Математический анализ
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5318 рубAn Introduction to Complex Analysis
O. Carruth McGehee Recent decades have seen profound changes in the way we understand complex analysis. This new work presents a much–needed modern treatment of the subject, incorporating the latest developments and providing a rigorous yet accessible introduction to the concepts and proofs of this fundamental branch of mathematics. With its thorough review of the prerequisites and well–balanced mix of theory and practice, this book will appeal both to readers interested in pursuing advanced topics as well as those wishing to explore the many applications of complex analysis to engineering and the physical sciences. ? Reviews the necessary calculus, bringing readers quickly up to speed on the material ? Illustrates the theory, techniques, and reasoning through the use of short proofs and many examples ? Demystifies complex versus real differentiability for functions from the plane to the plane ? Develops Cauchy?s Theorem, presenting the powerful and easy–to–use winding–number version ...
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5612 рубDiffusion systems and heat equations on networks: Symmetries and irreducibility
Stefano Cardanobile In these notes, a theory for sesquilinear forms on product spaces is developed, with the aim of unifying the treatment of diffusion systems and equation on networks. In the first part, a theoretical framework for sesquilinear forms defined on the direct sum of Hilbert spaces is developed. Conditions for the boundedness, ellipticity and coercivity of the sesquilinear form are proved. A criterion of E.-M. Ouhabaz is used in order to prove qualitative properties of the abstract Cauchy problem having as generator the operator associated with the sesquilinear form. In the second part we analyze quantum graphs as a special case of forms on subspaces of the direct sum of Hilbert spaces. First, we set up a framework for handling quantum graphs in the case of infinite networks. Then, the operator associated with such systems is identified and investigated. Finally, we turn our attention to symmetry properties of the associated parabolic problem and we investigate the connection with the...
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4050 рубDual Space: Mathematics, Vector space, Linear functional, Tensor, Tensor algebra, Measure (mathematics), Functional analysis, Topological vector space, ... (projective geometry), Pontryagin duality
In mathematics, any vector space, V, has a corresponding dual vector space (or just dual space for short) consisting of all linear functionals on V. Dual vector spaces defined on finite dimensional vector spaces can be used for defining tensors which are studied in tensor algebra. When applied to vector spaces of functions (which typically are infinite-dimensional), dual spaces are employed for defining and studying concepts like measures, distributions, and Hilbert spaces. Consequently, the dual space is an important concept in the study of functional analysis. There are two types of dual spaces: the algebraic dual space, and the continuous dual space. The algebraic dual space is defined for all vector spaces. When defined for a topological vector space there is a subspace of this dual space, corresponding to continuous linear functionals, which constitutes a continuous dual space. Contents
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7105 рубIntroductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences (13th Edition)
Ernest F. Haeussler, Richard S. Paul, Richard J. Wood Haeussler, Paul, and Wood establish a strong algebraic foundation that sets this text apart from other applied mathematics texts, paving the way for readers to solve real-world problems that use calculus. Emphasis on developing algebraic skills is extended to the exercises–including both drill problems and applications. The authors work through examples and explanations with a blend of rigor and accessibility. In addition, they have refined the flow, transitions, organization, and portioning of the content over many editions to optimize learning for readers. The table of contents covers a wide range of topics efficiently, enabling readers to gain a diverse understanding. ALGEBRA; Review of Algebra; Applications and More Algebra; Functions and Graphs; Lines, Parabolas, and Systems; Exponential and Logarithmic Functions; FINITE MATHEMATICS; Mathematics of Finance; Matrix Algebra; Linear Programming; Introduction to Probability and Statistics; Additional Topics in Probability;...
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6149 рубLectures on the Hyperreals: An Introduction to Nonstandard Analysis
Robert Goldblatt This is an introduction to nonstandard analysis based on a course of lectures given several times by the author. It is suitable for use as a text at the beginning graduate or upper undergraduate level, or for self-study by anyone familiar with elementary real analysis. It presents nonstandard analysis not just as a theory about infinitely small and large numbers, but as a radically different way of viewing many standard mathematical concepts and constructions; a source of new ideas, objects and proofs; and a wellspring of powerful new principles of reasoning (transfer, overflow, saturation, enlargement, hyperfinite approximation etc.). The book begins with the ultrapower construction of hyperreal number systems, and proceeds to develop one-variable calculus, analysis and topology from the nonstandard perspective, emphasizing the role of the transfer principle as a working tool of mathematical practice. It then sets out the theory of enlargements of fragments of the mathematical...
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4381 рубMathematical Analysis of Partial Differential Equations Modeling Electrostatic Mems (Courant Lecture Notes)
Pierpaolo Esposito, Nassif Ghoussoub, Yujin Guo Micro- and nanoelectromechanical systems (MEMS and NEMS), which combine electronics with miniature-size mechanical devices, are essential components of modern technology. It is the mathematical model describing 'electrostatically actuated' MEMS that is addressed in this monograph. Even the simplified models that the authors deal with still lead to very interesting second- and fourth-order nonlinear elliptic equations (in the stationary case) and to nonlinear parabolic equations (in the dynamic case). While nonlinear eigenvalue problems - where the stationary MEMS models fit - are a well-developed field of PDEs, the type of inverse square nonlinearity that appears here helps shed a new light on the class of singular supercritical problems and their specific challenges. Besides the practical considerations, the model is a rich source of interesting mathematical phenomena. Numerics, formal asymptotic analysis, and ODE methods give lots of information and point to many conjectures. ...
