Numerical Integration: Composite Formulas

This lecture covers the concept of numerical integration, focusing on composite formulas like the midpoint and trapezoidal rules. It explains the order of integration formulas based on error, accuracy degree, and estimation methods. The instructor demonstrates the accuracy of integration methods using polynomial examples and provides insights into the composite formulas' precision. The lecture also delves into the calculation of integrals using various composite methods and discusses the accuracy of the Simpson formula. Additionally, it includes exercises on determining the exact values of integrals and evaluating errors in the integration process.

About this result

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 lectures (152)

Related concepts (135)

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

Verlet integration

Verlet integration (vɛʁˈlɛ) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C.

Numerical methods for ordinary differential equations

Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.

Academic degree

An academic degree is a qualification awarded to a student upon successful completion of a course of study in higher education, usually at a college or university. These institutions often offer degrees at various levels, usually divided into undergraduate and postgraduate degrees. The most common undergraduate degree is the bachelor's degree, although some educational systems offer lower level undergraduate degrees such as associate and foundation degrees. Common postgraduate degrees include master's degrees and doctorates.

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.

Bachelor's degree

A bachelor's degree (from Middle Latin baccalaureus) or baccalaureate (from Modern Latin baccalaureatus) is an undergraduate academic degree awarded by colleges and universities upon completion of a course of study lasting three to six years (depending on institution and academic discipline). The two most common bachelor's degrees are the Bachelor of Arts (BA) and the Bachelor of Science (BS or BSc).

Topology of Riemann Surfaces MATH-410: Riemann surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Differential Forms Integration MATH-410: Riemann surfaces

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Graded Ring Structure on Cohomology MATH-506: Topology IV.b - cohomology rings

Explores the associative and commutative properties of the cup product in cohomology, with a focus on graded structures.

Characteristic Polynomials and Similar Matrices MATH-111(e): Linear Algebra

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Cohomology Groups: Hopf Formula MATH-506: Topology IV.b - cohomology rings

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.