Variational Calculus
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An Introduction To Variational Calculus
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Author : Hebert Montegranario
language : en
Publisher: Springer Nature
Release Date : 2024-12-23
An Introduction To Variational Calculus written by Hebert Montegranario and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-23 with Computers categories.
This textbook introduces variational calculus and regularization methods for inverse problems, seamlessly blending classical concepts with contemporary computational applications, particularly in the field of image processing. The classical perspective draws upon foundational topics explored by pioneers such as Euler and Lagrange, establishing a solid theoretical groundwork. In recent decades, the advent of disciplines such as computer vision has expanded the horizons of variational calculus, showcasing its effectiveness in addressing complex problems that necessitate computational solutions. Consequently, this book places a strong emphasis on the synergy between mathematical theory, practical applications, and algorithmic development. To ensure the text is comprehensive and accessible, essential principles of functional analysis and Fourier analysis are incorporated, facilitating a deeper and more nuanced understanding of the applications presented. Covering both classic and more recent aspects of variational calculus, this book suggests that many topics of modern technology such as computer vision, robotics and especially digital image processing can be formulated in terms of variational problems.
Variational Calculus With Engineering Applications
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Author : Constantin Udriste
language : en
Publisher: John Wiley & Sons
Release Date : 2022-10-20
Variational Calculus With Engineering Applications written by Constantin Udriste and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-20 with Mathematics categories.
VARIATIONAL CALCULUS WITH ENGINEERING APPLICATIONS 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.
Calculus Of Variations
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Author : I. M. Gelfand
language : en
Publisher: Courier Corporation
Release Date : 2012-04-26
Calculus Of Variations written by I. M. Gelfand and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-26 with Mathematics categories.
Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Calculus Of Variations
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Author : A. M. Arthurs
language : en
Publisher: Routledge & Kegan Paul Books
Release Date : 1975
Calculus Of Variations written by A. M. Arthurs and has been published by Routledge & Kegan Paul Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
Differential Equations And Their Applications
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Author : ZAFAR AHSAAN
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2004-01-01
Differential Equations And Their Applications written by ZAFAR AHSAAN and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
Primarily intended for the undergraduate students in Mathematics, Physics and Engineering, this text gives in-depth coverage of differential equations and the methods of solving them. The book begins with the basic definitions, the physical and geometric origins of differential equations, and the methods for solving first-order differential equations. Then it goes on to give the applications of these equations to such areas as biology, medical sciences, electrical engineering and economics. The text also discusses, systematically and logically, higher-order differential equations and their applications to telecom-munications, civil engineering, cardiology and detec-tion of diabetes, as also the methods of solving simultaneous differential equations and their applica-tions. Besides, the book provides a detailed discussion on Laplace transform and their applications, partial differential equations and their applications to vibration of a stretched string, heat flow, transmission lines, etc., and calculus of variations and its applications. This book, which is a happy fusion of theory and application, would also be useful to postgraduate students.
Calculus Of Variations With Applications
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Author : GUPTA, A. S.
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 1996-01-01
Calculus Of Variations With Applications written by GUPTA, A. S. and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.
Calculus of variations is one of the most important mathematical tools of great scientific significance used by scientistis and engineers. Unfortunately, a few books that are available are written at a level which is not easily comprehensible for postgraduate students.This book, written by a highly respected academic, presents the materials in a lucid manner so as to be within the easy grasp of the students with some background in calculus, differential equations and functional analysis. The aim is to give a thorough and systematic analysis of various aspects of calculus of variations.
Variational Methods In Mathematical Physics
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Author : Philippe Blanchard
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Variational Methods In Mathematical Physics written by Philippe Blanchard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
The first edition (in German) had the prevailing character of a textbook owing to the choice of material and the manner of its presentation. This second (translated, revised, and extended) edition, however, includes in its new parts considerably more recent and advanced results and thus goes partially beyond the textbook level. We should emphasize here that the primary intentions of this book are to provide (so far as possible given the restrictions of space) a selfcontained presentation of some modern developments in the direct methods of the cal culus of variations in applied mathematics and mathematical physics from a unified point of view and to link it to the traditional approach. These modern developments are, according to our background and interests: (i) Thomas-Fermi theory and related theories, and (ii) global systems of semilinear elliptic partial-differential equations and the existence of weak solutions and their regularity. Although the direct method in the calculus of variations can naturally be considered part of nonlinear functional analysis, we have not tried to present our material in this way. Some recent books on nonlinear functional analysis in this spirit are those by K. Deimling (Nonlinear Functional Analysis, Springer, Berlin Heidelberg 1985) and E. Zeidler (Nonlinear Functional Analysis and Its Applications, Vols. 1-4; Springer, New York 1986-1990).
Introduction To The Calculus Of Variations
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Author : Hans Sagan
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
Introduction To The Calculus Of Variations written by Hans Sagan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.
Quantum Variational Calculus
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Author : Agnieszka B. Malinowska
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29
Quantum Variational Calculus written by Agnieszka B. Malinowska and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-29 with Mathematics categories.
This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.
Energy Principles And Variational Methods In Applied Mechanics
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Author : J. N. Reddy
language : en
Publisher: John Wiley & Sons
Release Date : 2002-08-09
Energy Principles And Variational Methods In Applied Mechanics written by J. N. Reddy and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-09 with Mathematics categories.
A systematic presentation of energy principles and variationalmethods The increasing use of numerical and computational methods inengineering and applied sciences has shed new light on theimportance of energy principles and variational methods. EnergyPrinciples and Variational Methods in Applied Mechanicsprovides a systematic and practical introduction to the use ofenergy principles, traditional variational methods, and the finiteelement method to the solution of engineering problems involvingbars, beams, torsion, plane elasticity, and plates. Beginning with a review of the basic equations of mechanics andthe concepts of work, energy, and topics from variational calculus,this book presents the virtual work and energy principles, energymethods of solid and structural mechanics, Hamilton'sprinciple for dynamical systems, and classical variational methodsof approximation. A unified approach, more general than that foundin most solid mechanics books, is used to introduce the finiteelement method. Also discussed are applications to beams andplates. Complete with more than 200 illustrations and tables, EnergyPrinciples and Variational Methods in Applied Mechanics, SecondEdition is a valuable book for students of aerospace, civil,mechanical, and applied mechanics; and engineers in design andanalysis groups in the aircraft, automobile, and civil engineeringstructures, as well as shipbuilding industries.