Kategoria BISAC: Mathematics >> Calculus

This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.

Operational methods have been used for over a century to solve problems such as ordinary and partial differential equations. When solving such problems, in many cases it is fairly easy to obtain the Laplace transform, while it is very demanding to determine the inverse Laplace transform that is the solution of a given problem. Sometimes, after some difficult contour integration, we may find that a series solution results, but this may be quite difficult to evaluate in order to get an answer at a particular time value.

The advent of computers has given an impetus to developing...

One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.

The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincare series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.

On these pages, the ideas and formulas due to...

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels.

This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed...

Die Wahrscheinlichkeitstheorie hat durch neue Anwendungen in der Wirtschaft auch in der Lehre an Bedeutung gewonnen. Sie beruht auf der Mass- und Integrationstheorie gleichzeitig eine der Grundlagen der Funktionalanalysis. Das Buch bietet eine Einfuhrung in die Wahrscheinlichkeitstheorie. Dabei wird die systematische Darstellung der klassischen Themen durch Beispiele und Aufgaben erganzt, so dass die Theorie, aber auch Anwendungen vertieft werden konnen. Der Stoff wurde so aufbereitet, dass er ohne Vorkenntnisse erarbeitet werden kann.

In diesem Buch finden Sie eine Einfuhrung in die Funktionalanalysis und Operatortheorie auf dem Niveau eines Master-Studiengangs.

Ausgehend von Fragen zu partiellen Differenzialgleichungen und Integralgleichungen untersuchen Sie lineare Gleichungen im Hinblick auf Existenz und Struktur von Losungen sowie deren Abhangigkeit von Parametern. Dazu lernen Sie verschiedene Konzepte und Methoden kennen: Distributionen, Fourier-Transformation, Sobolev-Raume, Dualitatstheorie im Rahmen lokalkonvexer Raume, topologische Tensorprodukte, exakte Sequenzen, Banachalgebren, Fredholmoperatoren,...

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kahler structure.

On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kahler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kahler structure.

We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning...

Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.

The book begins with a discussion of the geometry of Hilbert spaces, convex functions and domains, and differential forms, particularly k-forms. The exposition continues with an introduction to the calculus of variations with...

The lines of development of the theory are made clear by the order in which the main theorems are presented. Frequent references to earlier theorems made in the proofs emphasize the interdependence of the theorems and help to show how the various definitions and theorems fit together. Counter-examples are included to show why a hypothesis in a theorem cannot...