Nazaikinskii V.E., Shatalov V.E., Sternin B.Y. Contact Geometry and Linear Differential Equations

Springer, 2009. - 150 pages. This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two- or three-space dimensions. Over...

Cambridge University Press, 1975. - 292 p. In this book, Professor Copson gives a rigorous account of the theory of partial differential equations of the first order and of linear partial differential equations of the second order, using the methods of classical analysis. In spite of the advent of computers and the applications of the methods of functional analysis to the theory of partial differential equations, the classical theory retains its...

Springer, 2007. - 386 pages. This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. The primary topics of the dressing method covered here are: the Moutard and Darboux transformations discovered in XIX century as appli...

Oxford University Press, 2010. - 368 Pages. Most nonlinear differential equations arising in natural sciences admit chaotic behavior and cannot be solved analytically. Integrable systems lie on the other extreme. They possess regular, stable, and well behaved solutions known as solitons and instantons. These solutions play important roles in pure and applied mathematics as well as in theoretical physics where they describe configurations topolo...

Cаmbridge Univеrsity Prеss, 1984. - 668 pages. This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schr?dinger and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and...

Academic Press, 2002. - 394 Pages. This book is written to meet the needs of undergraduates in applied mathematics, physics and engineering studying partial differential equations. Many books deal with partial differential equations, some at an elementary level and others at more advanced levels, so it is necessary that some justification should be given for the publication of another introductory text. With few exceptions, existing texts writt...

2003. - 1165 pages. Chapters: Linear Algebra, Vector Spaces, Inner Products and Norms, Minimization and Least Squares Approximation, Orthogonality, Equilibrium, Linear Functions, Linear Transformations, Eigenvalues, Linear Dynamical Systems, Iteration of Linear Systems, Boundary Value Problems in One Dimension, Fourier Series, Fourier Analysis, Vibration and Diffusion in One-Dimensional Media, The Laplace Equation, Complex Analysis, Dynamics of...

Springer, 2010. - 614 Pages. This second in the series of three volumes builds upon the basic theory of linear PDE given in volume 1, and pursues more advanced topics. Analytical tools introduced here include pseudodifferential operators, the functional analysis of self-adjoint operators, and Wiener measure. The book also develops basic differential geometrical concepts, centered about curvature. Topics covered include spectral theory of ellipti...

Springer, 2010. - 715 Pages. The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear d...

Springer, 1999. - 563 pages. This text provides an introduction to the theory of partial differential equations. It introduces basic examples of partial differential equations, arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, including particularly Fourier analysis, distribution theory, and Sobolev spaces. These tools are applied to the treatment of basic probl...