In mathematics, an integrating factor is a function, chosen to facilitate the solving of a given equation involving differentials. It is used to solve ordinary differential equations, but is used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential; this is useful in thermodynamics where temperature becomes the integrating factor that makes entropy an exact differential. An integrating factor is any expression that a differential equation is multiplied by to facilitate integration. For example, the nonlinear second order equation d 2 y d t 2 = A y 2 / 3 admits d y d t as an integrating factor: d 2 y d t 2 d y d t = A y 2 / 3 d y d t. To integrate, note that both sides of the equation may be expressed as derivatives by going backwards with the chain rule: d d t = d d t. Therefore, 2 = 6 A 5 y 5 / 3 + C 0. Where C 0 is a constant; this form may be more useful, depending on application. Performing a separation of variables will give ∫ y y d y 6 A 5 y 5 / 3 + C 0 = t This is an implicit solution which involves a nonelementary integral.

This same method is used to solve the period of a simple pendulum. Integrating factors are useful for solving ordinary differential equations that can be expressed in the form y ′ + P y = Q The basic idea is to find some function, say M, called the "integrating factor", which we can multiply through our differential equation in order to bring the left-hand side under a common derivative. For the canonical first-order linear differential equation shown above, the integrating factor is e ∫ P d x. Note that it is not necessary to include the arbitrary constant in the integral, or absolute values in case the integral of P involves a logarithm. Firstly, we only need one integrating factor to solve the equation, not all possible ones. For absolute values, this can be seen by writing | f | = f sgn ⁡ f, where sgn refers to the sign function, which will be constant on an interval if f is continuous; as ln ⁡ | f | is undefined when f = 0, a logarithm in the antiderivative only appears when the original function involved a logarithm or a reciprocal, such an interval will be the interval of validity of our solution.

To derive this, let M be the integrating factor of a first order linear differential equation such that multiplication by M transforms a partial derivative into a total derivative, then: M ( x

State Route 138 is a primary state highway in the U. S. state of Virginia. The state highway runs 16.90 miles from U. S. Route 1 in South Hill north to SR 40 in Kenbridge. SR 138, which runs concurrently with SR 137 near Kenbridge, connects that town with Interstate 85. SR 138 begins at an intersection with US 1 in the eastern end of the town of South Hill; this intersection is just west of US 1's partial cloverleaf interchange with I-85. SR 138 heads north as two-lane Union Mill Road, which exits the town of South Hill and leaves Mecklenburg County at its bridge over the Meherrin River; the state highway continues through Lunenburg County as South Hill Road. At Lafoons Corner, SR 138 intersects SR 137; the two state highways cross over an abandoned railroad grade and curve northwest to the town of Kenbridge, where they continue as 5th Avenue. SR 138 reaches its northern terminus and SR 137 has its western terminus at the highways' intersection with SR 40 in downtown Kenbridge. Virginia Highways Project: VA 138

"Kingston Town" is a 1970 song by Lord Creator released as a single on producer Clancy Eccles' Clandisc label. It was recorded in 1989 by reggae group UB40 and was released as the second single from their album Labour of Love II, reaching number four on the UK Singles Chart and number one in France and the Netherlands. In June 2007, the copyright holders of the song, Sparta Florida Music Group, started legal action against Paris Hilton and Warner Chappell Music for plagiarism due to alleged similarities between "Kingston Town" and Hilton's song "Stars Are Blind", it was wrongly stated that UB40 was the suing party, which the band confirmed as being incorrect on their website. English reggae band UB40 covered "Kingston Town" in 1989 and released it as a single in early 1990, it became the group's sixth top-five hit on the UK Singles Chart, peaking at number four for three weeks in April 1990. Throughout the rest of 1990, the song charted in a number of countries, topping the Dutch Top 40 for two weeks in May and the French Singles Chart for three weeks in October and November.

Infodisc estimates it is the 426th-best-selling single of all time in France with 581,000 copies sold. In Australia, the song did not reach the top 100 on the ARIA Singles Chart during its original release. However, in 1991, after a re-release of "Here I Am" reached number three, "Kingston Town" was re-released and peaked at number 17 on the ARIA Singles Chart. Virgin / DEPX 35 "Kingston Town" – 3:52 "Lickwood" – 5:04 "Kingston Town" – 5:16 Virgin / DEP 35, DEPX 35, DEP C35 "Kingston Town" – 3:52 "Lickwood" – 5:04 Virgin / DEP 35-12 "Kingston Town" – 5:16 "Lickwood" – 5:04 "Kingston Town" – 3:52

