Differential Equations

This collection includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting..

The second edition of this bestselling handbook contains the solutions for an additional 700 ordinary differential equations (ODEs) and now provides more than 6200 solutions. It also includes a new introductory chapter that describes exact, asymptotic, and approximate analytical methods for solving ..

Harmonic Maps Into Homogeneous Spaces..

Impulsive Differential Equations..

First published in 1990...

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Introduction to Hamiltonian Fluid Dynamics and Stability Theory offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic..

With a special emphasis on engineering and science applications, this textbook provides a mathematical introduction to PDEs at the undergraduate level. It takes a new approach to PDEs by presenting computation as an integral part of the study of differential equations. The authors use Mathematica® a..

Inverse boundary problems are a rapidly developing area of applied mathematics. Inverse boundary spectral problems (IBSP) constitute an important and distinct part of the field because of the special character of the data involved, the specific methods used to deal with that data, and their relevanc..

Explains the modern theory of the method of averaging and provides an understanding of the results obtained when applying this theory. This book describes stability theory and Shtokalo's method, and examines various applications, including parametric resonance and the construction of asymptotics. It..

This book collects recent research—including the authors’ own substantial projects—on uncertainty propagation and quantification. It covers two sources of uncertainty: where uncertainty is present primarily due to measurement errors and where uncertainty is present due to the modeling formulation it..

Integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. This text addresses common types of first order ordinary differential equations and the basic theory of linear second order..

This Research Note introduces a new Morse (index) theory that is easier to use, less technical, and more flexible than existing theories for strongly indefinite functionals. It also contains an extensive survey of material that is now classical but has never appeared in book form. Until now, these r..