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Course# MATH-202(c): Analysis III

Summary

The course studies the fundamental concepts of vector analysis and Fourier-Laplace analysis with a view to their use in solving multidisciplinary problems in scientific engineering.

Official source

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Related concepts (96)

Related courses (43)

Related MOOCs (32)

Lectures in this course (43)

Mathematical physics

Mathematical physics refers to the development of mathematical methods for application to problems in physics. The Journal of Mathematical Physics defines the field as "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories". An alternative definition would also include those mathematics that are inspired by physics (also known as physical mathematics).

Generalized Stokes theorem

In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. In particular, the fundamental theorem of calculus is the special case where the manifold is a line segment, Green’s theorem and Stokes' theorem are the cases of a surface in or and the divergence theorem is the case of a volume in Hence, the theorem is sometimes referred to as the Fundamental Theorem of Multivariate Calculus.

Wave equation

The (two-way) wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields - as they occur in classical physics - such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics. Single mechanical or electromagnetic waves propagating in a pre-defined direction can also be described with the first-order one-way wave equation, which is much easier to solve and also valid for inhomogeneous media.

Curvilinear coordinates

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be derived from a set of Cartesian coordinates by using a transformation that is locally invertible (a one-to-one map) at each point. This means that one can convert a point given in a Cartesian coordinate system to its curvilinear coordinates and back. The name curvilinear coordinates, coined by the French mathematician Lamé, derives from the fact that the coordinate surfaces of the curvilinear systems are curved.

Fourier series

A Fourier series (ˈfʊrieɪ,_-iər) is an expansion of a periodic function into a sum of trigonometric functions. The Fourier series is an example of a trigonometric series, but not all trigonometric series are Fourier series. By expressing a function as a sum of sines and cosines, many problems involving the function become easier to analyze because trigonometric functions are well understood. For example, Fourier series were first used by Joseph Fourier to find solutions to the heat equation.

MATH-203(c): Analysis III

Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour
résoudre des problèmes pluridisciplinaires d'ingénierie scientifique.

MATH-201: Analysis III

Calcul différentiel et intégral.
Eléments d'analyse complexe.

MATH-203(b): Analysis III

Le cours étudie les concepts fondamentaux de l'analyse vectorielle et l'analyse de Fourier en vue de leur utilisation pour résoudre des problèmes pluridisciplinaires d'ingénierie scientifique.

MATH-101(g): Analysis I

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

PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant l

Trigonometric Functions, Logarithms and Exponentials

Ce cours donne les connaissances fondamentales liées aux fonctions trigonométriques, logarithmiques et exponentielles. La présentation des concepts et des propositions est soutenue par une grande gamm

Trigonometric Functions, Logarithms and Exponentials

Ce cours donne les connaissances fondamentales liées aux fonctions trigonométriques, logarithmiques et exponentielles. La présentation des concepts et des propositions est soutenue par une grande gamm

Analyse I

Le contenu de ce cours correspond à celui du cours d'Analyse I, comme il est enseigné pour les étudiantes et les étudiants de l'EPFL pendant leur premier semestre. Chaque chapitre du cours correspond

Explores curl in 2D vector fields, demonstrating its rotation concept through examples and its application in physics.

Explores curve integrals, emphasizing parameterizations, geometric curves, and Riemann sums.

Explores curve integrals of vector fields, energy calculations, potential functions, and tangential vectors, with a focus on line integrals and domains.

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Covers integrating functions over graph surfaces in vector calculus, emphasizing the interpretation of divergence theorem and special cases of domain between two graphs.