Analysis I

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Lectures in this MOOC (216)

Integration by Recurrence MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Explores integration by recurrence method with examples of square roots and polynomials.

Mathematical Induction: Principle and Example MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Introduces the principle of mathematical induction through an example.

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.

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

Explains the inverse function identity and provides examples with ln(x), sin(x), and cos(x).

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.

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

Covers the polar form of complex numbers, emphasizing the importance of the argument.

The Mean Value Theorem MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the Mean Value Theorem for integrals and its applications.

Hyperbolic Functions: sinh(x) and cosh(x)MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Explores the properties of sinh(x) and cosh(x) functions and their symmetry.

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.

Non existence de la limite MOOC: Analysis I MOOC: Analysis I (part 4) : Limit of a function, continuous functions

Demonstrates the non-existence of a limit using sine functions and specific sequences.

Integration by Change of Variables MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers integration by change of variables and the derivation in chain rule.

Bijective Functions MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers bijective functions, establishing one-to-one correspondences between sets and the importance of reducing domain and codomain for injectivity and surjectivity.

Integral: Motivation MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the motivation behind indefinite integrals and the non-injectivity of the derivative operator.

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

Showcases examples of complex numbers in polar form and their operations.

Continuous Functions on Closed Interval MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explores continuous functions on closed intervals, emphasizing the importance of understanding definitions for continuity.

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.

Surjectivity of Derivative Application MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the surjectivity of the derivative application for continuous functions on closed intervals.

Definition of Differentiable Functions MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Covers the definition of differentiable functions and explores the representation of the remainder in derivatives.

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.

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