Lecture

Integration Basics

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In course

PHYS-101(j): General physics : mechanics

Le but du cours de physique générale est de donner à l'étudiant les notions de base nécessaires à la compréhension des phénomènes physiques. L'objectif est atteint lorsque l'étudiant est capable de prévoir quantitativement les conséquences de ces phénomène ...

Description

This lecture covers the fundamentals of integration, including techniques and applications. Topics include definite integrals, antiderivatives, and the fundamental theorem of calculus. The instructor discusses various methods for solving integration problems.

Instructors (2)

Jean-Paul Richard Kneib

Expertise Cosmology, Gravitational Lensing, Redshift Survey, First Galaxies, Cluster of Galaxies, Fiber-positioner robotic system, Radio Astronomy, Space Sustainibility Current work

Former Principal investigator of the SDSS-IV eBOSS project. This is an international project assembling more than 150 participants located mainly in Europe, USA and China. This project will observe 1.5 million galaxy and quasars over 2014-2020 to accurately measure the expansion history of the Universe. * Member of the DESI co

Yves Revaz

Yves Revaz is a scientist at LASTRO/EPFL. After successful studies in physics at EPFL, he accomplished his PhD entitled: "Dynamics of external regions of spiral galaxies and constraints on the dark matter", at the Geneva Observatory in the galactic dynamics group of Prof. D. Pfenniger. He then moved to the Paris Observatory to work at the LERMA (Laboratory for Studies of Radiation and Matter in Astrophysics) under the supervision of Prof. F. Combes on the understanding of cooling flows in galaxy clusters. He joined LASTRO at EPFL in 2007, where, in collaboration with Pascale Jablonka, he developed a new TreePM/SPH chemo-dynamical code called GEAR, designed to study the chemical evolution of galaxies. His current main research focus on the evolution of dwarf spheroidal galaxies and their link with the cosmology. Yves Revaz is also the author of pNbody, a parallelized python toolbox designed to manipulate large N-body systems.

Official source

Related concepts (31)

Antiderivative

In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite operation is called differentiation, which is the process of finding a derivative. Antiderivatives are often denoted by capital Roman letters such as F and G.

Fundamental theorem of calculus

The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). The two operations are inverses of each other apart from a constant value which depends on where one starts to compute area.

Data integration

Data integration involves combining data residing in different sources and providing users with a unified view of them. This process becomes significant in a variety of situations, which include both commercial (such as when two similar companies need to merge their databases) and scientific (combining research results from different bioinformatics repositories, for example) domains. Data integration appears with increasing frequency as the volume (that is, big data) and the need to share existing data explodes.

Semantic integration

Semantic integration is the process of interrelating information from diverse sources, for example calendars and to do lists, email archives, presence information (physical, psychological, and social), documents of all sorts, contacts (including social graphs), search results, and advertising and marketing relevance derived from them. In this regard, semantics focuses on the organization of and action upon information by acting as an intermediary between heterogeneous data sources, which may conflict not only by structure but also context or value.

Nonelementary integral

In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field operations). A theorem by Liouville in 1835 provided the first proof that nonelementary antiderivatives exist. This theorem also provides a basis for the Risch algorithm for determining (with difficulty) which elementary functions have elementary antiderivatives.

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