : 354 |
| Release | : 2011-10-14 |
| Genre | : Mathematics |
| ISBN | : 1118031539 |
An accessible, practical introduction to the principles of differential equations The field of differential equations is a keystone of scientific knowledge today, with broad applications in mathematics, engineering, physics, and other scientific fields. Encompassing both basic concepts and advanced results, Principles of Differential Equations is the definitive, hands-on introduction professionals and students need in order to gain a strong knowledge base applicable to the many different subfields of differential equations and dynamical systems. Nelson Markley includes essential background from analysis and linear algebra, in a unified approach to ordinary differential equations that underscores how key theoretical ingredients interconnect. Opening with basic existence and uniqueness results, Principles of Differential Equations systematically illuminates the theory, progressing through linear systems to stable manifolds and bifurcation theory. Other vital topics covered include: Basic dynamical systems concepts Constant coefficients Stability The Poincaré return map Smooth vector fields As a comprehensive resource with complete proofs and more than 200 exercises, Principles of Differential Equations is the ideal self-study reference for professionals, and an effective introduction and tutorial for students.
| Author | : Alexander Komech |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 165 |
| Release | : 2009-10-05 |
| Genre | : Mathematics |
| ISBN | : 1441910956 |
This concise book covers the classical tools of Partial Differential Equations Theory in today’s science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.
| Author | : C. Corduneanu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 205 |
| Release | : 2008-05-09 |
| Genre | : Mathematics |
| ISBN | : 0821846221 |
In summary, the author has provided an elegant introduction to important topics in the theory of ordinary differential equations and integral equations. -- Mathematical Reviews This book is intended for a one-semester course in differential and integral equations for advanced undergraduates or beginning graduate students, with a view toward preparing the reader for graduate-level courses on more advanced topics. There is some emphasis on existence, uniqueness, and the qualitative behavior of solutions. Students from applied mathematics, physics, and engineering will find much of value in this book. The first five chapters cover ordinary differential equations. Chapter 5 contains a good treatment of the stability of ODEs. The next four chapters cover integral equations, including applications to second-order differential equations. Chapter 7 is a concise introduction to the important Fredholm theory of linear integral equations. The final chapter is a well-selected collection of fascinating miscellaneous facts about differential and integral equations. The prerequisites are a good course in advanced calculus, some preparation in linear algebra, and a reasonable acquaintance with elementary complex analysis. There are exercises throughout the text, with the more advanced of them providing good challenges to the student.
| Author | : Murray H. Protter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 271 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461252822 |
Maximum Principles are central to the theory and applications of second-order partial differential equations and systems. This self-contained text establishes the fundamental principles and provides a variety of applications.
| Author | : A. K. Nandakumaran |
| Publisher | : Cambridge University Press |
| Total Pages | : 349 |
| Release | : 2017-05-11 |
| Genre | : Mathematics |
| ISBN | : 1108416411 |
An easy to understand guide covering key principles of ordinary differential equations and their applications.
| Author | : Nail H. Ibragimov |
| Publisher | : World Scientific |
| Total Pages | : 365 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 9814291951 |
A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
| Author | : J. Grifone |
| Publisher | : World Scientific |
| Total Pages | : 236 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9789810237349 |
The inverse problem of the calculus of variations was first studied by Helmholtz in 1887 and it is entirely solved for the differential operators, but only a few results are known in the more general case of differential equations. This book looks at second-order differential equations and asks if they can be written as Euler-Lagrangian equations. If the equations are quadratic, the problem reduces to the characterization of the connections which are Levi-Civita for some Riemann metric.To solve the inverse problem, the authors use the formal integrability theory of overdetermined partial differential systems in the Spencer-Quillen-Goldschmidt version. The main theorems of the book furnish a complete illustration of these techniques because all possible situations appear: involutivity, 2-acyclicity, prolongation, computation of Spencer cohomology, computation of the torsion, etc.
| Author | : Yihong Du |
| Publisher | : World Scientific |
| Total Pages | : 202 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9812566244 |
The maximum principle induces an order structure for partial differential equations, and has become an important tool in nonlinear analysis. This book is the first of two volumes to systematically introduce the applications of order structure in certain nonlinear partial differential equation problems.The maximum principle is revisited through the use of the Krein-Rutman theorem and the principal eigenvalues. Its various versions, such as the moving plane and sliding plane methods, are applied to a variety of important problems of current interest. The upper and lower solution method, especially its weak version, is presented in its most up-to-date form with enough generality to cater for wide applications. Recent progress on the boundary blow-up problems and their applications are discussed, as well as some new symmetry and Liouville type results over half and entire spaces. Some of the results included here are published for the first time.
| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 1584 |
| Release | : 2017-11-15 |
| Genre | : Mathematics |
| ISBN | : 1351643916 |
The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.
| Author | : Demetrios Christodoulou |
| Publisher | : Princeton University Press |
| Total Pages | : 332 |
| Release | : 2000-01-17 |
| Genre | : Mathematics |
| ISBN | : 9780691049571 |
This book introduces new methods in the theory of partial differential equations derivable from a Lagrangian. These methods constitute, in part, an extension to partial differential equations of the methods of symplectic geometry and Hamilton-Jacobi theory for Lagrangian systems of ordinary differential equations. A distinguishing characteristic of this approach is that one considers, at once, entire families of solutions of the Euler-Lagrange equations, rather than restricting attention to single solutions at a time. The second part of the book develops a general theory of integral identities, the theory of "compatible currents," which extends the work of E. Noether. Finally, the third part introduces a new general definition of hyperbolicity, based on a quadratic form associated with the Lagrangian, which overcomes the obstacles arising from singularities of the characteristic variety that were encountered in previous approaches. On the basis of the new definition, the domain-of-dependence theorem and stability properties of solutions are derived. Applications to continuum mechanics are discussed throughout the book. The last chapter is devoted to the electrodynamics of nonlinear continuous media.
