The History of Approximation Theory From Euler to Bernstein [Paperback]

* 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

Dedication Foreword Preface Introduction Forerunners 1.1 Eulers Analysis of Delisles Map 1.2 Laplaces Approximation of Earths Surface Pafnuti Lvovich Chebyshev 2.1 Chebyshevs 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. Markovs Lectures 3.7 R?sum? Development Outside Russia 4.1 The Mediator: Felix Klein 4.2 Blichfeldts Note 4.3 Kirchbergers Thesis 4.4 Other Non-Quantitative Contributions 4.5 On Convergence and Series Expansions 4.6 Fej?r and Runge 4.7 Quantitative Approximation Theory 4.8 Jacksons Thesis 4.9 A Note About G?ttingens 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 Chebyshevs 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 AlksandrovlĐ