An Elementary Course On Variational Problems In Calculus PDF Download
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Author | : Naveen Kumar |
Publisher | : Alpha Science Int'l Ltd. |
Total Pages | : 144 |
Release | : 2005 |
Genre | : Computers |
ISBN | : 9781842651957 |
Download An Elementary Course on Variational Problems in Calculus Book in PDF, ePub and Kindle
"The book covers topics in detail supported by figures and exercises and also lists some direct (approximate) methods to solve boundary value problems containing ordinary/partial differential equations by variational and residue methods, some of them being of immense importance in the treatment of finite element numerical methods. Variety of disciplines being used in the subject, are given in brief, in respective appendices."--BOOK JACKET.
Author | : Filippo Santambrogio |
Publisher | : Springer Nature |
Total Pages | : 354 |
Release | : 2024-01-18 |
Genre | : Mathematics |
ISBN | : 3031450361 |
Download A Course in the Calculus of Variations Book in PDF, ePub and Kindle
This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.
Author | : Frederic Wan |
Publisher | : Routledge |
Total Pages | : 660 |
Release | : 2017-10-19 |
Genre | : Mathematics |
ISBN | : 1351436511 |
Download Introduction To The Calculus of Variations And Its Applications Book in PDF, ePub and Kindle
This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.
Author | : I. M. Gelfand |
Publisher | : Courier Corporation |
Total Pages | : 260 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 0486135012 |
Download Calculus of Variations Book in PDF, ePub and Kindle
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.
Author | : J.L. Troutman |
Publisher | : Springer Science & Business Media |
Total Pages | : 373 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468401580 |
Download Variational Calculus with Elementary Convexity Book in PDF, ePub and Kindle
The calculus of variations, whose origins can be traced to the works of Aristotle and Zenodoros, is now Ii vast repository supplying fundamental tools of exploration not only to the mathematician, but-as evidenced by current literature-also to those in most branches of science in which mathematics is applied. (Indeed, the macroscopic statements afforded by variational principles may provide the only valid mathematical formulation of many physical laws. ) As such, it retains the spirit of natural philosophy common to most mathematical investigations prior to this century. How ever, it is a discipline in which a single symbol (b) has at times been assigned almost mystical powers of operation and discernment, not readily subsumed into the formal structures of modern mathematics. And it is a field for which it is generally supposed that most questions motivating interest in the subject will probably not be answerable at the introductory level of their formulation. In earlier articles,1,2 it was shown through several examples that a complete characterization of the solution of optimization problems may be available by elementary methods, and it is the purpose of this work to explore further the convexity which underlay these individual successes in the context of a full introductory treatment of the theory of the variational calculus. The required convexity is that determined through Gateaux variations, which can be defined in any real linear space and which provide an unambiguous foundation for the theory.
Author | : Mark Kot |
Publisher | : American Mathematical Society |
Total Pages | : 311 |
Release | : 2014-10-06 |
Genre | : Mathematics |
ISBN | : 1470414953 |
Download A First Course in the Calculus of Variations Book in PDF, ePub and Kindle
This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.
Author | : |
Publisher | : Academic Publishers |
Total Pages | : 52 |
Release | : |
Genre | : |
ISBN | : 9788189781705 |
Download Lecture course On VARIATIONAL CALCULUS Book in PDF, ePub and Kindle
Author | : Mariano Giaquinta |
Publisher | : Springer Science & Business Media |
Total Pages | : 498 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 3662032783 |
Download Calculus of Variations I Book in PDF, ePub and Kindle
This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.
Author | : Luigi Ambrosio |
Publisher | : Springer Science & Business Media |
Total Pages | : 347 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642571867 |
Download Calculus of Variations and Partial Differential Equations Book in PDF, ePub and Kindle
At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
Author | : Dazhong Lao |
Publisher | : Springer Nature |
Total Pages | : 1006 |
Release | : 2020-09-02 |
Genre | : Technology & Engineering |
ISBN | : 9811560706 |
Download Fundamental Theories and Their Applications of the Calculus of Variations Book in PDF, ePub and Kindle
This book focuses on the calculus of variations, including fundamental theories and applications. This textbook is intended for graduate and higher-level college and university students, introducing them to the basic concepts and calculation methods used in the calculus of variations. It covers the preliminaries, variational problems with fixed boundaries, sufficient conditions of extrema of functionals, problems with undetermined boundaries, variational problems of conditional extrema, variational problems in parametric forms, variational principles, direct methods for variational problems, variational principles in mechanics and their applications, and variational problems of functionals with vector, tensor and Hamiltonian operators. Many of the contributions are based on the authors’ research, addressing topics such as the extension of the connotation of the Hilbert adjoint operator, definitions of the other three kinds of adjoint operators, the extremum function theorem of the complete functional, unified Euler equations in variational methods, variational theories of functionals with vectors, modulus of vectors, arbitrary order tensors, Hamiltonian operators and Hamiltonian operator strings, reconciling the Euler equations and the natural boundary conditions, and the application range of variational methods. The book is also a valuable reference resource for teachers as well as science and technology professionals.