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Titlebook: Scientific Computing -An Introduction using Maple and MATLAB; Walter Gander,Martin J. Gander,Felix Kwok Textbook 2014 Springer Internation

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发表于 2025-3-21 17:50:33 | 显示全部楼层 |阅读模式
书目名称Scientific Computing -An Introduction using Maple and MATLAB
编辑Walter Gander,Martin J. Gander,Felix Kwok
视频video
概述Equal emphasis on theory, symbolic computation and numerical algorithms.Numerous complete, ready-to-run programs in Matlab and Maple, complete with many examples.In-depth treatment of many advanced to
丛书名称Texts in Computational Science and Engineering
图书封面Titlebook: Scientific Computing -An Introduction using Maple and MATLAB;  Walter Gander,Martin J. Gander,Felix Kwok Textbook 2014 Springer Internation
描述Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.
出版日期Textbook 2014
关键词numerical mathematics; scientific computing
版次1
doihttps://doi.org/10.1007/978-3-319-04325-8
isbn_softcover978-3-319-38158-9
isbn_ebook978-3-319-04325-8Series ISSN 1611-0994 Series E-ISSN 2197-179X
issn_series 1611-0994
copyrightSpringer International Publishing Switzerland 2014
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978-3-319-38158-9Springer International Publishing Switzerland 2014
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Linear Systems of Equations,physics and engineering have been modeled by linear differential equations, since they are much easier to analyze than nonlinear ones. In addition, even when the model is nonlinear, the problem is often solved iteratively as a sequence of linear problems, e.g., by Newton’s method (Chapter .).
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Interpolation,rt this chapter with several introductory examples in Section 4.1, through which we explain the interpolation principle. The most common interpolation technique is to use polynomials, and we show in Section 4.2 four classical techniques: using monomials, Lagrange polynomials, Newton polynomials, and orthogonal polynomials.
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Differentiation, subject to errors (see quote above). They appear however also in other con- texts, and form an important subclass of more general optimization problems, see Chapter .. After several typical examples of least squares problems, we start in Section 6.2 with the linear least squares problem and the natural solution given by the normal equations.
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Numerical Ordinary Differential Equations,roblems, namely ordinary differential equations, for which the field has reached a certain maturity. This is much less so for partial differential equa tions, for which the theory about existence of solutions is also much less complete.
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