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Complex analysis --- 517.51 --- Functions of a real variable. Real functions --- Analytic functions. --- Monotonic functions. --- Analytic continuation. --- 517.51 Functions of a real variable. Real functions

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517.51 --- Mathematical analysis --- 517.1 Mathematical analysis --- 517.51 Functions of a real variable. Real functions --- Functions of a real variable. Real functions --- 517.1. --- 517.1

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Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering; algebraic techniques functions and graphs an informal discussion of limits techniques of differentiation and integration Maclaurin and Taylor expansions geometrical applications 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. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web. .

Functions of real variables. --- Real variables --- Functions of complex variables --- Mathematics. --- Real Functions. --- Math --- Science

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Inequalities (Mathematics) --- Congresses --- 517.51 --- -Processes, Infinite --- Functions of a real variable. Real functions --- -Functions of a real variable. Real functions --- 517.51 Functions of a real variable. Real functions --- -517.51 Functions of a real variable. Real functions --- Processes, Infinite --- Inequalities (Mathematics) - Congresses

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Fonctions d'une variable réelle Les Éléments de mathématique de Nicolas BOURBAKI ont pour objet une présentation rigoureuse, systématique et sans prérequis des mathématiques depuis leurs fondements. Ce Livre est le quatrième du traité ; il est consacré aux bases de l’analyse réelle. Il comprend les chapitres : Dérivées ; Primitives et intégrales ; Fonctions élémentaires ; Équations différentielles ; Étude locale des fonctions ; Développements tayloriens généralisés. Formule sommatoire d’Euler-Maclaurin ; La function gamma. Il contient également des notes historiques. Ce volume est une réimpression de l’édition de 1976.

Functions of real variables. --- Real variables --- Functions of complex variables --- Mathematics. --- Real Functions. --- Math --- Science