Kategoria BISAC: Mathematics >> Differential Equations - General

Pseudodifferential methods are central to the study of partial differential equations, because they permit an "algebraization." A replacement of compositions of operators in n-space by simpler product rules for thier symbols. The main purpose of this book is to set up an operational calculus for operators defined from differential and pseudodifferential boundary values problems via a resolvent construction. A secondary purposed is to give a complete treatment of the properties of the calculus of pseudodifferential boundary problems with transmission, both the first version by...

* Devoted to the motion of surfaces for which the normal velocity at every point is given by the mean curvature at that point; this geometric heat flow process is called mean curvature flow.

* Mean curvature flow and related geometric evolution equations are important tools in mathematics and mathematical physics.

Equations of the Ginzburg Landau vortices have particular applications to a number of problems in physics, including phase transition phenomena in superconductors, superfluids, and liquid crystals. Building on the results presented by Bethuel, Brazis, and Helein, this current work further analyzes Ginzburg-Landau vortices with a particular emphasis on the uniqueness question.

The authors begin with a general presentation of the theory and then proceed to study problems using weighted Holder spaces and Sobolev Spaces. These are particularly powerful tools and help us obtain a deeper...

Control theory has applications to a number of areas in engineering and communication theory. This introductory text on the subject is fairly self-contained and aimed primarily at advanced mathematics and engineering students in various disciplines.

The topics covered include realization problems, linear-quadratic optimal control, stability theory, stochastic modeling and recursive estimation algorithms in communications and control, and distributed system modeling. These topics have a wide range of applicability, and provide background for further study in the control and...

Developed in this book are several deep connections between time--frequency (Fourier/Gabor) analysis and time--scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of developments in time--frequency and time--scale analysis are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book...

Although finite element courses have become more popular in the undergraduate and graduate engineering, science, and applied mathematics curricula, there are very few introductory textbooks geared toward students accustomed to using computers for everyday assignments and research. 'An Introduction to Linear and Nonlinear Finite Element Analysis' fills this gap, offering a concise, integrated presentation of methods, applications, computational software tools, and hands-on programming projects. Suitable for junior/senior undergraduate and first-year graduate courses, the book is aimed at...

The second in a series of three volumes that survey the theory of theta functions, this volume emphasizes the special properties of the theta functions associated with compact Riemann surfaces and how they lead to solutions of the Korteweg-de-Vries equations as well as other non-linear differential equations of mathematical physics.

It presents an explicit elementary construction of hyperelliptic Jacobian varieties and is a self-contained introduction to the theory of the Jacobians. It also ties together nineteenth-century discoveries due to Jacobi, Neumann, and Frobenius with...

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written and] an excellent book, with a wealth of mathematical material and techniques."