Titlebook: Mathematical Analysis and the Mathematics of Computation; Werner Römisch,Thomas Zeugmann Textbook 2016 Springer International Publishing S

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Approximative Representation of Functions, solution of differential equations, or even more generally, of operator equations. Further applications comprise machine learning, engineering, the reconstruction of complicated graphs of functions from measurements, and so on.

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978-3-319-82655-4Springer International Publishing Switzerland 2016

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Inner Product Spaces,In this chapter we generalize the Euclidean vector space with its scalar product. The resulting spaces are called inner product spaces, and their general properties are studied. As an important subset we investigate Hilbert spaces, i.e., complete inner product spaces. Then our attention is focused on Fourier series and their properties.

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https://doi.org/10.1007/978-3-319-42755-3Approximation; Differential Calculus; Integral Calculus; Integral Equations; Interpolation; Mathematical

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Metric Spaces,such as open and closed sets, accumulation point, and interior point.We define the convergence of sequences and investigate their major properties. Subsequently, we prove the Banach fixed point theorem. Then the important concept of the compactness of a set is defined and thoroughly studied. We cont