Lectures On Applied Mathematics The Calculus Of Variations PDF Download
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Author | : Francis Dominic Murnaghan |
Publisher | : |
Total Pages | : 116 |
Release | : 1962 |
Genre | : Calculus of variations |
ISBN | : |
Download Lectures on Applied Mathematics: The calculus of variations Book in PDF, ePub and Kindle
Author | : Francis Dominic Murnaghan |
Publisher | : |
Total Pages | : 116 |
Release | : 1962 |
Genre | : Calculus of variations |
ISBN | : |
Download Lectures on Applied Mathematics: The calculus of variations Book in PDF, ePub and Kindle
Author | : Jürgen Moser |
Publisher | : Birkhäuser |
Total Pages | : 139 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 303488057X |
Download Selected Chapters in the Calculus of Variations Book in PDF, ePub and Kindle
0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re lated and have the same mathematical foundation. We will not follow those ap proaches but will make a connection to classical results of Jacobi, Legendre, Weier strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be tween minimals and extremal fields. In this way, we will be led to Mather sets.
Author | : Francis Dominic Murnaghan |
Publisher | : |
Total Pages | : 186 |
Release | : 1961 |
Genre | : Calculus |
ISBN | : |
Download Lectures on Applied Mathematics Book in PDF, ePub and Kindle
Contents: The Lagrangian function and the parametric integrand Extremal curves; The Euler-Lagrange equation Lagrangian functions which are linear in x sub t The Legendre condition for a minimal curve Proof of the Legendre condition Constrained problems; The Hamilton canonical equations The reciprocity between L and H; The transversality conditions Extremal fields; The Hilbert invariant integral The Weierstrass E-function; Positively regular problems A simple example of the construction of an extremal field; Rayleigh quotients and the method of Rayleigh-Ritz The principle of maupertuis; The propagation of waves Problems whose Lagrangian functions involve derivatives of higher order than the first Multiple-Integral problems of the calculus of variations Constrained problems; Characteristic numbers Multiple-integral problems whose Langrangian functions involve derivatives of higher order than the first The Courant maximum-minimum principle.
Author | : Luigi Ambrosio |
Publisher | : Springer Science & Business Media |
Total Pages | : 213 |
Release | : 2008-01-02 |
Genre | : Mathematics |
ISBN | : 3540759131 |
Download Calculus of Variations and Nonlinear Partial Differential Equations Book in PDF, ePub and Kindle
With a historical overview by Elvira Mascolo
Author | : Mariano Giaquinta |
Publisher | : Springer |
Total Pages | : 194 |
Release | : 2006-11-14 |
Genre | : Science |
ISBN | : 3540460756 |
Download Topics in Calculus of Variations Book in PDF, ePub and Kindle
Author | : Asen L. Dontchev |
Publisher | : Springer Nature |
Total Pages | : 223 |
Release | : 2022-02-04 |
Genre | : Mathematics |
ISBN | : 3030799115 |
Download Lectures on Variational Analysis Book in PDF, ePub and Kindle
This book presents an introduction to variational analysis, a field which unifies theories and techniques developed in calculus of variations, optimization, and control, and covers convex analysis, nonsmooth analysis, and set-valued analysis. It focuses on problems with constraints, the analysis of which involves set-valued mappings and functions that are not differentiable. Applications of variational analysis are interdisciplinary, ranging from financial planning to steering a flying object. The book is addressed to graduate students, researchers, and practitioners in mathematical sciences, engineering, economics, and finance. A typical reader of the book should be familiar with multivariable calculus and linear algebra. Some basic knowledge in optimization, control, and elementary functional analysis is desirable, but all necessary background material is included in the book.
Author | : Oskar Bolza |
Publisher | : University of Michigan Library |
Total Pages | : 306 |
Release | : 1904 |
Genre | : Mathematics |
ISBN | : |
Download Lectures on the Calculus of Variations Book in PDF, ePub and Kindle
Author | : Kung-ching Chang |
Publisher | : World Scientific |
Total Pages | : 325 |
Release | : 2016-09-16 |
Genre | : Mathematics |
ISBN | : 981314470X |
Download Lecture Notes On Calculus Of Variations Book in PDF, ePub and Kindle
This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1-8 focus on the classical theory of calculus of variations. Lectures 9-14 introduce direct methods along with their theoretical foundations. Lectures 15-20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.
Author | : Gilbert Ames Bliss |
Publisher | : |
Total Pages | : 292 |
Release | : 1946 |
Genre | : Calculus of variations |
ISBN | : 9780226058962 |
Download Lectures on the Calculus of Variations Book in PDF, ePub and Kindle