Differential calculus and equations Books

The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the...

Solitons are nonlinear waves which behave like interacting particles. When first proposed in the 19th century, leading mathematical physicists denied that such a thing could exist. Now they are regularly observed in nature, shedding light on phenomena...

As the title of the book indicates, this is primarily a book on partial differential equations (PDEs) with two definite slants: toward inverse problems and to the inclusion of fractional derivatives. The standard paradigm, or direct problem, is to take a...

This is the second in a pair of works which study small disturbances to the plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations at high Reynolds number Re. In this work, we show that there is constant 0 0 exist at least until t...

Symbolic dynamics is essential in the study of dynamical systems of various types and is connected to many other fields such as stochastic processes, ergodic theory, representation of numbers, information and coding, etc. This graduate text introduces...

This memoir is concerned with quantitative unique continuation estimates for equations involving a "sum of squares" operator L on a compact manifold M assuming: (i) the Chow-Rashevski-H?ormander condition ensuring the hypoellipticity of L,and(ii) the...

This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincare's vision for the field over a century ago. Taking into account the remarkable development of...

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Guy David, University of Paris-Sud, Orsay, France. Joseph Feneuil, Temple University, Philadelphia, PA. Svitlana Mayboroda, University of Minnesota, Minneapolis, MN.

This paper is a corrigendum and improvements to Carleman Estimates, Observability Inequalities and Null Controllability for Interior Degenerate Nonsmooth Parabolic Equations and its consequences. We give here the corrected proofs of the concerned...

This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only...

Scattering resonances generalize bound states/eigenvalues for systems in which energy can scatter to infinity. A typical resonance has a rate of oscillation (just as a bound state does) and a rate of decay. Although the notion is intrinsically dynamical,...

This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22-26, 2016 and Probabilistic Methods in Topology, held from November 14-18, 2016 at the Centre de Recherches Mathematiques,...

This volume contains the proceedings of the AMS Special Session on New Developments in the Analysis of Nonlocal Operators, held from October 28-30, 2016, at the University of St. Thomas, Minneapolis, Minnesota. Problems represented in this volume include...

Inverse problems are those where, from ""external"" observations of a hidden ""black box"" system (a patient's body, nontransparent industrial object, interior of the Earth, etc.), one needs to recover the unknown parameters of the system. A prototypical...

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing...

Implicit-explicit (IMEX) time discretization methods have proven to be highly effective for the numerical solution of a wide class of evolutionary partial differential equations (PDEs) across various contexts. These methods have become mainstream for...

Divided into two self-contained parts, this textbook is an introduction to modern real analysis. More than 350 exercises and 100 examples are integrated into the text to help clarify the theoretical considerations and the practical applications to...

In this textbook on calculus of one variable, applications to the natural sciences play a central role. Examples from biology, chemistry, and physics are discussed in detail without compromising the discussion of the mathematics essential to differential...

This text presents a unique treatment of network control systems. Drawing from fundamental principles of dynamical systems theory and dynamical thermodynamics, the authors develop a continuous-time, discrete-time, and hybrid dynamical system and control...

Dynamical systems are a principal tool in the modeling, prediction, and control of a wide range of complex phenomena. As the need for improved accuracy leads to larger and more complex dynamical systems, direct simulation often becomes the only available...

This second edition provides an enhanced exposition of the long-overlooked Hadamard semidifferential calculus, first introduced in the 1920s by mathematicians Jacques Hadamard and Maurice Rene Frechet. Hadamard semidifferential calculus is possibly the...

Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world-wave propagation, thermodynamics, fluid flow, solid...

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world-wave propagation, thermodynamics, fluid flow, solid...

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical...

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of...

Discrete Painleve equations are nonlinear difference equations, which arise from translations on crystallographic lattices. The deceptive simplicity of this statement hides immensely rich mathematical properties, connecting dynamical systems, algebraic...

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R3: ?ttu ? ?u +m j=1 Vj (x ? vj t) u = 0. The energy estimate and the local energy decay of a scattering state are...

This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21-22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at...

This book introduces a semi-analytical method, Improved Residual Power Series Method (IRPSM) for solving boundary value problems (BVPs). Unlike traditional numerical and analytical techniques, IRPSM offers quick convergence and minimal computational time.

Stochastic Differential Equations for Science and Engineering is aimed at students at the M.Sc. and PhD level. The book describes the mathematical construction of stochastic differential equations with a level of detail suitable to the audience, while...