The Mathematics of Sonya KovalevskayaThis book is the result of a decision taken in 1980 to begin studying the history of mathematics in the nineteenth century. I hoped by doing it to learn some thing of value about Kovalevskaya herself and about the mathematical world she inhabited. Having been trained as a mathematician, I also hoped to learn something about the proper approach to the history of the subject. The decision to begin the study with Kovalevskaya, apart from the intrinsic interest of Kovalevskaya herself, was primarily based upon the fact that the writing on her in English had been done by people who were interested in sociological and psychological aspects of her life. None of these writings discussed her mathematical work in much detail. This omission seemed to me a serious one in biographical studies of a woman whose primary significance was her mathematical work. In regard to both the content of nineteenth century mathematics and the nature of the history of mathematics I learned a great deal from writing this book. The attempt to put Kovalevskaya's work in historical context involved reading dozens of significant papers by great mathematicians. In many cases, I fear, the purport of these papers is better known to many of my readers than to me. If I persevered despite misgivings, my excuse is that this book is, after all, primarily about Kovalevskaya. If specialists in Euler, Cauchy, etc. |
Contents
3 | |
1 | 9 |
1 | 15 |
Partial Differential Equations | 22 |
4 | 28 |
7 | 34 |
The Shape of Saturns Rings | 66 |
18751891 | 84 |
The Lamé Equations | 119 |
1 | 137 |
Bruns Theorem | 165 |
The Method of Majorants | 185 |
Weierstrass Formula | 201 |
209 | |
226 | |
Other editions - View all
Common terms and phrases
Abelian functions Abelian integrals algebraic analytic function angles Aniuta applied axes axis Berlin Cauchy Cauchy-Kovalevskaya theorem Cauchy's chapter coefficients completely complex numbers convergence coordinates denoted derivatives discussion dissertation elliptic functions elliptic integrals Euler equations expressed fact formula given Hermite hyperelliptic hyperelliptic integrals interest inverse functions inversion problem Jacobi inversion problem Klein Koblitz Kochina Kovalevskaya Kovalevskaya's paper Kovalevsky Lagrange Lamé Lamé's Laplace Legendre letter linear mathe mathematicians mathematics memoir method Mittag-Leffler motion multivalued function obtained Paris partial differential equations physical plane polynomial power series published rational function refraction result Riemann surface rigid body rotation Russian S. V. Kovalevskaya satisfy Saturn showed single-valued solution solve Sonya Stockholm t₁ theorem theory theta functions transformation u₁ v₁ values variables Vasily velocity Vladimir wave surface Weierstrass Werke wrote ди ду дх მა