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MOOC

Analysis I

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Lectures in this MOOC (216)

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.

Examples: Complex Numbers MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers

Covers examples related to complex numbers and their properties.

Terminologie conventions MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Covers the terminology and conventions related to the limit of a function and introduces algebraic and transcendental functions.

Series: Definitions MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

Covers the definition of infinite sums (series) of real numbers and their convergence properties, including absolute convergence and the Cauchy criterion.

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.

Demonstration MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Demonstrates a theorem using a specific function to evaluate another, showing inherited properties.

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.

Restriction, Prolongement et Graphe d'une Fonction MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explains the relationship between two functions through restriction and prolongation, emphasizing the importance of defining a function by its graph.

Exponential Function: Change of Variables MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Covers the concept of exponential functions and their change of variables.

Theorem and Explanations MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Covers the theorem of finite increments in derivative functions.

The Fundamental Theorem of Algebra MOOC: Analysis I MOOC: Analysis I (part 2) : Introduction to complex numbers

Covers the fundamental theorem of algebra, explaining how every polynomial has complex roots.

Application to Numerical Series MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the application of numerical series, comparing An, Bu, and Cn.

Cauchy Sequences MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

Explores Cauchy sequences in real numbers, convergence criteria, and limit definitions.

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.

Lower and Upper Sums MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers lower and upper sums for functions on closed intervals and their relation to continuity.

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.

Continuity of Reciprocal Function MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explains the criteria for a strictly monotone function to be injective and the properties of reciprocal functions.

Derivable ↔ Differentiable MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explores the equivalence between being derivable and differentiable functions, with examples like sin(x) at x=0.

Application to Recurrence Defined Sequences MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Covers the application of functions defined by recurrence to sequences and the theorem of the fixed point.

Counter-example: Continuity and Differentiability MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explores a counter-example of a function that is continuous and differentiable on an interval, challenging students to understand limits geometrically.

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