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Course# MATH-106(en): Analysis II (English)

Summary

The course studies fundamental concepts of analysis and the calculus of functions of several variables.

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Instructor

Lectures in this course (62)

Related MOOCs (30)

Related courses (110)

Related concepts (261)

Analysis 2: Properties and Integrability

Covers properties of sets of measure zero, integrability criteria, and Fubini's theorem.

Change of Variables Formula

Explores the change of variables formula for rewriting functions in new coordinate systems.

Multivariable Integral Calculus

Covers multivariable integral calculus, including rectangular cuboids, subdivisions, Douboux sums, Fubini's Theorem, and integration over bounded sets.

Implicit Examples: Hyperplane and Stationary Points

Illustrates finding hyperplanes for surfaces and determining stationary points.

Analysis 2: Horizontal Domains and Integrals

Explores horizontal domains in R², integrals, and center of mass calculations in different mass distributions.

Learn to optimize on smooth, nonlinear spaces: Join us to build your foundations (starting at "what is a manifold?") and confidently implement your first algorithm (Riemannian gradient descent).

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.

MATH-106(f): Analysis II

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

MATH-101(g): Analysis I

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

MATH-105(b): Advanced analysis II

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

MATH-106(e): Analysis II

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

MATH-105(a): Advanced analysis II

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

Notepad++

Notepad++ is a free and open-source text and source code editor for use with Microsoft Windows. It supports tabbed editing, which allows working with multiple open files in a single window. The product's name comes from the C postfix increment operator; it is sometimes referred to as npp or NPP. Notepad++ is distributed as free software. At first, the project was hosted on SourceForge.net, from where it was downloaded over 28 million times and twice won the SourceForge Community Choice Award for Best Developer Tool.

Source-code editor

A source-code editor is a text editor program designed specifically for editing source code of computer programs. It may be a standalone application or it may be built into an integrated development environment (IDE). Source-code editors have characteristics specifically designed to simplify and speed up typing of source code, such as syntax highlighting, indentation, autocomplete and brace matching functionality. These editors also provide a convenient way to run a compiler, interpreter, debugger, or other program relevant for the software-development process.

Text editor

A text editor is a type of computer program that edits plain text. Such programs are sometimes known as "notepad" software (e.g. Windows Notepad). Text editors are provided with operating systems and software development packages, and can be used to change files such as s, documentation files and programming language source code. Plain text and Rich text There are important differences between plain text (created and edited by text editors) and rich text (such as that created by word processors or desktop publishing software).

Euclidean space

Euclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes.

Normed vector space

In mathematics, a normed vector space or normed space is a vector space over the real or complex numbers on which a norm is defined. A norm is a generalization of the intuitive notion of "length" in the physical world. If is a vector space over , where is a field equal to or to , then a norm on is a map , typically denoted by , satisfying the following four axioms: Non-negativity: for every ,. Positive definiteness: for every , if and only if is the zero vector.