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 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 continuous research, their work is to identify and translate documents and texts that shed new insight into this important period of history.

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.

Other books in this cycle include Methuselah's Children, Time Enough for Love, The Number of the Beast, and The Cat Who Walks Through Walls.

Through the night of the 22nd to dawn of the 23rd, Mullá Husayn became the first to accept the Báb's claims as the gateway to Truth and the initiator of a new prophetic cycle ; the Báb had replied in a satisfactory way to all of Mullá Husayn's questions and had written in his presence, with extreme rapidity, a long commentary of Surih of Joseph, which has come to be known as the Qayyúmu ' l-Asmá ' and is considered the Báb's first revealed work.

Through the funding and creation of programs and partnerships, they support innovative community efforts to break the cycle of poverty and homelessness.

Through the use of the second lied of his Lieder eines fahrenden Gesellen cycle, "", we can see how the composer manipulates the song's form to accommodate the symphonic form.

Through its life cycle, Obelia takes two forms: polyp and medusa.

Through its 130 worldwide wholesale operating locations, Manheim impacts every stage of a used vehicle's life cycle, helping commercial sellers and automobile dealers maximize the value of their vehicles.

Through selected tones and rhythms, the music is performed as a cycle of life recognizing our journey from birth to death, spring to winter, as circle, vibrating higher after each revolution to experience Love In its Fullest Effect.

Through the ritual of cremation Baldessari draws a connection between artistic practice and the human life cycle.

Through the early twentieth century the zamindars of Surul ( Sarkar Family ), another neighbouring village, a few minutes by cycle from the Uttarayan Complex, and the zamindars of Taltore, a village just north of the university town, continued to sell their lands and other properties to the ashram and the college that was being built on this spot.

Through his father, Alfred Nobel was a descendant of the Swedish scientist Olaus Rudbeck ( 1630 – 1702 ), and in his turn the boy was interested in engineering, particularly explosives, learning the basic principles from his father at a young age.

Through the reputation of its venerable founder and its position as a major European centre of learning, Columba's Iona became a place of pilgrimage.

Through the activities of the theologian Origen ( 185 / 6 – 254 ) and the school of his follower Pamphilus ( later 3rd century – 309 ), Caesarea became a center of Christian learning.

Through focusing their English language learning on reading books instead of endless worksheets the teachers were able to improve the rate at which their students learned English.

Through the lens of Otto Rank ’ s work on understanding art and artists, action learning can be seen as the never-completed process of learning how to “ step out of the frame ” of the ruling mindset, whether one ’ s own or the culture ’ s – in other words, of learning how to unlearn.

Through learning from his parents, Mao Dun developed great interest in writing during his childhood.

Through his trusteeship, the town ’ s first water distribution system ( later the Columbia Water Company ) was established, as well as the Washington Institute ( the town ’ s first school of higher learning ) and the Locust Street Park, located at what is now Locust Street and Route 462.

Through the Middle Ages Etymologiae was the textbook most in use, regarded so highly as a repository of classical learning that, in a great measure, it superseded the use of the individual works of the classics themselves, full texts of which were no longer copied and thus were lost.

Through his learning and his manner of discussion, he co-operated with S. J. Baumgarten of Halle ( 1706 – 1757 ) in disengaging the current dogmatic theology from Lutheran Orthodoxy, along with any Lutheran scholastic or mystical influences, and thus paved a way for a Rationalist revolution in theology.

Through situated learning students will be able to learn the skills and also be able to accurately use the skills they have learned.

Through situated learning students will be able to learn the skills and also be able to accurately use the skills they have learned.

Through its distance and alternative learning programs, the college provides off-campus and online services throughout western Nebraska.

Through effective communication skills, the teacher is able to address student needs, interests, and overall engagement in the learning material.

Through a socio-cultural perspective on learning, scaffolding is important when fostering independent thinking skills.

Through communicative learning, learners must work towards critically reflecting assumptions that underlie intentions, values, beliefs, and feelings.

Through motor learning the human is capable of achieving very skilled behavior, and through repetitive training a degree of automation can be expected.

Through academics, hands-on activities, and team-based learning, students explore the connections between math and science and real world applications ; Engineering Alliance-Developed through a partnership between Project Lead the Way ( PLTW ), TSA and SkillsUSA, Engineering Alliance offers a series of classroom level competitions and leadership development activities designed specifically for PLTW-affiliated middle and high school pre-engineering instructional programs ; VEX Robotics-The TSA VEX Robotics Competition provides students with a hands-on co-curricular competition for learning about science, technology, engineering and mathematics through robotics.

Through the University of London, Heythrop is also able to offer students access to a wide range of digital journals and learning resources, such as JSTOR.

Through this ongoing year-round learning process, students also gain a knowledge and appreciation of the unique harmony and balance the ancient Hawaiian people maintained with their island environment.

Through a blended learning approach, technology will be more important.

Through the improvement of its infrastructure, such as the library, the stadium, and auditorium, the university works hard to provide students with a good learning environment and to improved the living community.