Debra J. Parrish is an American academic administrator, she was a president of Keweenaw Bay Ojibwa Community College for 30 years. Parrish completed a B. A. from Northern Michigan University. Parrish began working for the Keweenaw Bay Indian Community in 1972 as a legal secretary for Gar Hood, a tribal attorney, she assisted Georgianna Emery to create the first National Congress of American Indians meeting at the tribal center. Parrish worked as a secretary and administrative assistant for the Young Adult Community Corp program and the chairman's office, she was an administrative assistant for Don LaPointe. She worked on the Elderly Nutrition Programs with James Schutte and helped set up the Ojibwa Seniors Gift Shop. Parrish was a program coordinator in the business development office, she assisted in the creation of the Ojibwa Lanes and Lounge project with Mike Chosa and Tim Shanahan and in the creation of the Ojibwa Industrial Park. Parrish helped develop the Economic Development Corporation and volunteered during the establishment of KBIC's Big Bucks Bingo in Zeba Bingo Hall.

She was an early manager of the Even Start Program where she established the indoor play center, now part of the Pre-Primary Program. Parrish served on the Keweenaw Bay Tribal Council as the secretary, she participated in committees including hiring, economic development, constitutional task force, health board, the Ojibwa senior board. Parrish worked at Keweenaw Bay Indian Community for 46 years including nearly 20 years as president of Keweenaw Bay Ojibwa Community College, she reestablished KBOCC as an institution of higher learning. In 1998, Tribal Council granted Parrish permission to reopen KBOCC, charted in 1975 but closed down in 1980, it first started in a section of the Ojibwa Senior Citizen's center before expanding to its own buildings in Baraga in 2000. Under Parrish's leadership, KBOCC joined the American Indian Higher Education Consortium. At KBOCC, she expanded the campus in L'Anse, Michigan. Initiatives she worked with included Indian tuition waivers, creation of a L'Anse campus land trust, advocating for the continuance of the Title III Higher Education Act.

In 2013, KBOCC became accredited by the Higher Learning Commission and was granted became a Land-grant university in 2014. On January 26, 2018, she announced her resignation and retirement from KBOCC. Parrish stated she would still work as a consultant but wanted to take time to "relax and enjoy family." Parrish was succeeded by interim president Cherie Dakota. In August 2018, Lori Ann Sherman became president of KBOCC. Parrish received funding from the Economic Research Service to conduct health assessments and a nutrition screening of the Keweenaw Bay Indian Community; this study consisted of nutrition surveys for families with children ages 1 to 4. A major obstacle facing the project included the distribution of surveys because the tribal operations did not have a central mailing list, her study aimed to document the prevalence of nutrition related diseases in tribal youth, reduce the incidence of chronic diseases, to create programs to teach Ojibwe culture with the goal of encouraging healthy lifestyles.

Parrish has Sharon Geroux of New Mexico and deceased son, Rick Geroux. After his death, a memorial scholarship was established at KBOCC. Parrish has seven grandchildren and cared for twelve foster children

Nikola Zoricic was a Canadian ski cross skier who died following a severe crash during the eighth-finals of a World Cup event in Grindelwald, Switzerland. Zoricic was born in SR Bosnia-Herzegovina, SFR Yugoslavia, he grew up in Toronto after emigrating to Canada with his family at the age of five. As is common among ski-cross athletes, Zoricic was an alpine ski racer before taking up ski-cross. In December 1998, he was No. 1 ranked in the world in slalom for his age group. Zoricic started his first FIS race in Park City and scored his first top 10 finish at the Nor-Am Cup in Colorado. During the 2003–04 and 2004–05 seasons, he competed in four World Cup slaloms but was never able to advance past the first round of competition. For several years, he tried in vain to compete with the world's best slalom skiers but injuries did not let him to move up the ranking. In 2008 he decided to switch to freestyle skiing instead. Zoricic made his ski-cross debut at the Freestyle World Cup on 19 January 2009 in Lake Placid, finishing in 61st.

He earned his first World Cup points on 24 February of that year when he finished 15th at Branäs, Sweden. During the 2009–10 season, he failed to qualify for the 2010 Winter Olympics in Vancouver. Zoricic's greatest success came in the 2010–11 season; that year, he was never ranked lower than eighth and made his first World Cup podium on 7 January 2011 by finishing second at St. Johann in Tyrol. A year on 15 January 2012, he finished third in the World Cup race at Les Contamines-Montjoie. At the World Cup race on 10 March 2012 in Grindelwald, Zoricic crashed hard head first into netting lining the course after going wide and falling on the final jump, he was knocked unconscious, suffered severe skull and brain trauma and was airlifted to a hospital in Interlaken where he was pronounced dead. After his death there has been much controversy over the possible avoidance of his death. Swiss police have said the tragedy was a sporting accident and not due to any flaw in the ski course. Zoricic's family and some racers suggest there were a number of issues with the final jump and the course finish.

Zoricic's family threatened to sue the International Ski Federation and Alpine Canada if they refuse to launch an independent investigation. Nic Zoricic Foundation