Analyse II. Calcul différentiel et équations différentielles. (Analysis II. Differential calculus and differential equations). Nouvelle éd. corrigée. Nouvelle éd. corrigée. (Analyse II. Calcul différentiel et équations différentielles.) (French) Zbl 0920.00001

Schwartz, Laurent

Collection Enseignement des Sciences. 43. Paris: Hermann. 436 p. (1997).

The author’s famous “Cours d’analyse” was first published in 1967. This is the second volume of a completely revised, 1997 edition. The first volume of this new edition was previoused published in 1991 (see Zbl 0872.54001). This volume includes Chapter III (Differential Calculus) and Chapter IV (Differential Equations). The book ends with a useful Errata.
Contents: Chapter III. Differential Calculus: \(\S 1\) Affine spaces; \(\S 2\) Functions of one real variable; \(\S 3\) The derivative of a map; \(\S 4\) Chain rule and change of variable; \(\S 5\) Mean-value theorems; \(\S 6\) Higher derivatives; \(\S 7\) Taylor formula; \(\S 8\) Implicit functions; \(\S 9\) Manifolds; \(\S 10\) Constrained maxima and minima; \(\S 11\) Variational problems.
Chapter IV. Differential Equations: \(\S 1\) Existence and unicity of the solution (a particular case); \(\S 2\) Existence and unicity of the solution (the general case); \(\S 3\) Linear differential equations; \(\S 4\) Linear differential equations with constant coefficients.

Reviewer: C.Badea (Villeneuve d’Ascq)

MSC:

00A05	Mathematics in general
26-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
49-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
34-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to ordinary differential equations

Keywords:

textbook; calculus; differential equations

Citations:

Zbl 0920.00002; Zbl 0920.00003; Zbl 0872.54001