Course in Analysis, a - Vol. IV: Fourier Analysis, Ordinary Differential Equations, Calculus of Variations, Jacob Niels, Evans Kristian P.
Автор: Ahmad Shair Название: Textbook on Ordinary Differential Equations ISBN: 3319164074 ISBN-13(EAN): 9783319164076 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics. A complete Solutions Manual, containing solutions to all the exercises published in the book, is available.
Описание: This book is mainly intended as a textbook for students at the Sophomore-Junior level, majoring in mathematics, engineering, or the sciences in general. The book includes the basic topics in Ordinary Differential Equations, normally taught in an undergraduate class, as linear and nonlinear equations and systems, Bessel functions, Laplace transform, stability, etc. It is written with ample exibility to make it appropriate either as a course stressing applications, or a course stressing rigor and analytical thinking. This book also offers sufficient material for a one-semester graduate course, covering topics such as phase plane analysis, oscillation, Sturm-Liouville equations, Euler-Lagrange equations in Calculus of Variations, first and second order linear PDE in 2D. There are substantial lists of exercises at the ends of chapters. A solutions manual, containing complete and detailed solutions to all the exercises in the book, is available to instructors who adopt the book for teaching their classes.
In the part on Fourier analysis, we discuss pointwise convergence results, summability methods and, of course, convergence in the quadratic mean of Fourier series. More advanced topics include a first discussion of Hardy spaces. We also spend some time handling general orthogonal series expansions, in particular, related to orthogonal polynomials. Then we switch to the Fourier integral, i.e. the Fourier transform in Schwartz space, as well as in some Lebesgue spaces or of measures.
Our treatment of ordinary differential equations starts with a discussion of some classical methods to obtain explicit integrals, followed by the existence theorems of Picard-Lindel f and Peano which are proved by fixed point arguments. Linear systems are treated in great detail and we start a first discussion on boundary value problems. In particular, we look at Sturm-Liouville problems and orthogonal expansions. We also handle the hypergeometric differential equations (using complex methods) and their relations to special functions in mathematical physics. Some qualitative aspects are treated too, e.g. stability results (Ljapunov functions), phase diagrams, or flows.
Our introduction to the calculus of variations includes a discussion of the Euler-Lagrange equations, the Legendre theory of necessary and sufficient conditions, and aspects of the Hamilton-Jacobi theory. Related first order partial differential equations are treated in more detail.
The text serves as a companion to lecture courses, and it is also suitable for self-study. The text is complemented by ca. 260 problems with detailed solutions.
Автор: Dacorogna Bernard Название: Introduction to the Calculus of Variations: 3rd Edition ISBN: 1783265515 ISBN-13(EAN): 9781783265510 Издательство: World Scientific Publishing Цена: 13781.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology.
This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist -- mathematicians, physicists, engineers, students or researchers -- in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions.
In this new edition, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Название: Introduction to the Calculus of Variations ISBN: 1783265523 ISBN-13(EAN): 9781783265527 Издательство: World Scientific Publishing Цена: 8870.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and still evolving.
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 Рейтинг: Цена: 10296.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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: Molica Bisci Название: Variational Methods for Nonlocal Fractional Problems ISBN: 1107111943 ISBN-13(EAN): 9781107111943 Издательство: Cambridge Academ Рейтинг: Цена: 21226.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Devoted to the variational analysis of problems described by nonlocal operators, this book will appeal to a wide range of researchers and graduate students in mathematics, especially those interested in nonlinear phenomena. A careful balance is struck between rigorous mathematics and physical applications.
Описание: This book is based on the experience of teaching the subject by the author in Russia, France, South Africa and Sweden. The author provides students and teachers with an easy to follow textbook spanning a variety of topics on tensors, Riemannian geometry and geometric approach to partial differential equations. Application of approximate transformation groups to the equations of general relativity in the de Sitter space simplifies the subject significantly.
Автор: Maitine Bergounioux, Gabriel Peyr?, Christoph Schn Название: Variational Methods: In Imaging and Geometric Control ISBN: 3110439239 ISBN-13(EAN): 9783110439236 Издательство: Walter de Gruyter Рейтинг: Цена: 26024.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents:Part ISecond-order decomposition model for image processing: numerical experimentationOptimizing spatial and tonal data for PDE-based inpaintingImage registration using phase?amplitude separationRotation invariance in exemplar-based image inpaintingConvective regularization for optical flowA variational method for quantitative photoacoustic tomography with piecewise constant coefficientsOn optical flow models for variational motion estimationBilevel approaches for learning of variational imaging modelsPart IINon-degenerate forms of the generalized Euler?Lagrange condition for state-constrained optimal control problemsThe Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controlsControllability of Keplerian motion with low-thrust control systemsHigher variational equation techniques for the integrability of homogeneous potentialsIntroduction to KAM theory with a view to celestial mechanicsInvariants of contact sub-pseudo-Riemannian structures and Einstein?Weyl geometryTime-optimal control for a perturbed Brockett integratorTwist maps and Arnold diffusion for diffeomorphismsA Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part IIndex
Автор: Maitine Bergounioux, ?douard Oudet, Martin Rumpf, Название: Topological Optimization and Optimal Transport: In the Applied Sciences ISBN: 3110439263 ISBN-13(EAN): 9783110439267 Издательство: Walter de Gruyter Рейтинг: Цена: 26024.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered.
Contents Part I
Geometric issues in PDE problems related to the infinity Laplace operator
Solution of free boundary problems in the presence of geometric uncertainties
Distributed and boundary control problems for the semidiscrete Cahn-Hilliard/Navier-Stokes system with nonsmooth Ginzburg-Landau energies
High-order topological expansions for Helmholtz problems in 2D
On a new phase field model for the approximation of interfacial energies of multiphase systems
Optimization of eigenvalues and eigenmodes by using the adjoint method
Discrete varifolds and surface approximation
Part II
Weak Monge-Ampere solutions of the semi-discrete optimal transportation problem
Optimal transportation theory with repulsive costs
Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations
On the Lagrangian branched transport model and the equivalence with its Eulerian formulation
On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows
Pressureless Euler equations with maximal density constraint: a time-splitting scheme
Convergence of a fully discrete variational scheme for a thin-film equatio
Interpretation of finite volume discretization schemes for the Fokker-Planck equation as gradient flows for the discrete Wasserstein distance
Автор: Anatoly Kochubei, Yuri Luchko Название: Basic Theory ISBN: 3110570815 ISBN-13(EAN): 9783110570816 Издательство: Walter de Gruyter Цена: 24165.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
Автор: Anatoly Kochubei, Yuri Luchko Название: Fractional Differential Equations ISBN: 3110570823 ISBN-13(EAN): 9783110570823 Издательство: Walter de Gruyter Цена: 24165.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This second volume collects authoritative chapters covering the mathematical theory of fractional calculus, including ordinary and partial differential equations of fractional order, inverse problems, and evolution equations.
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