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Analysis I (part 6) : Study of functions, limited developments

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Lectures in this MOOC (44)

Nth Derivative MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores obtaining n-th derivatives through a recursive process and the regularity of functions defined by power series.

Taylor Series of a Function MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores the Taylor series of a function and its significance in mathematical analysis.

Demonstration of Rolle's Theorem MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Demonstrates how to use a specific function to prove Rolle's Theorem.

Functions of Class Cn: Theorem 2 MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Focuses on Theorem 2 for functions of class Cn and their Taylor expansion around a.

Series entières: Définitions MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the definition of a power series and its convergence based on the choice of parameter x.

Points 7-9 du procédé MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the analysis of local and global extrema, concavity, and inflection points.

Taylor Polynomials and Remainders MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores Taylor polynomials, remainders, and various function expansions around a point.

Demonstration of BH Theorem MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the demonstration of the BH theorem and the continuity of functions.

Functions of Class Ck: Terminology and Definitions MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the terminology and definitions of functions of class Ck on real number intervals.

Bernoulli's Hospital Rule MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the statement of the Bernoulli's Hospital Rule and its application.

Functions n+1 Derivatives MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the concept of functions being n+1 times differentiable and the Taylor formula.

Applications: Trigonometric Functions MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores applications of trigonometric functions, focusing on the tangent function and its derivatives.

Inflection Points MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores inflection points in functions, emphasizing the role of the second derivative.

General Case MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores determining local maximums, minimums, and inflection points of functions.

Limit Calculations Applications MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Demonstrates efficient limit calculations using Taylor expansions and basic algebraic operations.

Discussion of Function f MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the discussion of the function f(x) = |2x-1| -x²+1 on a given domain and its continuity, zeros, and derivatives.

Developing Cosine Composition MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Developing Taylor's Theorem MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers Taylor's theorem, power series, and representing functions by their Taylor series.

Derivability and Extrema Analysis MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores derivability at specific points and the analysis of local extrema.

Convexity and Concavity MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the definitions of convexity, concavity, stationary points, and inflection points.

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