Numerical integrationIn 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.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Numerical methods for ordinary differential equationsNumerical 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.
Verlet integrationVerlet 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.
Symplectic integratorIn mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, accelerator physics, plasma physics, quantum physics, and celestial mechanics. Symplectic integrators are designed for the numerical solution of Hamilton's equations, which read where denotes the position coordinates, the momentum coordinates, and is the Hamiltonian.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
Notebook for Anna Magdalena BachThe title Notebook for Anna Magdalena Bach (Notenbüchlein für Anna Magdalena Bach) refers to either of two manuscript notebooks that the German Baroque composer Johann Sebastian Bach presented to his second wife, Anna Magdalena. Keyboard music (minuets, rondeaux, polonaises, chorales, sonatas, preludes, musettes, marches, gavottes) makes up most of both notebooks, and a few pieces for voice (songs, and arias) are included. The Notebooks provide a glimpse into the domestic music of the 18th century and the musical tastes of the Bach family.
ISO week dateThe ISO week date system is effectively a leap week calendar system that is part of the ISO 8601 date and time standard issued by the International Organization for Standardization (ISO) since 1988 (last revised in 2019) and, before that, it was defined in ISO (R) 2015 since 1971. It is used (mainly) in government and business for fiscal years, as well as in timekeeping. This was previously known as "Industrial date coding". The system specifies a week year atop the Gregorian calendar by defining a notation for ordinal weeks of the year.
Determination of the day of the weekThe determination of the day of the week for any date may be performed with a variety of algorithms. In addition, perpetual calendars require no calculation by the user, and are essentially lookup tables. A typical application is to calculate the day of the week on which someone was born or a specific event occurred. In numerical calculation, the days of the week are represented as weekday numbers. If Monday is the first day of the week, the days may be coded 1 to 7, for Monday through Sunday, as is practiced in ISO 8601.
Alfred and EmilyAlfred and Emily is a book by Doris Lessing in a new hybrid form. Part fiction, part notebook, part memoir, it was first published in 2008. The book is based on the lives of Lessing's parents. Part one is a novella, a fictional portrait of how her parents' lives might have been without the interruption of the First World War. Part two is a retelling of how her parents' lives really developed. The novella begins in England in 1902, when Alfred and Emily meet at a cricket match.
Absolute convergenceIn mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series is said to converge absolutely if for some real number Similarly, an improper integral of a function, is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if Absolute convergence is important for the study of infinite series because its definition is strong enough to have properties of finite sums that not all convergent series possess – a convergent series that is not absolutely convergent is called conditionally convergent, while absolutely convergent series behave "nicely".
EelEels are ray-finned fish belonging to the order Anguilliformes (æŋˈɡwɪlᵻfɔːrmiːz), which consists of eight suborders, 19 families, 111 genera, and about 800 species. Eels undergo considerable development from the early larval stage to the eventual adult stage and are usually predators. The term "eel" is also used for some other eel-shaped fish, such as electric eels (genus Electrophorus), spiny eels (family Mastacembelidae), swamp eels (family Synbranchidae), and deep-sea spiny eels (family Notacanthidae).
Tom Friedman (artist)Tom Friedman (born 1965) is an American conceptual sculptor. He was born in St. Louis, Missouri and received a BFA in graphic illustration from Washington University in St. Louis (1988) and an MFA in sculpture from the University of Illinois at Chicago (1990.). As a conceptual artist he works in diverse media including sculpture, painting, drawing, video, and installation. For over twenty years, Friedman has been investigating the viewer/object relationship, and "the space in between.
Fritz the CatFritz the Cat is a comic strip created by Robert Crumb. Set in a "supercity" of anthropomorphic animals, it focused on Fritz, a tabby cat who frequently went on wild adventures that sometimes involved sexual escapades. Crumb began drawing the character in homemade comic books as a child. Fritz became one of his best-known characters, thanks largely to the motion picture adaptation by Ralph Bakshi.
Frank PiatekFrank Piatek (born 1944) is an American artist, known for abstract, illusionistic paintings of tubular forms and three-dimensional works exploring spirituality, cultural memory and the creative process. Piatek emerged in the mid-1960s, among a group of Chicago artists exploring various types of organic abstraction that shared qualities with the Chicago Imagists; his work, however relies more on suggestion than expressionistic representation.
Convergence testsIn mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series . If the limit of the summand is undefined or nonzero, that is , then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test.
Jean-Claude Van DammeJean-Claude Camille François Van Varenberg (ʒɑ̃ klod kamij fʁɑ̃swa vɑ̃ vaʁɑ̃bɛʁɡ; vɑn ˈvarə(n)ˈbɛrx; born 18 October 1960), known professionally as Jean-Claude Van Damme (vɑ̃ dam; vɑn ˈdɑmə), is a Belgian martial artist, actor, filmmaker, and fight choreographer. Born and raised in Brussels, Belgium, at the age of ten his father enrolled him in a Shotokan school. Starting in the late 1970s, Van Damme competed in several semi-contact and full-contact matches in both karate and kickboxing.
House of BourbonThe House of Bourbon (ˈbʊərbən, also UKˈbɔrbɒn; buʁbɔ̃) is a dynasty that originated in the Kingdom of France and is a branch of the Capetian dynasty, the royal House of France. Bourbon kings first ruled France and Navarre in the 16th century, and by the 18th century, members of the Spanish Bourbon dynasty held thrones in Spain, Naples, Sicily, and Parma. Today Spain and Luxembourg have monarchs of the House of Bourbon. The royal Bourbons originated in 1272, when Robert, the youngest son of King Louis IX of France, married the heiress of the lordship of Bourbon.
Eel life historyThe eel is a long, thin bony fish of the order Anguilliformes. The species has a catadromous life cycle, that is: at different stages of development migrating between inland waterways and the deep ocean. Because fishermen never caught anything they recognized as young eels, the life cycle of the eel was a mystery for a very long period of scientific history. The European eel (Anguilla anguilla) was historically the one most familiar to Western scientists, beginning with Aristotle, who wrote the earliest known inquiry into the natural history of eels.
