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Titlebook: Methods in Approximation; Techniques for Mathe Richard E. Bellman,Robert S. Roth Book 1986 D. Reidel Publishing Company, Dordrecht, Holland

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书目名称Methods in Approximation
副标题Techniques for Mathe
编辑Richard E. Bellman,Robert S. Roth
视频video
丛书名称Mathematics and Its Applications
图书封面Titlebook: Methods in Approximation; Techniques for Mathe Richard E. Bellman,Robert S. Roth Book 1986 D. Reidel Publishing Company, Dordrecht, Holland
描述Approach your problems from the right end It isn‘t that they can‘t see the solution. It is and begin with the answers. Then one day, that they can‘t see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father ‘The Hermit Clad in Crane Feathers‘ in R. Brown ‘The point of a Pin‘. van Gulik‘s The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non­ trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are
出版日期Book 1986
关键词continuous function; differential equation; function space; maximum; orthogonal polynomials
版次1
doihttps://doi.org/10.1007/978-94-009-4600-2
isbn_softcover978-94-010-8544-1
isbn_ebook978-94-009-4600-2
copyrightD. Reidel Publishing Company, Dordrecht, Holland 1986
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Basic Concepts,A successful approximation has the following three properties:
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Polynomial Approximation,In this chapter we shall consider polynomial approximation in its most simple form. As in the last chapter we shall restrict ourselves, for convenience, to the closed interval (0,1), and we will let f(x) be a real valued continuous function defined in the interval.
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Differential Approximation,In the last chapter we considered the technique of quasilinearization for fitting a known function f(x) to a differential equation by determining the initial conditions and system parameters associated with the chosen differential equation. This was done by numerical methods.
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Differential Quadrature,In this chapter we wish to explore yet another application of approximation methods, the numerical solution of nonlinear partial differential equations. In many cases all that is desired is a moderately accurate solution at a few points which can be computed rapidly.
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Exponential Approximation,A problem common to many fields is that of determining the parameters . where u(t) is known.
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