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MOOC

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

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Lectures in this MOOC (44)

Demonstrations and Remarks MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers convergence criteria for series, including absolute convergence and specific convergence tests.

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

Explores convergence theorems and the unique radius for series convergence.

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

Covers the study of functions with a focus on asymptotes and includes various examples.

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

Covers the study of functions, focusing on convexity criteria within closed subintervals.

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

Explains the definition and uniqueness of developments limites for continuous functions on open intervals.

Developments Limits: Re-discover MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explains the procedure to find limits of functions and series.

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

Discusses local and global extrema conditions for functions over intervals.

Theorem of Generalized Mean Value: Study of Functions MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores the conditions for continuity and differentiability of functions on a closed interval.

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

Covers the demonstration of Euler's formula and its applications.

Functions defined by entire series MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the concept of functions defined by entire series and their association with functions f(x).

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

Covers analyzing the graph of a function using a nine-point process.

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

Explores using Bernoulli de l'Hospital's theorem to compare functions' asymptotic behavior.

Exemples et contre-exemple MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Discusses even and odd functions, limits, and theorem applications.

Interpretation of Taylor's Formula: An Example MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the interpretation of Taylor's formula through an example, focusing on developing limited series for sin(x) around a=0.

Derivation Term by Term MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Introduces the study of functions defined by power series and emphasizes the importance of separately considering boundary points.

Counter-example of basic condition MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores the basic counter-example of a condition's insufficiency for series representation.

Terminologie: Functions Graph Discussion MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the terminology related to the graph of a function and intervals.

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

Covers the concept of deriving terms and exchanging limits in mathematical calculations.

Geometric Series: Basic Example MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the basic example of a geometric series and its convergence properties.

Remarks and Demonstrations MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers remarks and demonstrations on function continuity and differentiability, focusing on class C functions.

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