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2204 рубNumerical Recipes Example Book (C)
William T. Vetterling, William H. Press, Saul A. Teukolsky, Brian P. Flannery The example books published as part of the Numerical Recipes second edition series contain source programs that exercise and demonstrate all of the Numerical Recipes subroutines. Each example program contains comments and is prefaced by a short description of what it does. The books contain all of the old material from the original edition as well as new material from the second edition. They will be valuable for readers who wish to incorporate procedures and subroutines into their own source programs. They are available in both FORTRAN and C. Source programs that demonstrate all of the Numerical Recipes subroutines. Valuable for readers who wish to incorporate procedures and subroutines into their own.
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7561 рубOblique Boundary Value Problems and Limit Formulae of Potential Theory: An Analysis Motivated by Geomathematical Problems
Thomas Raskop This book deals with two main subjects which are of interest in the field of geomathematics. Here we search for harmonic functions satisfying certain boundary conditions. Often this is a condition on the derivative in direction of the gravity vector. Thus an oblique boundary problem occurs, because the gravity vector is not the normal vector of the earths surface. In this book we provide weak solutions to oblique boundary problems for very general coefficients, surfaces and inhomogeneities. We start with the problem for bounded domains solving a weak formulation for inhomogeneities in Sobolev spaces. Going to unbounded domains, we use the Kelvin transformation to get a corresponding bounded problem. Moreover Stochastic inhomogeneities, a Ritz Galerkin approximation and some examples are provided. The limit formulae are strongly related to boundary problems of potential theory, because they can be used to construct harmonic functions. We prove the formulae in several norms. The...
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4127 рубPractical Financial Optimization: A Library of GAMS Models (The Wiley Finance Series)
Soren S Nielson, Andrea Consiglio This companion book thoroughly describes the actual implementation of the majority of the models developed in Practical Financial Optimization, in the General Algebraic Modelling System, GAMS. In addition, the volume contains executable versions of these models, and a CD containing the software needed to execute them.
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11992 рубQuantum Mechanics of Non-Hamiltonian and Dissipative Systems, Volume 7
Vasily Tarasov Quantum Mechanics of Non-Hamiltonian and Dissipative Systems is self-contained and can be used by students without a previous course in modern mathematics and physics. The book describes the modern structure of the theory, and covers the fundamental results of last 15 years. The book has been recommended by Russian Ministry of Education as the textbook for graduate students and has been used for graduate student lectures from 1998 to 2006. Requires no preliminary knowledge of graduate and advanced mathematics. Discusses the fundamental results of last 15 years in this theory. Suitable for courses for undergraduate students as well as graduate students and specialists in physics mathematics and other sciences. From the Back Cover. In many books about quantum mechanics for graduate students, only the unitary evolution, Hamiltonian systems and pure states are considered. In the suggested book, the modern mathematical concepts, which are the general...
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10881 рубRandom Dynamical Systems (Springer Monographs in Mathematics)
Ludwig Arnold This book is the first systematic presentation of the theory of dynamical systems under the influence of randomness. It includes products of random mappings as well as random and stochastic differential equations. The basic mulitplicative ergodic theorem is presented and provides a random substitute for linear algebra. On its basis random invariant manifolds are constructed, systems are simplified by smooth random coordinate transformations (random normal forms), and qualitative changes in families of random systems (random bifurcation theory) are studied. Numerous instructive examples are treated analytically or numerically. The main intention, however, is to present a reliable and rather complete source of reference which lays the foundation for future work and applications.
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4532 рубReproducing Kernel Hilbert Space: Functional Analysis, Mathematics, Hilbert Space, Function Space, Bounded Operator, Complex Analysis, Quantum Mechanics, ... Riesz Representation Theorem, Hardy Space
High Quality Content by WIKIPEDIA articles! In functional analysis (a branch of mathematics), a reproducing kernel Hilbert space is a Hilbert space of functions in which pointwise evaluation is a continuous linear functional. Equivalently, they are spaces that can be defined by reproducing kernels. The subject was originally and simultaneously developed by Nachman Aronszajn (1907?1980) and Stefan Bergman (1895?1977) in 1950. In this article we assume that Hilbert spaces are complex. The main reason for this is that many of the examples of reproducing kernel Hilbert spaces are spaces of analytic functions, although some real Hilbert spaces also have reproducing kernels.
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3800 рубSequential Decision–Making Problems
Cedric Pralet In the first part of this book, the authors introduce a generic algebraic framework that encompasses and unifies a large number of such formalisms. This formalism, called the Plausibility–Feasibility–Utility (PFU) framework, is based on algebraic structures, graphical models, and sequences of quantifications.
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6456 рубSignal Processing, Image Processing and Pattern Recognition,: International Conference, SIP 2009, Held as Part of the Future Generation Information Technology ... in Computer and Information Science)
This book constitutes the proceedings of the International Conference on Signal Processing, Image Processing and Pattern Recognition, SIP 2009, held as part of the Future Generation Information Technology Conference, FGIT 2009, held on Jeju Island, Korea, December 10-12, 2009. The 38 papers presented in this volume were carefully reviewed and selected from numerous submissions. The topics covered are from multifaceted aspects of signal processing, image processing and pattern recognition.
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12046 рубSolving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
Ernst Hairer, Gerhard Wanner The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.
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