Differential calculus and equations

The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way.

The aim of this book is to present hyperbolic partial di?

A large number of physical phenomena are modeled by nonlinear partialdifferential equations, subject to appropriate initial/ boundary conditions; theseequations, in general, do not admit exact solution.

This book gives a systematic investigation of convection in systems comprised of liquid layers with deformatable interfaces.

In the study of mathematical models that arise in the context of concrete - plications, the following two questions are of fundamental importance: (i) we- posedness of the model, including existence and uniqueness of solutions; and (ii) qualitative properties of solutions.

This book aims to give a user friendly tutorial of an interdisciplinary research topic (fronts or interfaces in random media) to senior undergraduates and beginning grad uate students with basic knowledge of partial differential equations (PDE) and prob ability.

Sobolev spaces become the established and universal language of partial differential equations and mathematical analysis.

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures.

Problems in Real Analysis: Advanced Calculus on the Real Axis features a comprehensive collection of challenging problems in mathematical analysis that aim to promote creative, non-standard techniques for solving problems.

Many nonlinear problems in physics, engineering, biology and social sciences can be reduced to finding critical points of functionals.

This book presents an account of theories of ?

Extremes Values, Regular Variation and Point Processes is a readable and efficient account of the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors.

ThisresearchmonographdevelopstheHamilton-Jacobi-Bellman(HJB)theory viathedynamicprogrammingprincipleforaclassofoptimalcontrolproblems for stochastic hereditary di?

Accurate models to describe real-world phenomena are indispensable for research in such scientific fields as physics, engineering, biology, chemistry, and economics.

Drawing examples from mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world.

Stability is a very important property of mathematical models simulating physical processes which provides an adequate description of the process.

This richly illustrated book introduces the reader to a newly developed theory in Computer Vision yielding elementary techniques to analyze digital images.

Applied Delay Differential Equations is a friendly introduction to the fast-growing field of time-delay differential equations.

Symmetries in various forms pervade mathematics and physics.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983).

Mathematicsisplayinganevermoreimportantroleinthephysicalandbiol- ical sciences, provoking a blurring of boundaries between scienti?

This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials.

This book is written for quantitative finance professionals, students, educators, and mathematically inclined individual investors.

Ordinary di?

This book is a unified presentation of both classical and contemporary results in the calculus of variations.

Differential forms satisfying the A-harmonic equations have found wide applications in fields such as general relativity, theory of elasticity, quasiconformal analysis, differential geometry, and nonlinear differential equations in domains on manifolds.

The title gives a reasonable ?

This second edition is the successor to "e;Direct methods in the calculus of variations"e; which was published in the Applied Mathematical Sciences series and is currently out of print.

Our motivation for writing this book is twofold: First, the theory of waves propagating in randomly layered media has been studied extensively during the last thirty years but the results are scattered in many di?

This textbook is intended for students who wish to obtain an introduction to the theory of partial di?

Perturbation theory and in particular normal form theory has shown strong growth during the last decades.

Over the years, a number of books have been written on the theory of functional equations.

This is the first research monograph to focus on variational inequalities as part of nonsmooth variational systems research.

Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago.

This book has emerged from the study of a new concept in material science that has been realized about a decade ago.

This book contains a systematic investigation of the convection in systems with interfaces.

For many years, first as a student and later as a teacher, I have ob- served graduate students in ecology and other environmental sci- ences who had been required as undergraduates to take calculus courses.

Although some examples of phase portraits of quadratic systems can already be found in the work of Poincare, the first paper dealing exclusively with these systems was published by Buchel in 1904.

Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.