Cauchy’s Cours d’analyse: An Annotated TranslationSpringer Science & Business Media, 2010 M01 14 - 412 páginas In 1821, Augustin-Louis Cauchy (1789-1857) published a textbook, the Cours d’analyse, to accompany his course in analysis at the Ecole Polytechnique. It is one of the most influential mathematics books ever written. Not only did Cauchy provide a workable definition of limits and a means to make them the basis of a rigorous theory of calculus, but he also revitalized the idea that all mathematics could be set on such rigorous foundations. Today, the quality of a work of mathematics is judged in part on the quality of its rigor, and this standard is largely due to the transformation brought about by Cauchy and the Cours d’analyse. For this translation, the authors have also added commentary, notes, references, and an index. |
Contenido
2 | |
5 | |
1 On real functions | 16 |
2 On infinitely small and infinitely large quantities and on the continuity of functions Singular values of functions in various particular cases | 21 |
3 On symmetric functions and alternating functions The use of these functions for the solution of equations of the first degree in any number of unk... | 49 |
4 Determination of integer functions when a certain number of particular values are known Applications | 59 |
5 Determination of continuous functions of a single variable that satisfy certain conditions | 71 |
6 On convergent and divergent series Rules for the convergence of series The summation of several convergent series | 84 |
Note I On the theory of positive and negative quantities | 266 |
Note II On formulas that result from the use of the signs or and on the averages among several quantities | 291 |
Note III On the numerical solution of equations | 309 |
Page Concordance of the 1821 and 1897 Editions | 323 |
Note IV On the expansion of the alternating function y x z x z y v x v y v z v u | 351 |
Note V On Lagranges interpolation formula | 355 |
Note VI On figurate numbers | 359 |
Note VII On double series | 367 |
7 On imaginary expressions and their moduli | 117 |
8 On imaginary functions and variables | 159 |
9 On convergent and divergent imaginary series Summation of some convergent imaginary series Notations used to represent imaginary functions th... | 180 |
10 On real or imaginary roots of algebraic equations for which the lefthand side is a rational and integer function of one variable The solution of equ... | 217 |
11 Decomposition of rational fractions | 241 |
12 On recurrent series | 257 |
Note VIII On formulas that are used to convert the sines or cosines of multiples of an arc into polynomials the different terms of which have the asce... | 375 |
Note IX On products composed of an infinite number of factors | 385 |
References | 403 |
407 | |
Otras ediciones - Ver todas
Cauchy’s Cours d’analyse: An Annotated Translation Robert E. Bradley,C. Edward Sandifer Sin vista previa disponible - 2009 |
Cauchy’s Cours d’analyse: An Annotated Translation Robert E. Bradley,C. Edward Sandifer Sin vista previa disponible - 2012 |