Homogeneous functionIn mathematics, a homogeneous function is a function of several variables such that, if all its arguments are multiplied by a scalar, then its value is multiplied by some power of this scalar, called the degree of homogeneity, or simply the degree; that is, if k is an integer, a function f of n variables is homogeneous of degree k if for every and For example, a homogeneous polynomial of degree k defines a homogeneous function of degree k.
Calculus of variationsThe calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations.
Darboux integralIn the branch of mathematics known as real analysis, the Darboux integral is constructed using Darboux sums and is one possible definition of the integral of a function. Darboux integrals are equivalent to Riemann integrals, meaning that a function is Darboux-integrable if and only if it is Riemann-integrable, and the values of the two integrals, if they exist, are equal. The definition of the Darboux integral has the advantage of being easier to apply in computations or proofs than that of the Riemann integral.
Theoretical definitionA theoretical definition defines a term in an academic discipline, functioning as a proposal to see a phenomenon in a certain way. A theoretical definition is a proposed way of thinking about potentially related events. Theoretical definitions contain built-in theories; they cannot be simply reduced to describing a set of observations. The definition may contain implicit inductions and deductive consequences that are part of the theory. A theoretical definition of a term can change, over time, based on the methods in the field that created it.
Contour integrationIn the mathematical field of complex analysis, contour integration is a method of evaluating certain integrals along paths in the complex plane. Contour integration is closely related to the calculus of residues, a method of complex analysis. One use for contour integrals is the evaluation of integrals along the real line that are not readily found by using only real variable methods. Contour integration methods include: direct integration of a complex-valued function along a curve in the complex plane; application of the Cauchy integral formula; and application of the residue theorem.
Riemann sumIn mathematics, a Riemann sum is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations. The sum is calculated by partitioning the region into shapes (rectangles, trapezoids, parabolas, or cubics) that together form a region that is similar to the region being measured, then calculating the area for each of these shapes, and finally adding all of these small areas together.
Integral equationIn mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals.
Riemann integralIn the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval. It was presented to the faculty at the University of Göttingen in 1854, but not published in a journal until 1868. For many functions and practical applications, the Riemann integral can be evaluated by the fundamental theorem of calculus or approximated by numerical integration, or simulated using Monte Carlo Integration.
Society for EthnomusicologyThe Society for Ethnomusicology is, with the International Council for Traditional Music and the British Forum for Ethnomusicology, one of three major international associations for ethnomusicology. Its mission is "to promote the research, study, and performance of music in all historical periods and cultural contexts." Officially founded in 1955, its origins extend back to November, 1953 at the annual meeting of the American Anthropological Association in Philadelphia with an informal agreement between Willard Rhodes, David McAllester, and Alan P.
School of Science and EngineeringThe School of Science and Engineering Magnet (known as the School of Science and Engineering or SEM) is a magnet college preparatory high school located in the Yvonne A. Ewell Townview Magnet Center, home of six magnet high schools in the Dallas Independent School District. SEM's mascot is an eagle, and its school colors are maroon and white. Its current principal is Andrew Palacios. Past principals include: Tiffany Huitt (who was promoted to DISD Executive Director), Jovan Carisa Wells, and Richard White.
Wyoming SeminaryWyoming Seminary, founded in 1844, is a Methodist college preparatory school located in the Wyoming Valley of Northeastern Pennsylvania. The "Lower School," which consists of preschool - 8th-grade students, is located in Forty Fort. The "Upper School," comprising 9th-grade to postgraduate students, is located in Kingston. It is near the Susquehanna River and the city of Wilkes-Barre. Locally and in some publications, it is sometimes referred to as "Sem." As a boarding school, only Upper School students may board on campus.
Raymond D. MindlinRaymond David Mindlin (New York City, 17 September 1906 – 22 November 1987) was an American mechanical engineer, Professor of Applied Science at Columbia University, and recipient of the 1946 Presidential Medal for Merit and many other awards and honours. He is known as mechanician, who made seminal contributions to many branches of applied mechanics, applied physics, and engineering sciences. In 1924 he enrolled at Columbia University, where he received a B.A. in 1928, followed by a B.S. in 1931, and in 1932 by a C.
