## ＜電子ブック＞Topology, Calculus and Approximation

責任表示 by Vilmos Komornik Komornik, Vilmos SpringerLink (Online service) English (英語) Springer London Imprint: Springer 2017- London, United Kingdom シリーズ Springer Undergraduate Mathematics Series Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotte..., classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure and applied mathematics, as well as physics and engineering should find this textbook useful. Only basic results of one-variable calculus and linear algebra are used, and simple yet pertinent examples and exercises illustrate the usefulness of most theorems. Many of these examples are new or difficult to locate in the literature, and so the original sources of most notions and results are given to help readers understand the development of the field.続きを見る Part 1. TopologyChapter 1. Metric spacesChapter 2. Topological spacesChapter 3. Normed spacesPart 2. Differential calculusChapter 4. The DerivativeChapter 5. Higher-order derivativesChapter 6. Ordinary differential equationsChapter 7. Implicit functions and their applicationsPart 3. Approximation methodsChapter 8. InterpolationChapter 9. Orthogonal polynomialsChapter 10. Numerical integrationChapter 11. Finding rootsChapter 12. Numerical solution of differential equations.続きを見る http://hdl.handle.net/2324/1001627818 Full text available from SpringerLINK ebooks - Mathematics and Statistics (2017)Full text available from SpringerLink ebooks - Mathematics and Statistics without Lecture Notes (2017)

### 詳細

レコードID 1810844 QA372 515.352 Mathematics. Approximation theory. Differential equations. Numerical analysis. Mathematics. Ordinary Differential Equations. Numerical Analysis. Approximations and Expansions. ssj0001820394 9781447173151[1447173155](print) 9781447173168[1447173163] 2017.07.11 2017.12.27