Описание: This graduate-level text offers a concise butwide-ranging introduction to methods of approximating continuous functions by functions depending only on a finite number of parameters. It places particular emphasis on approximation by polynomials andnot only discusses the theoretical underpinnings of many common algorithms but also demonstrates their practical applications. 1969 edition."
Автор: Zienkiewicz O. Название: Finite Elements and Approximation ISBN: 0486453014 ISBN-13(EAN): 9780486453019 Издательство: Dover Рейтинг: Цена: 1668 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Davis, Philip J. Название: Interpolation and Approximation ISBN: 0486624951 ISBN-13(EAN): 9780486624952 Издательство: Dover Рейтинг: Цена: 1919 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Interpolation and approximation offer important applications in computer science and elsewhere. This intermediate-level survey by a noted authority abounds in useful examples of related subjects and has been praised for its level of clarity and reliance on well-presented and useful examples. A brief introductory chapter presents helpful definitions and theorems. Subsequent chapters explore interpolation, remainder theory, convergence theorems for interpolatory processes, and some problems of infinite interpolation. Additional topics include uniform and best approximation, least square approximation, Hilbert space, orthogonal polynomials, the theory of closure and completeness, expansion theorems for orthogonal functions, degree of approximation, and approximation of linear functionals. A familiarity with real and complex variable theory and linear algebra is assumed. 1963 edition.
Описание: A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis. 1980 edition.
Автор: Zienkiewicz, O. Название: Finite Elements and Approximation ISBN: 0486788695 ISBN-13(EAN): 9780486788692 Издательство: Dover Цена: 3340 р. Наличие на складе: Поставка под заказ.
Описание: A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.
Автор: Niven Ivan Название: Diophantine Approximations ISBN: 0486462676 ISBN-13(EAN): 9780486462677 Издательство: Dover Рейтинг: Цена: 665 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This self-contained treatment covers basic results on homogeneous approximation of real numbers; the analogue for complex numbers; basic results for nonhomogeneous approximation in the real case; the analogue for complex numbers; and fundamental properties of the multiples of an irrational number, for both fractional and integral parts. 1963 edition.
Описание: Distribution theory, a relatively recent mathematical approach to classical Fourier analysis, not only opened up new areas of research but also helped promote the development of such mathematical disciplines as ordinary and partial differential equations, operational calculus, transformation theory, and functional analysis. This text was one of the first to give a clear explanation of distribution theory; it combines the theory effectively with extensive practical applications to science and engineering problems. Based on a graduate course given at the State University of New York at Stony Brook, this book has two objectives: to provide a comparatively elementary introduction to distribution theory and to describe the generalized Fourier and Laplace transformations and their applications to integrodifferential equations, difference equations, and passive systems. After an introductory chapter defining distributions and the operations that apply to them, Chapter 2 considers the calculus of distributions, especially limits, differentiation, integrations, and the interchange of limiting processes. Some deeper properties of distributions, such as their local character as derivatives of continuous functions, are given in Chapter 3. Chapter 4 introduces the distributions of slow growth, which arise naturally in the generalization of the Fourier transformation. Chapters 5 and 6 cover the convolution process and its use in representing differential and difference equations. The distributional Fourier and Laplace transformations are developed in Chapters 7 and 8, and the latter transformation is applied in Chapter 9 to obtain an operational calculus for the solution of differential and difference equations of the initial-condition type. Some of the previous theory is applied in Chapter 10 to a discussion of the fundamental properties of certain physical systems, while Chapter 11 ends the book with a consideration of periodic distributions. Suitable for a graduate course for engineering and science students or for a senior-level undergraduate course for mathematics majors, this book presumes a knowledge of advanced calculus and the standard theorems on the interchange of limit processes. A broad spectrum of problems has been included to satisfy the diverse needs of various types of students.
Автор: Bellman, Richard Название: A Brief Introduction to Theta Functions ISBN: 0486492958 ISBN-13(EAN): 9780486492957 Издательство: Dover Рейтинг: Цена: 1166 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Brief but intriguing, this monograph on the theory of elliptic functions was written by one of America's most prominent and widely read mathematicians. Richard Bellman encompasses a wealth of material in a succession of short chapters, spotlighting high points of the fundamental regions of elliptic functions and illustrating powerful and versatile analytic methods. Suitable for advanced undergraduates and graduate students in mathematics, this introductory treatment is largely self-contained. Topics include Fourier series, sufficient conditions, the Laplace transform, results of Doetsch and Kober-Erdelyi, Gaussian sums, and Euler's formulas and functional equations. Additional subjects include partial fractions, mock theta functions, Hermite's method, convergence proof, elementary functional relations, multidimensional Poisson summation formula, the modular transformation, and many other areas.
Автор: Bowman Frank Название: Introduction to Bessel Functions ISBN: 0486604624 ISBN-13(EAN): 9780486604626 Издательство: Dover Рейтинг: Цена: 832 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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