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Author : V. I. Krylov
ISBN : 9780486154671
Genre : Mathematics
File Size : 56.19 MB
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An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.

Author : A. H. Stroud
ISBN : UOM:39015040327796
Genre : Approximation theory
File Size : 28.69 MB
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Step-by-Step writing process instruction and the detailed concept modeling of Prentice Hall Writing and Grammar helps students improve their writing skills.

Author : V. I. Krylov
ISBN : CORNELL:31924102638511
Genre : Mathematics
File Size : 27.99 MB
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An introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. The 3-part treatment begins with concepts and theorems encountered in the theory of quadrature and then explores the problem of calculation of definite integrals and methods for the calculation of indefinite integral. 1962 edition.

This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.

Author : Leonid P. Lebedev
ISBN : 9780691168265
Genre : Mathematics
File Size : 58.71 MB
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This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences. Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience.

Author : Helmut Brass
ISBN : 9780821853610
Genre : Mathematics
File Size : 70.17 MB
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Every book on numerical analysis covers methods for the approximate calculation of definite integrals. The authors of this book provide a complementary treatment of the topic by presenting a coherent theory of quadrature methods that encompasses many deep and elegant results as well as a large number of interesting (solved and open) problems. The inclusion of the word ``theory'' in the title highlights the authors' emphasis on analytical questions, such as the existence and structure of quadrature methods and selection criteria based on strict error bounds for quadrature rules. Systematic analyses of this kind rely on certain properties of the integrand, called ``co-observations,'' which form the central organizing principle for the authors' theory, and distinguish their book from other texts on numerical integration. A wide variety of co-observations are examined, as a detailed understanding of these is useful for solving problems in practical contexts. While quadrature theory is often viewed as a branch of numerical analysis, its influence extends much further. It has been the starting point of many far-reaching generalizations in various directions, as well as a testing ground for new ideas and concepts. The material in this book should be accessible to anyone who has taken the standard undergraduate courses in linear algebra, advanced calculus, and real analysis.

Author : G.N. Milstein
ISBN : 9789401584555
Genre : Computers
File Size : 40.75 MB
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This book is devoted to mean-square and weak approximations of solutions of stochastic differential equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations. Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.

Author : William S. Levine
ISBN : 0849300533
Genre : Technology & Engineering
File Size : 52.92 MB
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Sifting through the variety of control systems applications can be a chore. Diverse and numerous technologies inspire applications ranging from float valves to microprocessors. Relevant to any system you might use, the highly adaptable Control System Fundamentals fills your need for a comprehensive treatment of the basic principles of control system engineering. This overview furnishes the underpinnings of modern control systems. Beginning with a review of the required mathematics, major subsections cover digital control and modeling. An international panel of experts discusses the specification of control systems, techniques for dealing with the most common and important control system nonlinearities, and digital implementation of control systems, with complete references. This framework yields a primary resource that is also capable of directing you to more detailed articles and books. This self-contained reference explores the universal aspects of control that you need for any application. Reliable, up-to-date, and versatile, Control System Fundamentals answers your basic control systems questions and acts as an ideal starting point for approaching any control problem.

This book provides a thorough introduction to one of the most efficient approximation methods for the analysis and solution of problems in theoretical physics and applied mathematics. It is written with practical needs in mind and contains a discussion of 50 problems with solutions, of varying degrees of difficulty. The problems are taken from quantum mechanics, but the method has important applications in any field of science involving second order ordinary differential equations. The power of the asymptotic solution of second order differential equations is demonstrated, and in each case the authors clearly indicate which concepts and results of the general theory are needed to solve a particular problem. This book will be ideal as a manual for users of the phase-integral method, as well as a valuable reference text for experienced research workers and graduate students.

Author : Theodore S Chihara
ISBN : 9780486141411
Genre : Mathematics
File Size : 81.91 MB
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Concise introduction covers general elementary theory, including the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula, special functions, and some specific systems. 1978 edition.

Author : A.D. Egorov
ISBN : 0792321936
Genre : Mathematics
File Size : 56.14 MB
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Integration in infinitely dimensional spaces (continual integration) is a powerful mathematical tool which is widely used in a number of fields of modern mathematics, such as analysis, the theory of differential and integral equations, probability theory and the theory of random processes. This monograph is devoted to numerical approximation methods of continual integration. A systematic description is given of the approximate computation methods of functional integrals on a wide class of measures, including measures generated by homogeneous random processes with independent increments and Gaussian processes. Many applications to problems which originate from analysis, probability and quantum physics are presented. This book will be of interest to mathematicians and physicists, including specialists in computational mathematics, functional and statistical physics, nuclear physics and quantum optics.

Clifford analysis, a branch of mathematics that has been developed since about 1970, has important theoretical value and several applications. In this book, the authors introduce many properties of regular functions and generalized regular functions in real Clifford analysis, as well as harmonic functions in complex Clifford analysis. It covers important developments in handling the incommutativity of multiplication in Clifford algebra, the definitions and computations of high-order singular integrals, boundary value problems, and so on. In addition, the book considers harmonic analysis and boundary value problems in four kinds of characteristic fields proposed by Luogeng Hua for complex analysis of several variables. The great majority of the contents originate in the authors’ investigations, and this new monograph will be interesting for researchers studying the theory of functions.

Author : Liviu Gr. Ixaru
ISBN : 1402020996
Genre : Mathematics
File Size : 76.92 MB
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Exponential Fitting is a procedure for an efficient numerical approach of functions consisting of weighted sums of exponential, trigonometric or hyperbolic functions with slowly varying weight functions. This book is the first one devoted to this subject. Operations on the functions described above like numerical differentiation, quadrature, interpolation or solving ordinary differential equations whose solution is of this type, are of real interest nowadays in many phenomena as oscillations, vibrations, rotations, or wave propagation. The authors studied the field for many years and contributed to it. Since the total number of papers accumulated so far in this field exceeds 200 and the fact that these papers are spread over journals with various profiles (such as applied mathematics, computer science, computational physics and chemistry) it was time to compact and to systematically present this vast material. In this book, a series of aspects is covered, ranging from the theory of the procedure up to direct applications and sometimes including ready to use programs. The book can also be used as a textbook for graduate students.

Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

Author : Augustus Edward Hough Love
ISBN : UCAL:$B530716
Genre : Calculus, Integral
File Size : 59.1 MB
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