Variational Methods In Mathematics Science And Engineering

Author : Karel Rektorys
Publisher : Springer Science & Business Media
Page : 566 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401164504

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Variational Methods in Mathematics, Science and Engineering by Karel Rektorys Pdf

The impulse which led to the writing of the present book has emerged from my many years of lecturing in special courses for selected students at the College of Civil Engineering of the Tech nical University in Prague, from experience gained as supervisor and consultant to graduate students-engineers in the field of applied mathematics, and - last but not least - from frequent consultations with technicians as well as with physicists who have asked for advice in overcoming difficulties encountered in solving theoretical problems. Even though a varied combination of problems of the most diverse nature was often in question, the problems discussed in this book stood forth as the most essential to this category of specialists. The many discussions I have had gave rise to considerations on writing a book which should fill the rather unfortunate gap in our literature. The book is designed, in the first place, for specialists in the fields of theoretical engineering and science. However, it was my aim that the book should be of interest to mathematicians as well. I have been well aware what an ungrateful task it may be to write a book of the present type, and what problems such an effort can bring: Technicians and physicists on the one side, and mathematicians on the other, are often of diametrically opposing opinions as far as books con ceived for both these categories are concerned.

Author : Karel Rektorys
Publisher : Unknown
Page : 287 pages
File Size : 47,8 Mb
Release : 1980
Category : Electronic
ISBN : OCLC:834118163

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Variational Methods in Mathematics, Science and Engineering by Karel Rektorys Pdf

Author : Kevin W. Cassel
Publisher : Unknown
Page : 432 pages
File Size : 44,5 Mb
Release : 2013
Category : Engineering
ISBN : 1316090671

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Variational Methods with Applications in Science and Engineering by Kevin W. Cassel Pdf

There is a resurgence of applications in which the calculus of variations has direct relevance. In addition to application to solid mechanics and dynamics, it is now being applied in a variety of numerical methods, numerical grid generation, modern physics, various optimization settings and fluid dynamics. Many applications, such as nonlinear optimal control theory applied to continuous systems, have only recently become tractable computationally, with the advent of advanced algorithms and large computer systems. This book reflects the strong connection between calculus of variations and the applications for which variational methods form the fundamental foundation. The mathematical fundamentals of calculus of variations (at least those necessary to pursue applications) is rather compact and is contained in a single chapter of the book. The majority of the text consists of applications of variational calculus for a variety of fields.

Author : Kevin W. Cassel
Publisher : Cambridge University Press
Page : 433 pages
File Size : 51,7 Mb
Release : 2013-07-22
Category : Mathematics
ISBN : 9781107022584

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Variational Methods with Applications in Science and Engineering by Kevin W. Cassel Pdf

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.

Author : K. B. M. Nambudiripad
Publisher : Unknown
Page : 0 pages
File Size : 43,8 Mb
Release : 2016-01-30
Category : Calculus of variations
ISBN : 8184875142

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Variational Methods in Engineering by K. B. M. Nambudiripad Pdf

As variational methods are of great importance to aerospace, civil and mechanical engineers, the emphasis in this book is on applications to engineering, but the mathematics that serves as the foundation is also given its due importance. Copious footnotes and a large number of illustrative examples are a feature of the book.

Author : Jagdish S. Rustagi
Publisher : Unknown
Page : 236 pages
File Size : 49,8 Mb
Release : 1976-01-01
Category : Calcul des variations
ISBN : 0126045607

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Variational Methods in Statistics by Jagdish S. Rustagi Pdf

Variational methods in statistics.

Author : Kevin W. Cassel
Publisher : Unknown
Page : 434 pages
File Size : 42,9 Mb
Release : 2013
Category : Electronic books
ISBN : 1107059046

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Variational Methods with Applications to Science and Engineering by Kevin W. Cassel Pdf

Author : J.T. Oden,J.N. Reddy
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642963124

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Variational Methods in Theoretical Mechanics by J.T. Oden,J.N. Reddy Pdf

This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .

