Differential calculus and equations

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

Ordinary di?

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 ?

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.

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.

Analysis and Optimization of Differential Systems focuses on the qualitative aspects of deterministic and stochastic differential equations.

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

Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods.

Boundary Element Methods (BEM) play an important role in modern numerical computations in the applied and engineering sciences.

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Therearemanyexcellenttextsonelementarydi?

Number Theory: Tradition and Modernization is a collection of survey and research papers on various topics in number theory.

In this new text, designed for sophomores studying mathematics and computer science, the authors cover the basics of difference equations and some of their applications in computing and in population biology.

Perturbation theory, one of the most intriguing and essential topics in mathematics, and its applications to the natural and engineering sciences is the main focus of this workbook.

Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]).