**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Numerical Integration

Description

This lecture covers numerical integration, including a summary of key concepts, exercises, and feedback on course variations. The instructor explains the composite quadrature formula, the importance of changing variables, and the efficiency of Simpson's rule. Students are guided through the process of transitioning from the interval [-1, 1] to a general interval, emphasizing the significance of linear transformations. The lecture also addresses the challenges and strategies for exam-like exercises, clarifying the use of computers for accurate integrations. The instructor aims to enhance clarity and organization in course materials and evaluations, seeking to reduce stress and improve understanding for students.

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related concepts (38)

In course

Instructors (2)

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

Integral

In mathematics, an integral is the continuous analog of a sum, which is used to calculate areas, volumes, and their generalizations. Integration, the process of computing an integral, is one of the two fundamental operations of calculus, the other being differentiation. Integration started as a method to solve problems in mathematics and physics, such as finding the area under a curve, or determining displacement from velocity. Today integration is used in a wide variety of scientific fields.

Integrator

An integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an important part of many engineering and scientific applications. Mechanical integrators are the oldest type and are still used for metering water flow or electrical power. Electronic analogue integrators are the basis of analog computers and charge amplifiers.

Digital twin

A digital twin is a digital representation of an intended or actual real-world physical product, system, or process (a physical twin) that serves as the effectively indistinguishable digital counterpart of it for practical purposes, such as simulation, integration, testing, monitoring, and maintenance. The digital twin has been intended from its initial introduction to be the underlying premise for Product Lifecycle Management and exists throughout the entire lifecycle (create, build, operate/support, and dispose) of the physical entity it represents.

Perovskite solar cell

A perovskite solar cell (PSC) is a type of solar cell that includes a perovskite-structured compound, most commonly a hybrid organic–inorganic lead or tin halide-based material as the light-harvesting active layer. Perovskite materials, such as methylammonium lead halides and all-inorganic cesium lead halide, are cheap to produce and simple to manufacture. Solar-cell efficiencies of laboratory-scale devices using these materials have increased from 3.8% in 2009 to 25.

MATH-251(c): Numerical analysis

Le cours présente des méthodes numériques pour la résolution de problèmes mathématiques comme des systèmes d'équations linéaires ou non linéaires, approximation de fonctions, intégration et dérivation

Related lectures (67)

Gauss-Legendre Quadrature Formulas

Explores Gauss-Legendre quadrature formulas using Legendre polynomials for accurate function approximation.

Numerical integration: continued

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

Numerical Analysis: Quadrature FormulasMATH-251(c): Numerical analysis

Covers numerical integration, focusing on quadrature formulas and interpolation polynomials.

Interpolatory Quadrature Formulas

Covers interpolatory quadrature formulas for approximating definite integrals using polynomials and discusses the uniqueness of solutions and practical applications in numerical integration.

Numerical Integration: Simpson Quadrature RuleMATH-250: Numerical analysis

Covers the Simpson quadrature rule for numerical integration, explaining the method to compute integrals using interpolation nodes and weights.