Steffens The History of Approximation Theory
2006
ISBN: 978-0-8176-4475-8
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
From Euler to Bernstein
E-Book, Englisch, 219 Seiten, eBook
ISBN: 978-0-8176-4475-8
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark
* Exciting exposition integrates history, philosophy, and mathematics
* Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development
* Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation
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Research
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Weitere Infos & Material
Dedication Foreword Preface Introduction Forerunners 1.1 Euler’s Analysis of Delisle’s Map 1.2 Laplace’s Approximation of Earth’s Surface Pafnuti Lvovich Chebyshev 2.1 Chebyshev’s Curriculum Vitae 2.2 Stimuli for the Development of a Theory 2.3 First Theoretical Approaches 2.4 First Theoretical Compositions 2.5 Theory of Orthogonal Polynomials 2.6 Other Contributions of P. L. Chebyshev 2.7 Chebyshev - Euler of the 18th Century? The Saint Petersburg Mathematical School 3.1 Aleksandr Nikolaevich Korkin 3.2 Egor Ivanovich Zolotarev 3.3 Andrey and Vladimir Andreevich Markov 3.4 Julian Karol Sochocki 3.5 Konstantin Aleksandrovich Posse 3.6 A. A. Markov’s Lectures 3.7 Résumé Development Outside Russia 4.1 The Mediator: Felix Klein 4.2 Blichfeldt’s Note 4.3 Kirchberger’s Thesis 4.4 Other Non-Quantitative Contributions 4.5 On Convergence and Series Expansions 4.6 Fejér and Runge 4.7 Quantitative Approximation Theory 4.8 Jackson’s Thesis 4.9 A Note About Göttingen’s Role Constructive Function Theory: Kharkiv 5.1 Antony-Bonifatsi Pavlovich Psheborski 5.2 A Short Biography of Sergey Natanovich Bernstein 5.3 First Contributions to Approximation Theory 5.4 Constructive Function Theory as the Development of Chebyshev’s Ideas Biographies... A.1 Matvey Aleksandrovich Tikhomandritski A.2 Nikolaj Yakovlevich Sonin A.3 Aleksandr Vasilevich Vasilev A.4 Ivan Lvovich Ptashitski A.5 Dmitry Fedorovich Selivanov A.6 Aleksandr Mikhaylovich Lyapunov A.7 Ivan Ivanovich Ivanov A.8 Dmitry Alksandrovich Grave A.9 Georgi Feodosievich Voronoy Explanations B.1 Russian Academic Degrees References Index List of Figures List of Tables
