الصفحة 1
الصفحة 1
Functions de variable réelle : Théorie élémentaire = Real variable functions : Elementary theory
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This Book is the fourth of the treaty; it is devoted to the basics of real analysis. It includes the chapters: Derivatives; Primitive and integral; Elementary functions; Differential equations ; Local study of functions; Generalized Taylorian developments. Euler-Maclaurin summation formula; The gamma function. It also contains historical notes.
Convex functions and their applications : A contemporary approach ; 2nd ed.
This second edition provides a thorough introduction to contemporary convex function theory with many new results. A large variety of subjects are covered, from the one real variable case to some of the most advanced topics. The new edition includes considerably more material emphasizing the rich applicability of convex analysis to concrete examples. Chapters 4, 5, and 6 are entirely new, covering important topics such as the Hardy-Littlewood-Pólya-Schur theory of majorization, matrix convexity, and the Legendre-Fenchel-Moreau duality theory.
Calculus of one variable
Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis.The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas.
