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"Among all of the mathematical disciplines the theory of differential equations is the most important … It furnishes the explanation of all those elementary manifestations of nature which involve time."
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Calculus"This is a tricky domain because, unlike simple arithmetic, to solve a calculus problem - and in particular to perform integration - you have to be smart about which integration technique should be used: integration by partial fractions, integration by parts, and so on."
Calculus is the mathematical study of continuous change, and the principal precursor of modern mathematical analysis. Originally called infinitesimal calculus or the calculus of infinitesimals, it has two major branches, differential calculus and integral calculus. Differential calculus studies instantaneous rates of change and slopes of curves; integral calculus studies accumulation of quantities
"Among all of the mathematical disciplines the theory of differential equations is the most important … It furnishes the explanation of all those elementary manifestations of nature which involve time."
"In England, where it originated, the calculus fared less well. ...by siding completely with Newton in the priority dispute, they cut themselves off from developments on the Continent. They stubbornly stuck to Newtons dot notation of fluxions, failing to see the advantages of Leibnizs differential notation. As a result, over the next hundred years, while mathematics fluorished in Europe as never before, England did not produce a single first-rate mathematician. When the period of stagnation finally ended around 1830, it was not in analysis but in algebra that the new generation of English mathematicians made their greatest mark."
"Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature’s God must work in the same channels."
"Calculus is the study of limits. In simple terms, a limit allows us to look at what happens to the dependent variable as the independent variable gets close to something."
"That Leibniz here (in the field of calculus) wholly uninfluenced by others, gained his crucial insights unaided, is beyond all doubt."
"Who has not been amazed to learn that the function y = ex, like a phoenix rising from its own ashes, is its own derivative?"