Lecture

Taylor's approximation: Mean Value Theorem, l'Hopital rule, Examples

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In course

MATH-101(en): Analysis I (English)

We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable. ...

Description

This lecture covers the application of the Mean Value Theorem, the l'Hopital rule, and Taylor's approximation formula with examples. It also discusses the derivative and monotone functions, along with the concept of strictly increasing and decreasing functions. The lecture explores the development of functions to the nth order around a point, the uniqueness of Taylor's formula, and the control of error in an approximation. It concludes with the expansion and composition of functions, showcasing the computation of the expansion of a composite function using Taylor's formula.

Instructor

Thomas Mountford

Teaching & PhD Past EPFL PhD Students Damien Gauthier, Samir Brahim Belhaouari, Driss Baraka, Daniel Rodrigues Valesin, Samuel Schöpfer, Kamran Kalbasi, Jacques Saliba, Hao Xue, Keming Chen Past EPFL PhD Students as codirector Guillaume Charles Woessner Courses Analysis I MATH-101(d) Study the fundamental concepts of analysis, and the differential and integral calculus of real-valued functions of one real variable. Markov chains MATH-332 The course follows the text of Norris

Official source

Ontological neighbourhood

Mathematics

Analysis: Calculus

Art

Visual arts: Painting

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