Author: V.N. Bogaevski
Publisher: Springer Science & Business Media
ISBN: 1461244382
Category : Science
Languages : en
Pages : 276
Get Book Here
Book Description
Of interest to everybody working on perturbation theory in differential equations, this book requires only a standard mathematical background in engineering and does not require reference to the special literature. Topics covered include: matrix perturbation theory; systems of ordinary differential equations with small parameters; reconstruction and equations in partial derivatives. While boundary problems are not discussed, the book is clearly illustrated by numerous examples.
Author: Richard H. Rand
Publisher: Springer Science & Business Media
ISBN: 1461210607
Category : Mathematics
Languages : en
Pages : 254
Get Book Here
Book Description
Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.
Author: Jan A. Sanders
Publisher: Springer Science & Business Media
ISBN: 0387489185
Category : Mathematics
Languages : en
Pages : 447
Get Book Here
Book Description
Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.
Author: Bernard Dacorogna
Publisher: Springer Science & Business Media
ISBN: 0387552499
Category : Mathematics
Languages : en
Pages : 616
Get Book Here
Book Description
This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.
Author: Alexandre J. Chorin
Publisher: Springer Science & Business Media
ISBN: 1441987282
Category : Mathematics
Languages : en
Pages : 181
Get Book Here
Book Description
This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.
Author: Morton E. Gurtin
Publisher: Springer Science & Business Media
ISBN: 0387226567
Category : Science
Languages : en
Pages : 248
Get Book Here
Book Description
Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture.
Author: Fritz John
Publisher: Springer Science & Business Media
ISBN: 0387906096
Category : Mathematics
Languages : en
Pages : 266
Get Book Here
Book Description
This book is a very well-accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation without solutions.
Author: Claus Müller
Publisher: Springer Science & Business Media
ISBN: 1461205816
Category : Mathematics
Languages : en
Pages : 227
Get Book Here
Book Description
This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. Based on many years of lecturing to mathematicians, physicists and engineers in scientific research institutions in Europe and the USA, the author uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. One of the highlights is the extension of the classical results of the spherical harmonics into the complex - particularly important for the complexification of the Funk-Hecke formula which successfully leads to new integrals for Bessel- and Hankel functions with many applications of Fourier integrals and Radon transforms. Numerous exercises stimulate mathematical ingenuity and bridge the gap between well-known elementary results and their appearance in the new formations.
Author: G. Haller
Publisher: Springer Science & Business Media
ISBN: 1461215080
Category : Mathematics
Languages : en
Pages : 444
Get Book Here
Book Description
A unified treatment of resonant problems with special emphasis on the recently discovered phenomenon of homoclinic jumping. After a survey of the necessary background, the book develops a general finite dimensional theory of homoclinic jumping, illustrating it with examples. The main mechanism of chaos near resonances is discussed in both the dissipative and the Hamiltonian context, incorporating previously unpublished new results on universal homoclinic bifurcations near resonances, as well as on multi-pulse Silnikov manifolds. The results are applied to a variety of different problems, which include applications from beam oscillations, surface wave dynamics, nonlinear optics, atmospheric science and fluid mechanics.
Author: George R. Sell
Publisher: Springer Science & Business Media
ISBN: 9780387983479
Category : Mathematics
Languages : en
Pages : 692
Get Book Here
Book Description
The theory and applications of infinite dimensional dynamical systems have attracted the attention of scientists for quite some time. Dynamical issues arise in equations that attempt to model phenomena that change with time. The infi nite dimensional aspects occur when forces that describe the motion depend on spatial variables, or on the history of the motion. In the case of spatially depen dent problems, the model equations are generally partial differential equations, and problems that depend on the past give rise to differential-delay equations. Because the nonlinearities occurring in thse equations need not be small, one needs good dynamical theories to understand the longtime behavior of solutions. Our basic objective in writing this book is to prepare an entree for scholars who are beginning their journey into the world of dynamical systems, especially in infinite dimensional spaces. In order to accomplish this, we start with the key concepts of a semiflow and a flow. As is well known, the basic elements of dynamical systems, such as the theory of attractors and other invariant sets, have their origins here.
