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Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated.   The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems.   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Typically, this topic is presented to students in specialized courses such as logic, functional analysis, or geometric group theory. In this book, the basic facts about ultrafilters and ultraproducts are presented to readers with no prior knowledge of the subject and then these techniques are applied to a wide variety of topics. The first part of the book deals solely with ultrafilters and presents applications to voting theory, combinatorics, and topology, while also dealing also with foundational issues.  The second part presents the classical ultraproduct construction and provides applications to algebra, number theory, and nonstandard analysis. The third part discusses a metric generalization of the ultraproduct construction and gives example applications to geometric group theory and functional analysis. The final section returns to more advanced topics of a more foundational nature.  The book should be of interest to undergraduates, graduate students, and researchers from all areas of mathematics interested in learning how ultrafilters and ultraproducts can be applied to their specialty.","brand":"WoB","offers":[{"title":"GB \/ LIKE_NEW \/ INTERNAL","offer_id":50021184307473,"sku":"GOR012530067","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":50384718823697,"sku":"CIN1470469618G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470469618.jpg?v=1763477844"},{"product_id":"functional-analysis-book-yuli-eidelman-9780821836460","title":"Functional Analysis","description":"This textbook provides an introduction to the methods and language of functional analysis, including Hilbert spaces, Fredholm theory for compact operators, and spectral theory of self-adjoint operators. It also presents the basic theorems and methods of abstract functional analysis and a few applications of these methods to Banach algebras and the theory of unbounded self-adjoint operators. The text corresponds to material for two semester courses (Part I and Part II, respectively) and is essentially self-contained. Prerequisites for the first part are minimal amounts of linear algebra and calculus. For the second part, some knowledge of topology and measure theory is recommended. Each of the 11 chapters is followed by numerous exercises, with solutions given at the end of the book. The amount of mathematics presented in the book can well be absorbed in a year's study and will provide a sound basis for future reading. It is suitable for graduate students and researchers interested in operator theory and functional analysis.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50032489562385,"sku":"CIN0821836463VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821836463.jpg?v=1763479117"},{"product_id":"partial-differential-equations-book-lawrence-c-evans-9781470469429","title":"Partial Differential Equations","description":"This is the second edition of the now definitive text on partial differential equations (PDE). It offers a comprehensive survey of modern techniques in the theoretical study of PDE with particular emphasis on nonlinear equations. Its wide scope and clear exposition make it a great text for a graduate course in PDE. For this edition, the author has made numerous changes, including a new chapter on nonlinear wave equations, more than 80 new exercises, several new sections,a significantly expanded bibliography.  About the First Edition: \"\"I have used this book for both regular PDE and topics courses. It has a wonderful combination of insight and technical detail. ... Evans' book is evidence of his mastering of the field and the clarity of presentation.\"\" - Luis Caffarelli, University of Texas  \"\"It is fun to teach from Evans' book. It explains many of the essential ideas and techniques of partial differential equations ... Every graduate student in analysis should read it.\"\" - David Jerison, MIT  \"\"I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ... I am very happy with the preparation it provides my students.\"\" - Carlos Kenig, University of Chicago  \"\"Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ... An outstanding reference for many aspects of the field.\"\" - Rafe Mazzeo, Stanford University","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":50055276888337,"sku":"NGR9781470469429","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1470469421.jpg?v=1750859014"},{"product_id":"partial-differential-equations-book-lawrence-c-evans-9780821849743","title":"Partial Differential Equations","description":"This is the second edition of the now definitive text on partial differential equations (PDE). 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(David Jerison, MIT) I use Partial Differential Equations to prepare my students for their Topic exam, which is a requirement before starting working on their dissertation. The book provides an excellent account of PDE's ...I am very happy with the preparation it provides my students. (Carlos Kenig, University of Chicago) Evans' book has already attained the status of a classic. It is a clear choice for students just learning the subject, as well as for experts who wish to broaden their knowledge ...An outstanding reference for many aspects of the field. (Rafe Mazzeo, Stanford University.","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50059262525713,"sku":"GOR007954622","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ WELL_READ \/ SBYB","offer_id":50151024820497,"sku":"CIN0821849743A","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ GOOD \/ SBYB","offer_id":50924692209937,"sku":"CIN0821849743G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821849743.jpg?v=1750850133"},{"product_id":"function-theory-of-one-complex-variable-book-robert-e-greene-9780821839621","title":"Function Theory of One Complex Variable","description":"Earth, Air, Fire, and Water - not only are these elements the building blocks of the universe, but also potent keys to heightened self-understanding. The Way of Four helps