Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant. Partial derivatives are used in differential geometry; the partial derivative of a function f with respect to the variable x is variously denoted by f x ′, f x, ∂ x f, D x f, D 1 f, ∂ ∂ x f, or ∂ f ∂ x. Sometimes, for z = f, the partial derivative of z with respect to x is denoted as ∂ z ∂ x. Since a partial derivative has the same arguments as the original function, its functional dependence is sometimes explicitly signified by the notation, such as in: f x, ∂ f ∂ x; the symbol used to denote partial derivatives is ∂. One of the first known uses of this symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences; the modern partial derivative notation was created by Adrien-Marie Legendre, though he abandoned it. Suppose that f is a function of more than one variable. For instance, z = f = x 2 + x y + y 2.

The graph of this function defines a surface in Euclidean space. To every point on this surface, there are an infinite number of tangent lines. Partial differentiation is the act of finding its slope; the lines of most interest are those that are parallel to the x z -plane, those that are parallel to the yz-plane. To find the slope of the line tangent to the function at P and parallel to the x z -plane, we treat y as a constant; the graph and this plane are shown on the right. Below, we see how the function looks on the plane y = 1. By finding the derivative of the equation while assuming that y is a constant, we find that the slope of f at the point is: ∂ z ∂ x = 2 x + y. So at, by substitution, the slope is 3. Therefore, ∂ z ∂ x = 3 at the point; that is, the partial derivative of z with respect to x at is 3, as shown in the graph. The function f can be reinterpreted as a family of functions of one variable indexed by the other variables: f = f y = x 2 + x y + y 2. In other words, every value of y defines a function, denoted fy, a function of one variable x.

That is, f y = x 2 + x y + y 2. In this section the subscript notation fy denotes a function contingent on a fixed value of y, not a partial derivative. Once a value of y is chosen, say a f determines a function fa which traces a curve x2 + ax + a2 on the x z -plane: f a = x 2 + a x + a 2. In this expression, a is a constant, not a variable, so fa is a function of only one real va

Anne Marie DeCicco-Best

Anne Marie DeCicco-Best was the 60th and longest-serving mayor of London, Canada. DeCicco graduated from Fanshawe College's broadcast journalism program in 1986 and worked for CHYR in Leamington, before returning in 1987 to work at CJBK and CJBX, a country music station in London as a reporter covering city hall. From 1994 to 1997, while serving on city council, she was a part-time instructor in a communications course at Fanshawe College. DeCicco was first elected to London City Council in 1991 as a councillor in Ward Five, becoming the youngest person to serve there, after former Ward Five councillor Grant Hopcroft made the jump to the Board of Control. In 1996 she was an avid supporter of London's bid for the 2001 Canada Summer Games, which were subsequently awarded to London. In 1997, after two, three-year terms as a ward councillor, she topped the polls when she was elected to the London Board of Control and acted as deputy mayor and budget chief to Dianne Haskett, whom she succeeded as mayor in the 2000 election.

She was re-elected to a second term in 2003. She serves on the board of governors of the University of Western Ontario and the London Police Services Board. On June 17, 2006, DeCicco married Tim Best, a 44-year-old native Londoner who'd lived in Texas, that she first met at the John Labatt Centre in downtown London during the 2005 Memorial Cup hockey championship. On November 13, 2006, DeCicco-Best was re-elected for a third consecutive term as the mayor of London in the 2006 municipal election, her main opponent was former London North Centre Liberal Member of Parliament Joe Fontana. Her victory in this election, with its four-year term mandated by the province of Ontario, made DeCicco-Best the longest-serving mayor in London's history, in office for 10 consecutive years. On October 25, 2010, Fontana defeated DeCicco-Best in the 2010 municipal election to become the mayor of London. DeCicco-Best works for Fanshawe college assisting with public relations. During her time as mayor, DeCicco-Best spent $480,000 of taxpayers' money installing metal trees inside of London.

Local surveys showed an overwhelming dislike of the objects, questioned their cost. "I would have much preferred if real trees were planted instead of cold, vomit-coloured, poorly trimmed telephone poles," said students at the University of Western Ontario. DeCicco-Best was criticized for the actions of her husband, who opened up a "for profit" check-cashing business outside the city's welfare office, was charged with six criminal counts, including impaired driving causing bodily harm, sentenced to six months in jail, owned a bar downtown which many believed was an eyesore on the city; the Jewish National Fund of London honoured Anne Marie DeCicco-Best as its 2011 London Negev Dinner Honouree. As London's longest-serving Mayor and member of London City Council for 19 years, DeCicco-Best was recognized for her dedicated contributions to the community throughout her many years of public service, her unwavering support of the Jewish community. City of London Web site Ex-mayor lands PR job at Fanshawe


Legenere limosa is an annual wildflower of the bellflower family endemic to limited portions of Northern California. This species is the sole member of the genus Legenere; the species common name is false Venus' looking glass. Blooming in May and June, it occurs below elevations of 610 meters in vernal pools and certain other moist habitats. Principal colonies are in Solano County, Sacramento County, Lake County, Napa County, Sonoma County, Tehama County and Yuba County. According to the California Native Plant Society L. limosa is classified on List 1B: Rare, threatened, or endangered. Main threats to the species are grazing, invasive species, development. Stems are reclining and of length ten to thirty centimeters, but the lateral slender branches are rigid. An alternate common name for this organism is Greene's Legenere, after Edward Lee Greene who first described this plant in 1890; the species name limosa derives from the Latin words limus and sella: the plant, seated in mud. Wetland Jepson Manual Treatment U.

S. Department of Agriculture plant profile for Legenere limosa Photo gallery