Author : Eduardo Souza de Cursi
Publisher : John Wiley & Sons
Page : 430 pages
File Size : 54,6 Mb
Release : 2015-10-19
Category : Mathematics
ISBN : 9781848219144

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Variational Methods for Engineers with Matlab by Eduardo Souza de Cursi Pdf

This book is issued from a 30 years’ experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineer-oriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are presented. MATLAB programs illustrate the implementation and make the book suitable as a textbook and for self-study. The evolution of knowledge, of the engineering studies and of the society in general has led to a change of focus from students and researchers. New generations of students and researchers do not have the same relations to mathematics as the previous ones. In the particular case of variational methods, the presentations used in the past are not adapted to the previous knowledge, the language and the centers of interest of the new generations. Since these methods remain a core knowledge – thus essential - in many fields (Physics, Engineering, Applied Mathematics, Economics, Image analysis ...), a new presentation is necessary in order to address variational methods to the actual context.

Author : Philipp Grohs,Martin Holler,Andreas Weinmann
Publisher : Springer Nature
Page : 701 pages
File Size : 46,9 Mb
Release : 2020-04-03
Category : Mathematics
ISBN : 9783030313517

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Handbook of Variational Methods for Nonlinear Geometric Data by Philipp Grohs,Martin Holler,Andreas Weinmann Pdf

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Author : Constantin Udriste,Ionel Tevy
Publisher : John Wiley & Sons
Page : 228 pages
File Size : 53,5 Mb
Release : 2023-02-13
Category : Mathematics
ISBN : 9781119944362

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Variational Calculus with Engineering Applications by Constantin Udriste,Ionel Tevy Pdf

A comprehensive overview of foundational variational methods for problems in engineering Variational calculus is a field in which small alterations in functions and functionals are used to find their relevant maxima and minima. It is a potent tool for addressing a range of dynamic problems with otherwise counter-intuitive solutions, particularly ones incorporating multiple confounding variables. Its value in engineering fields, where materials and geometric configurations can produce highly specific problems with unconventional or unintuitive solutions, is considerable. Variational Calculus with Engineering Applications provides a comprehensive survey of this toolkit and its engineering applications. Balancing theory and practice, it offers a thorough and accessible introduction to the field pioneered by Euler, Lagrange and Hamilton, offering tools that can be every bit as powerful as the better-known Newtonian mechanics. It is an indispensable resource for those looking for engineering-oriented overview of a subject whose capacity to provide engineering solutions is only increasing. Variational Calculus with Engineering Applications readers will also find: Discussion of subjects including variational principles, levitation, geometric dynamics, and more Examples and instructional problems in every Chapter, along with MAPLE codes for performing the simulations described in each Engineering applications based on simple, curvilinear, and multiple integral functionals Variational Calculus with Engineering Applications is ideal for advanced students, researchers, and instructors in engineering and materials science.

Author : Otmar Scherzer,Markus Grasmair,Harald Grossauer,Markus Haltmeier,Frank Lenzen
Publisher : Springer Science & Business Media
Page : 323 pages
File Size : 47,8 Mb
Release : 2008-09-26
Category : Mathematics
ISBN : 9780387692777

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Variational Methods in Imaging by Otmar Scherzer,Markus Grasmair,Harald Grossauer,Markus Haltmeier,Frank Lenzen Pdf

This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Author : Anonim
Publisher : Unknown
Page : 240 pages
File Size : 41,7 Mb
Release : 1968
Category : Engineering mathematics
ISBN : UIUC:30112007275602

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Mathematics in Science and Engineering by Anonim Pdf

Author : Hans Petter Langtangen,Kent-Andre Mardal
Publisher : Springer Nature
Page : 395 pages
File Size : 48,9 Mb
Release : 2019-09-26
Category : Mathematics
ISBN : 9783030237882

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Introduction to Numerical Methods for Variational Problems by Hans Petter Langtangen,Kent-Andre Mardal Pdf

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms. The finite element library FEniCS is used throughout the book, but the content is provided in sufficient detail to ensure that students with less mathematical background or mixed programming-language experience will equally benefit. All program examples are available on the Internet.

Author : Barbara S Bertram,Christian Constanda,Allan A. Struthers
Publisher : CRC Press
Page : 371 pages
File Size : 52,6 Mb
Release : 2019-05-20
Category : Mathematics
ISBN : 9781420036039

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Integral Methods in Science and Engineering by Barbara S Bertram,Christian Constanda,Allan A. Struthers Pdf

Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.