Analysis on the Straight Line - Elon Lages Lima - Class 06/19 - [IMPA Scientific Initiation Program 2011]

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Felipe Albino dos Santos

Published on Sep 16, 2012
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Mathematical induction. Basic properties of real numbers. Limit of a sequence. Series of real numbers. Absolute and conditional convergence. Main tests of series convergence. Notions of topology on the line. Continuous functions; operations. Intermediate value theorem. Weierstrass's theorem on extrema of continuous functions. Uniform continuity. Derivative at a point. Chain rule. Relationship between derivative and growth. Mean value theorem. Convex functions. Integrable functions. Fundamental theorem of calculus. Change of variable. Integration by parts. Mean theorem. Taylor's formula. IMPA publications can be purchased at its headquarters (Estrada Dona Castorina, 110, Jardim Botânico, room 205) or at its Virtual Bookstore, where it is possible to purchase the book Real Analysis - Functions of a Variable - ELON LAGES LIMA for R$ 20.00 (link: http://institucional.impa.br/livros/l...) among other titles.

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