you determine which of the four elements are prominent and which are lacking in your world using a variety of custom-made quizzes. It includes a multitude of methods to incorporate and balance the elements in your environment, wardrobe, and even your perfume. This is a fun and valuable sourcebook for anyone seeking balance and beauty in a hectic world. \u003cp\u003e\u003c\/p\u003e","brand":"WoB","offers":[{"title":"US \/ WELL_READ \/ SBYB","offer_id":50128414867729,"sku":"CIN0821839624A","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821839624.jpg?v=1751233765"},{"product_id":"introduction-to-global-analysis-book-john-douglas-moore-9781470429508","title":"Introduction to Global Analysis","description":"During the last century, global analysis was one of the main sources of interaction between geometry and topology. One might argue that the core of this subject is Morse theory, according to which the critical points of a generic smooth proper function on a manifold $M$ determine the homology of the manifold.  Morse envisioned applying this idea to the calculus of variations, including the theory of periodic motion in classical mechanics, by approximating the space of loops on $M$ by a finite-dimensional manifold of high dimension. Palais and Smale reformulated Morse's calculus of variations in terms of infinite-dimensional manifolds, and these infinite-dimensional manifolds were found useful for studying a wide variety of nonlinear PDEs.  This book applies infinite-dimensional manifold theory to the Morse theory of closed geodesics in a Riemannian manifold. It then describes the problems encountered when extending this theory to maps from surfaces instead of curves. It treats critical point theory for closed parametrized minimal surfaces in a compact Riemannian manifold, establishing Morse inequalities for perturbed versions of the energy function on the mapping space. It studies the bubbling which occurs when the perturbation is turned off, together with applications to the existence of closed minimal surfaces. The Morse-Sard theorem is used to develop transversality theory for both closed geodesics and closed minimal surfaces.  This book is based on lecture notes for graduate courses on \"Topics in Differential Geometry\", taught by the author over several years. 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The concluding chapter serves as an illustration of the concepts introduced in previous chapters.In particular, some interesting calculations with quadratic fields show the use of the norm residue symbol. For the second edition the author added some new material, expanded many proofs, and corrected errors found in the first edition. The main objective, however, remains the same as it was for the first edition: to give an exposition of the introductory material and the main theorems about class fields of algebraic number fields that would require as little background preparation as possible. Janusz's book can be an excellent textbook for a year-long course in algebraic number theory; the first three chapters would be suitable for a one-semester course. 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This book is an introduction to a relatively new theory of the integral (called the 'generalized Riemann integral' or the 'Henstock-Kurzweil integral') that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from calculus. One virtue of the new approach is that no measure theory and virtually no topology is required.Indeed, the book includes a study of measure theory as an application of the integral. Part 1 fully develops the theory of the integral of functions defined on a compact interval. This restriction on the domain is not necessary, but it is the case of most interest and does not exhibit some of the technical problems that can impede the reader's understanding. Part 2 shows how this theory extends to functions defined on the whole real line. 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The book also contains many exercises, some included to clarify simple points of exposition, others to introduce new ideas and techniques, and a few containing relatively deep mathematical results. With the modest prerequisite of a first course in calculus, the book is suitable for undergraduates and graduate students in mathematics, finance, and economics and can be read, using appropriate selections, at a number of levels.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50297890504977,"sku":"CIN0821839519G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":50826974363921,"sku":"GOR002712986","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ WELL_READ \/ SBYB","offer_id":50953700344081,"sku":"CIN0821839519A","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821839519.jpg?v=1750746044"},{"product_id":"fourier-analysis-book-javier-duoandikoetxea-9780821821725","title":"Fourier Analysis","description":"Fourier analysis encompasses a variety of perspectives and techniques. 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Chapters 4 and 5 discuss singular integrals, including modern generalizations. Chapter 6 studies the relationship between $H^1$, $BMO$, and singular integrals; and Chapter 7 presents the elementary theory of weighted norm inequalities. Chapter 8 discusses Littlewood-Paley theory, which had developments that resulted in a number of applications. The final chapter concludes with an important result, the $T1$ theorem, which has been of crucial importance in the field.This volume has been updated and translated from the Spanish edition that was published in 1995. Minor changes have been made to the core of the book; however, the sections, 'Notes and Further Results' have been considerably expanded and incorporate new topics, results, and references. It is geared toward graduate students seeking a concise introduction to the main aspects of the classical theory of singular operators and multipliers. Prerequisites include basic knowledge in Lebesgue integrals and functional analysis.