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Course# MATH-105(a): Advanced analysis II

Summary

Etudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables.

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Related courses (232)

Instructors (2)

Related MOOCs (46)

MATH-506: Topology IV.b - cohomology rings

Singular cohomology is defined by dualizing the singular chain complex for spaces. We will study its basic properties, see how it acquires a multiplicative structure and becomes a graded commutative a

MATH-101(g): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable.

MATH-106(f): Analysis II

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables.

MATH-111(e): Linear Algebra

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et ses applications.

MATH-105(b): Advanced analysis II

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs variables.

Lectures in this course (101)

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Un MOOC francophone d'algèbre linéaire accessible à tous, enseigné de manière rigoureuse et ne nécessitant aucun prérequis.

Convergence of Integrals: Criteria and Examples

Explores the convergence of integrals through criteria and examples, emphasizing the importance of understanding both sides' convergence.

Cantor-Heine Theorem

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Advanced Analysis II: Multi-Index and Taylor Formula

Explores multi-index, Taylor formula, partial derivatives, and remainders estimation in Taylor series.

Uniform Continuity: Definitions and Examples

Explores uniform continuity in functions, covering definitions, examples, and properties.

Advanced analysis II

Covers advanced topics in analysis, including examples of sets, volume, Fubini's theorem, and integrability.

Related concepts (661)

Lagrange multiplier

In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied.

Rotation

Rotation or rotational motion is the circular movement of an object around a central line, known as axis of rotation. A plane figure can rotate in either a clockwise or counterclockwise sense around a perpendicular axis intersecting anywhere inside or outside the figure at a center of rotation. A solid figure has an infinite number of possible axes and angles of rotation, including chaotic rotation (between arbitrary orientations), in contrast to rotation around a axis.

Definition

A definition is a statement of the meaning of a term (a word, phrase, or other set of symbols). Definitions can be classified into two large categories: intensional definitions (which try to give the sense of a term), and extensional definitions (which try to list the objects that a term describes). Another important category of definitions is the class of ostensive definitions, which convey the meaning of a term by pointing out examples. A term may have many different senses and multiple meanings, and thus require multiple definitions.

Divergence

In vector calculus, divergence is a vector operator that operates on a vector field, producing a scalar field giving the quantity of the vector field's source at each point. More technically, the divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region.

World Wide Web

The World Wide Web (WWW), commonly known as the Web, is an information system enabling information to be shared over the Internet through simplified ways meant to appeal to users beyond IT specialists and hobbyists, as well as documents and other web resources to be accessed over the Internet according to specific rules, the Hypertext Transfer Protocol (HTTP). Documents and downloadable media are made available to the network through web servers and can be accessed by programs such as web browsers.