Lecture

Fresnel Integrals: Curvilinear Integrals in R^2

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In course

MATH-201: Analysis III

Calcul différentiel et intégral. Eléments d'analyse complexe. ...

Description

This lecture covers the concept of Fresnel integrals through curvilinear integrals in R^2, exploring the calculations of cos(x²-y) and sin(x) functions, and their applications in various mathematical contexts.

Instructors (2)

Marco Picasso

Expertise Computational Science and Engineering Mission I am teaching analysis and numerical analysis for engineers and mathematicians at bachelor and master levels.My research pertains to the numerical simulation of complex physical systems with partial differential equations.Here is some bibliometry: Google Scholar, Research Gate, Orcid, here is my most recent CV. Ongoing research projects: - Numerical simulation of aluminium electrolysis, collaboration with RioTinto LRF lab, Ycoorsystems SA and Jacques

Joachim Stubbe

Official source

Related concepts (32)

Mathematical economics

Mathematical economics is the application of mathematical methods to represent theories and analyze problems in economics. Often, these applied methods are beyond simple geometry, and may include differential and integral calculus, difference and differential equations, matrix algebra, mathematical programming, or other computational methods. Proponents of this approach claim that it allows the formulation of theoretical relationships with rigor, generality, and simplicity.

Fresnel integral

The Fresnel integrals S(x) and C(x) are two transcendental functions named after Augustin-Jean Fresnel that are used in optics and are closely related to the error function (erf). They arise in the description of near-field Fresnel diffraction phenomena and are defined through the following integral representations: The simultaneous parametric plot of S(x) and C(x) is the Euler spiral (also known as the Cornu spiral or clothoid).

Fresnel diffraction

In optics, the Fresnel diffraction equation for near-field diffraction is an approximation of the Kirchhoff–Fresnel diffraction that can be applied to the propagation of waves in the near field. It is used to calculate the diffraction pattern created by waves passing through an aperture or around an object, when viewed from relatively close to the object. In contrast the diffraction pattern in the far field region is given by the Fraunhofer diffraction equation. The near field can be specified by the Fresnel number, F, of the optical arrangement.

Trigonometry

Trigonometry () is a branch of mathematics concerned with relationships between angles and ratios of lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation.

Mathematical analysis

Analysis is the branch of mathematics dealing with continuous functions, limits, and related theories, such as differentiation, integration, measure, infinite sequences, series, and analytic functions. These theories are usually studied in the context of real and complex numbers and functions. Analysis evolved from calculus, which involves the elementary concepts and techniques of analysis. Analysis may be distinguished from geometry; however, it can be applied to any space of mathematical objects that has a definition of nearness (a topological space) or specific distances between objects (a metric space).

Related lectures (64)

Exemples à connaître MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)MOOC: Analysis I

Covers various examples related to mathematical functions, including derivatives and integrals.

Mathematical Functions

Covers mathematical functions, including limits, derivatives, integrals, and trigonometric functions.

Integration Techniques: Part 2

Explores integration techniques, including indefinite integrals and variable changes, through trigonometric functions.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Derivatives of Trigonometric Functions MOOC: Trigonometric, Logarithmic and Exponential Functions