Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if f is a continuous real-valued function defined on a closed interval, then, once an antiderivative F of f is known, the definite integral of f over that interval is given by

Through history, Metz population has been impacted by the vicissitudes of the wars and the annexations involving the city and avoiding a continuous population growth.

Through maneuver and continuous assault, Chinese, Persian, Arab and Eastern European armies could be stressed until they broke, and then were annihilated in pursuit.

Through daily efforts to rebuild, re-arm and improve the fortifications, he was able to finally connect them with a continuous defence system enceinte.

Through touring heavily throughout 1999 and 2000, Guided by Voices ' live act became legendary, with shows often stretching past the three-hour mark, and populated by an endless stream of new and classic songs, Pollard solo tracks, impromptu covers of The Who, David Bowie and The Rolling Stones, all accompanied by continuous alcohol consumption.

Through September 28, for example, Alabama ’ s 117th Air Refueling Wing kept aircraft aloft on a continuous basis.

Through innuendo, rumors, and public discrediting, a hostile environment is created in which one individual gathers others to willingly, or unwillingly, participate in continuous malevolent actions to force a person out of the workplace.

Through this strategy, 40 million bank and investment accounts were quietly converted into war bonds, providing the Reich government with a continuous supply of money.

Through the continuous cycle of learning, teacher ’ s often work with students to develop a framework of knowledge, which is to be evaluated based on student input to the lessons content.

Through unusual animation techniques the illusion is created that the film consists of one continuous shot or long take.

Through his continuous propagation of modern art as shown in his works and teachings, Edades proved that modernists were not fooling people as Guillermo Tolentino asserted.

Through this monitoring system, the concept of continuous self-upgrading and development after a training course can be impacted on all teachers in Rizal Province.

Through this area, it had a continuous center turn lane, losing the grassy median it had in places downtown.

His second book was The Man Who Walked Through Time ( 1968 ), in which Fletcher was the first person to walk a continuous route through Grand Canyon National Park in 1963.

Through the establishment of the SERC, the University seeks to help and support the local software industry in establishing and improving their processes and practices through continuous feedback and training.

Through the House of Burgesses, the Virginia House of Delegates is considered the oldest continuous legislative body in the New World.

Through continuous innovations, Rodenstock further expanded its market share during that time.

" Through continuous struggle the Afghan Mujahideen succeeded in their mission, and the Russian forces withdrew from Afghanistan in 1989 after the loss of tens of thousands of its soldiers.

Through links to research networks in other regions ( such as Internet2 and ESnet in the USA, TEIN in Asia-Pacific and RedCLARA in Latin America ), GÉANT allows collaboration between researchers on a global scale, reaching over 60 NRENs outside of Europe.

Through historical research this council has become better known.

Through this company, Lennon released a tribute song and EP, " Lucy ", honoring the memory of Lucy Vodden, the little girl who inspired the song Lucy in the Sky with Diamonds, with 50 % of the proceeds going to fund Lupus research.

Through translations made available by Danilo Montaldi and others, the Italian autonomists drew upon previous activist research in the United States by the Johnson – Forest Tendency and in France by the group Socialisme ou Barbarie.

Through programs like the Deshpande Center, MIT faculty leverage their research and discoveries into multi-million-dollar commercial ventures.

Through research and outreach that inspire action, the Worldwatch Institute works to accelerate the transition to a sustainable world that meets human needs.

Through her chemistry research, she became an expert in water quality and later began to focus on applying scientific principles to domestic situations.

Through their location the institutes have excellent access to poor rural areas, and consequently emphasis is placed on the role of research in improving quality of life and economic growth ( and especially sustainable job creation ).

Through this research, he identified three factors that could be measured to calculate language aptitude: verbal intelligence, auditory ability, and motivation.

Through government funding, a research and development program was developed within the Army, Navy, Air Force, and the Veterans Administration.

Through subsequent modification the Mansfield amendment moved the Department of Defense toward the support of more short-term applied research in universities.

Through his behaviorist approach, Watson conducted research on animal behavior, child rearing, and advertising.

Through research of Manville's history, Lost Valley was never to be built for this reason.

Through the Rotavirus Vaccine Program and the Accelerating Vaccine Introduction initiative, these groups are partnering with research institutions and governments to reduce child morbidity and mortality from diarrhoeal disease by making a vaccine against rotavirus available for use in developing countries.

Through the advances of innovation age technology, Socrates would provide " voluntary " but " systematic " coordination of resources across multiple " economic system " institutions including industry clusters, financial service organizations, university research facilities and government economic planning agencies.

Through AISI, the industry is able to work through collaborative partnerships and pursue market development programs aimed at expanding markets for steel, research and development ( R & D ) projects aimed at best practices in steelmaking and initiatives designed to achieve new milestones in energy efficiency and sustainability.

" Through the partnership, students have the chance to enroll in dual-degree programs and participate in student exchanges and joint research with a national or international scope.

Through its research UNE seeks to assist in the economic, social and cultural advancement of Australia and in the advanced training of undergraduate and postgraduate students.

Through the university's involvement, the DMC will benefit from the latest research in media and related technologies.

Through their research, Olcott and Blavatsky concluded that Buddhism best embodied elements of what they found significant in all religions.

Through the website, they would also be provided with music video previews, music downloads, and a wide range of market research tools for the individual portfolios of game participants, including airplay stats and sales charts.

Through the Laura Spelman Rockefeller Memorial, established by John D. Rockefeller, Jr. in 1918 and named after his mother, the family shifted the focus of philanthropy into the social sciences, stimulating the founding of university research centres and creating the Social Science Research Council.

Through anthropological research methods, McAra explores beyond the level of public discourse on Buddhism to investigate group members ' narratives about a stupa that they completed in 1997, and their changing sense of relationship with the land.

Through research grants, published journals, the upkeep of the American Philosophical Society Museum, an extensive library, and regular meetings, the society continues to advance a variety of disciplines in the humanities and the sciences.

Through PiHKAL ( and later TiHKAL ), Shulgin sought to ensure that his discoveries would escape the limits of professional research labs and find their way to the public ; a goal consistent with his stated beliefs that psychedelic drugs can be valuable tools for self-exploration.