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50362987938065,"sku":"CIN0821821725G","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ GOOD \/ INTERNAL","offer_id":53148698444049,"sku":"GOR014779038","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821821725.jpg?v=1750914885"},{"product_id":"general-topology-of-dynamical-systems-book-ethan-akin-9780821838006","title":"The General Topology of Dynamical Systems","description":"Topology, the foundation of modern analysis, arose historically as a way to organize ideas like compactness and connectedness which had emerged from analysis. Similarly, recent work in dynamical systems theory has both highlighted certain topics in the pre-existing subject of topological dynamics (such as the construction of Lyapunov functions and various notions of stability) and also generated new concepts and results (such as attractors, chain recurrence, and basic sets).This book collects these results, both old and new, and organizes them into a natural foundation for all aspects of dynamical systems theory. No existing book is comparable in content or scope. Requiring background in point-set topology and some degree of 'mathematical sophistication', Akin's book serves as an excellent textbook for a graduate course in dynamical systems theory. In addition, Akin's reorganization of previously scattered results makes this book of interest to mathematicians and other researchers who use dynamical systems in their work.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50363020247313,"sku":"CIN0821838008G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821838008.jpg?v=1750883253"},{"product_id":"elements-of-homology-theory-book-vv-prasolov-9780821838129","title":"Elements of Homology Theory","description":"The book is a continuation of the previous book by the author (Elements of Combinatorial and Differential Topology, Graduate Studies in Mathematics, Volume 74, American Mathematical Society, 2006). It starts with the definition of simplicial homology and cohomology, with many examples and applications. Then the Kolmogorov-Alexander multiplication in cohomology is introduced. A significant part of the book is devoted to applications of simplicial homology and cohomology to obstruction theory, in particular, to characteristic classes of vector bundles. The later chapters are concerned with singular homology and cohomology, and Cech and de Rham cohomology. The book ends with various applications of homology to the topology of manifolds, some of which might be of interest to experts in the area. The book contains many problems; almost all of them are provided with hints or complete solutions.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50363029651729,"sku":"CIN0821838121G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821838121.jpg?v=1763481594"},{"product_id":"solutions-manual-to-a-modern-theory-of-integration-book-american-mathematical-society-9780821828212","title":"Solutions Manual to a Modern Theory of Integration","description":"This solutions manual is geared toward instructors for use as a companion volume to the book, A Modern Theory of Integration, (AMS Graduate Studies in Mathematics series, Volume 32).","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50369570210065,"sku":"CIN0821828215G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821828215.jpg?v=1751265069"},{"product_id":"functions-of-several-complex-variables-and-their-singularities-book-american-mathematical-society-9780821833193","title":"Functions of Several Complex Variables and Their Singularities","description":"The book provides an introduction to the theory of functions of several complex variables and their singularities, with special emphasis on topological aspects. The topics include Riemann surfaces, holomorphic functions of several variables, classification and deformation of singularities, fundamentals of differential topology, and the topology of singularities. The aim of the book is to guide the reader from the fundamentals to more advanced topics of recent research. All the necessary prerequisites are specified and carefully explained. The general theory is illustrated by various examples and applications.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50369585381649,"sku":"CIN0821833197G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821833197.jpg?v=1756706684"},{"product_id":"integrals-of-lebesgue-denjoy-perron-and-henstock-book-russell-a-gordon-9780821838051","title":"The Integrals of Lebesgue, Denjoy, Perron and Henstock","description":"This book provides an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. The Lebesgue integral and its essential properties are first developed in detail. The other three integrals are all generalizations of the Lebesgue integral that satisfy the ideal version of the Fundamental Theorem of Calculus: if $F$ is differentiable on the interval $[a,b]$, then $F'$ is integrable on $[a,b]$ and $\\int_a^b F'= F(b) - F(a)$. One of the book's unique features is that the Denjoy, Perron, and Henstock integrals are each developed fully and carefully from their corresponding definitions.The last part of the book is devoted to integration processes which satisfy a theorem analogous to the Fundamental Theorem, in which $F$ is approximately differentiable. This part of this book is preceded by a detailed study of the approximate derivative and ends with some open questions. This book contains over 230 exercises (with solutions) that illustrate and expand the material in the text. It would be an excellent textbook for first-year graduate students who have background in real analysis.","brand":"WoB","offers":[{"title":"US \/ GOOD \/ SBYB","offer_id":50369608286481,"sku":"CIN0821838059G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821838059.jpg?v=1751329968"},{"product_id":"configurations-of-points-and-lines-book-grunbaum-branko-9780821843086","title":"Configurations of Points and Lines","description":"This is the only book on the topic of geometric configurations of points and lines. It presents in detail the history of the topic, with its surges and declines since its beginning in 1876. It covers all the advances in the field since the revival of interest in geometric configurations some 20 years ago. The author's contributions are central to this revival. 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