Pavel Drábek Books

This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved. The intention is that the reader understands the basic principles which are valid for particular types of PDEs, and to acquire some classical methods to solve them, thus the authors restrict their considerations to fundamental types of equations and basic methods. Only basic facts from calculus and linear ordinary differential equations of first and second order are needed as a prerequisite. An elementary introduction to the basic principles of partial differential equations. With many illustrations. The book is addressed to students who intend to specialize in mathematics as well as to students of physics, engineering, and economics.

In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book.

The series focuses on publishing high-level monographs that encompass the full range of current nonlinear analysis and its applications across various fields, including optimization, control theory, systems theory, mechanics, and engineering. Its primary aim is to provide the professional community with comprehensive expositions of foundational methods and results that are significant in both the theory and practical applications of nonlinear analysis. Contributions that explore the intersection of nonlinear analysis with related fields and encourage further research in these areas are especially encouraged. The editorial team is led by Editor-in-Chief Jürgen Appell from Würzburg, Germany, with an esteemed group of Honorary and Advisory Editors including Catherine Bandle, Alain Bensoussan, Avner Friedman, Umberto Mosco, Louis Nirenberg, and Alfonso Vignoli. The Editorial Board features members from various global institutions, such as Manuel del Pino, Mikio Kato, Wojciech Kryszewski, Vicenţiu D. Rădulescu, and Simeon Reich. Proposals for new titles are welcomed, with upcoming works planned on topics such as Morse index solutions of nonlinear elliptic equations, critical parabolic-type problems, periodic differential equations, and more, highlighting the ongoing commitment to advancing the field of nonlinear analysis.

Dieser Band der Reihe „Mathematik für Ingenieure und Naturwissenschaftler“ führt in die Grundlagen der Integralgleichungen ein, einem theoretisch wichtigen und anwendungsreichen Themenfeld. Grundkenntnisse aus den Anfangssemestern werden vorausgesetzt. Die Theorie wird hauptsächlich für stetige Funktionen auf kompakten Intervallen entwickelt, sodass das Riemannsche Integral als Basis genügt. Das Buch ist in fünf Teile gegliedert, wobei jeder der 15 Abschnitte nummeriert und strukturiert ist. Die Einführung bietet dem Leser erste Einblicke in Integralgleichungen und präsentiert praxisnahe Aufgabenstellungen, die zur mathematischen Formulierung von Integralgleichungen führen. Der zweite Teil behandelt die Lösung spezieller Typen von Integralgleichungen, wobei die Laplace-Transformation als Werkzeug zur Lösung von Volterraschen Gleichungen mit Faltungskern verwendet wird. Zudem wird der Zusammenhang zwischen der Theorie der Integralgleichungen und der linearen Algebra bei Fredholmschen Integralgleichungen mit ausgeartetem Kern erläutert, gefolgt von der Formulierung der Fredholmschen Alternative. Der letzte Teil konzentriert sich auf die Lösbarkeit von Integralgleichungen.

Přinášíme Vám kuchařskou knihu receptů sesbíraných z celého světa. Tyto recepty jsou určeny pro vaření v MT, ale lze v nich čerpat inspiraci i pro klasické vaření.

Dějiny českých překladů Shakespeara doplněné antologií neznámých a vzácných textů z let 1782–1922.