Modern Methods in the Calculus of Variations, Irene Fonseca; Giovanni Leoni

Автор: Fuente, Angel de la.
Название: Mathematical methods and models for economists
ISBN: 0521585295 ISBN-13(EAN): 9780521585293
Издательство: Cambridge Academ
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Описание: This book is intended as a textbook for a first-year PhD course in mathematics for economists and as a reference for graduate students in economics. It provides a self-contained, rigorous treatment of most of the concepts and techniques required to follow the standard first-year theory sequence in micro and macroeconomics.

Автор: Almeida Ricardo, Pooseh Shakoor, Torres Delfim F.
Название: Computational Methods in the Fractional Calculus of Variations
ISBN: 1783266406 ISBN-13(EAN): 9781783266401
Издательство: World Scientific Publishing
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Описание: This book fills a gap in the literature by introducing numerical techniques to solve problems of the Fractional Calculus of Variations (FCV). In most cases, finding the analytic solution to such problems is extremely difficult or even impossible, and numerical methods need to be used.

Автор: Mariano Giaquinta; Giuseppe Modica; Jiri Soucek
Название: Cartesian Currents in the Calculus of Variations I
ISBN: 3642083749 ISBN-13(EAN): 9783642083747
Издательство: Springer
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Автор: Mariano Giaquinta; Stefan Hildebrandt
Название: Calculus of Variations I
ISBN: 364208074X ISBN-13(EAN): 9783642080746
Издательство: Springer
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Описание: This book describes the classical aspects of the variational calculus which are of interest to analysts, geometers and physicists alike. Volume 1 deals with the for- mal apparatus of the variational calculus and with nonparametric field theory, whereas Volume 2 treats parametric variational problems as well as Hamilton- Jacobi theory and the classical theory of partial differential equations of first ordel;. In a subsequent treatise we shall describe developments arising from Hilbert's 19th and 20th problems, especially direct methods and regularity theory. Of the classical variational calculus we have particularly emphasized the often neglected theory of inner variations, i. e. of variations of the independent variables, which is a source of useful information such as mono tonicity for- mulas, conformality relations and conservation laws. The combined variation of dependent and independent variables leads to the general conservation laws of Emmy Noether, an important tool in exploiting symmetries. Other parts of this volume deal with Legendre-Jacobi theory and with field theories. In particular we give a detailed presentation of one-dimensional field theory for nonpara- metric and parametric integrals and its relations to Hamilton-Jacobi theory, geometrical optics and point mechanics. Moreover we discuss various ways of exploiting the notion of convexity in the calculus of variations, and field theory is certainly the most subtle method to make use of convexity. We also stress the usefulness of the concept of a null Lagrangian which plays an important role in we give an exposition of Hamilton-Jacobi several instances.

Автор: Bernard Dacorogna
Название: Direct Methods in the Calculus of Variations
ISBN: 1441922598 ISBN-13(EAN): 9781441922595
Издательство: Springer
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Описание: This book is developed for the study of vectorial problems in the calculus of variations. It is a new edition of the earlier book published in 1989. Almost half of the book consists of new material and there are added examples.

Автор: George Leitmann
Название: The Calculus of Variations and Optimal Control
ISBN: 1489903356 ISBN-13(EAN): 9781489903358
Издательство: Springer
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Описание: This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Автор: Malliavin
Название: Stochastic Calculus of Variations in Mathematical Finance
ISBN: 3540434313 ISBN-13(EAN): 9783540434313
Издательство: Springer
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Описание: Malliavin calculus provides an infinite-dimensional differential calculus in the context of continuous paths stochastic processes. The calculus includes formulae of integration by parts and Sobolev spaces of differentiable functions defined on a probability space. This new book, demonstrating the relevance of Malliavin calculus for Mathematical Finance, starts with an exposition from scratch of this theory. Greeks (price sensitivities) are reinterpreted in terms of Malliavin calculus. Integration by parts formulae provide stable Monte Carlo schemes for numerical valuation of digital options. Finite-dimensional projections of infinite-dimensional Sobolev spaces lead to Monte Carlo computations of conditional expectations useful for computing American options. The discretization error of the Euler scheme for a stochastic differential equation is expressed as a generalized Watanabe distribution on the Wiener space. Insider information is expressed as an infinite-dimensional drift. The last chapter gives an introduction to the same objects in the context of jump processes where incomplete markets appear.