One place you can find a discussion of some of the ideas in the Resume is in my book, Origins of Cauchy's Rigorous Calculus (MIT 1981). There is an article in Historia Mathematica just focusing on the derivative, "The Origins of Cauchy's Theory of the Derivative." Hist. Math. 5, 1978, pp. 379-409. Perhaps these will address some of your questions.
In fact the 1821 Cours d'analyse by Cauchy is more accurately characterized as the source of much of his work on 19th-century analysis, notably the theory of convergence and, in an appendix, a proof of the intermediate-value theorem for continuous functions (which actually assumes uniform continuity). These are also treated in my book. I commend also to you the writings of Umberto Bottazzini and Ivor Grattan-Guinness on this subject.
Judith V. Grabiner Flora Sanborn Pitzer Professor of Mathematics Pitzer College (909) 607-3160