Approximate Calculation Of Integrals

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Approximate Calculation Of Integrals

Author : V. I. Krylov
ISBN : 9780486154671
Genre : Mathematics
File Size : 78.21 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.
Category: Mathematics

Approximate Calculation Of Multiple Integrals

Author : A. H. Stroud
ISBN : UOM:39015040327796
Genre : Approximation theory
File Size : 48.48 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.
Category: Approximation theory

Approximate Calculation Of Integrals

Author : V. I. Krylov
ISBN : CORNELL:31924102638511
Genre : Mathematics
File Size : 36.53 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.
Category: Mathematics

Functional Integrals

Author : A.D. Egorov
ISBN : 0792321936
Genre : Mathematics
File Size : 76.59 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.
Category: Mathematics

Numerical Integration Of Stochastic Differential Equations

Author : G.N. Milstein
ISBN : 079233213X
Genre : Computers
File Size : 54.96 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.
Category: Computers

Approximating Perfection

Author : Leonid P. Lebedev
ISBN : 9781400873258
Genre : Mathematics
File Size : 37.20 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.
Category: Mathematics

Coefficient Inverse Problems For Parabolic Type Equations And Their Application

Author : P. G. Danilaev
ISBN : 9783110940916
Genre : Mathematics
File Size : 90.79 MB
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As a rule, many practical problems are studied in a situation when the input data are incomplete. For example, this is the case for a parabolic partial differential equation describing the non-stationary physical process of heat and mass transfer if it contains the unknown thermal conductivity coefficient. Such situations arising in physical problems motivated the appearance of the present work. In this monographthe author considers numerical solutions of the quasi-inversion problems, to which the solution of the original coefficient inverse problems are reduced. Underground fluid dynamics is taken as a field of practical use of coefficient inverse problems. The significance of these problems for this application domain consists in the possibility to determine the physical fields of parameters that characterize the filtration properties of porous media (oil strata). This provides the possibility of predicting the conditions of oil-field development and the effects of the exploitation. The research carried out by the author showed that the quasi-inversion method can be applied also for solution of "interior coefficient inverse problems" by reducing them to the problem of continuation of a solution to a parabolic equation. This reduction is based on the results of the proofs of the uniqueness theorems for solutions of the corresponding coefficient inverse problems.
Category: Mathematics

Comparison Of Exact And Approximate Evaluations Of The Single Scattering Integral In Nucleon Deuteron Elastic Scattering

Author : John William Wilson
ISBN : UIUC:30112106693036
Genre : Deuterons
File Size : 36.9 MB
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The exact nucleon-deuteron elastic single scattering integral was calculated numerically in order to evaluate errors in sticking factor approximations. A similar analysis made by using S wave separable potentials concluded that errors for these approximations were negligible except near backward angles where they were found to be about 10 percent.
Category: Deuterons

Quadrature Theory

Author : Helmut Brass
ISBN : 9780821853610
Genre : Mathematics
File Size : 85.46 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.
Category: Mathematics

Mathematical Reviews

Author :
ISBN : UOM:39015046259548
Genre : Mathematics
File Size : 40.10 MB
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Category: Mathematics

An Approximate Calculation Of Heat Transfer In Transpired Boundary Layers

Author : Tse-Fou Zien
ISBN : UOM:39015095246768
Genre : Equations of motion
File Size : 90.75 MB
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An approximate method of calculating the surface heat transfer in a transpired boundary layer is presented. The method is based on an idea for refining the momentum integral technique. A semi-infinite, isothermal flat plate with uniform surface mass flux is used to demonstrate the method. The flow is assumed to be laminar. Results are presented for both incompressible and compressible boundary layers, and comparisons are made with numerical solutions or other approximate results. The findings are indicative of the potential of the method for development into an efficient tool for studying boundary-layer flows of a more complex nature. (Author Modified Abstract).
Category: Equations of motion