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Calculus is a branch of mathematics that studies the properties of, and relations between, curves, surfaces, volumes and differential equations. The main areas of calculus are differentiated functions, integration and Taylor Series. Differential equations were originally used to model one or more simultaneous equations involving a certain dependent variable. They are a staple in physics where they can be solved with separation of variables to get an explicit function. In this post we will talk about what calculus is and how it works including the history behind it as well as proposing some future applications for it. Calculus is the study of change. It involves skills of approximation, reasoning, modeling, numeration, computation?as well as notions of infinity. Calculus has its origins in the study of tangents to curves. It was founded by Newton and Leibnitz independently in about 1666. Newton was initially reluctant to publish his work on calculus because he feared it would be too complicated for other mathematicians to understand. Therefore, his work on calculus remained hidden until Leibnitz published his own derivative works that built off of what Newton had done. Calculus is basically the study of limits and differentials (a concept derived from infinitesimals). Calculus is seen as the study of the place where mathematics and physics meet. It has been used in virtually all of the sciences, including engineering, physics, chemistry, biology, physics, economics, geology and computer science. The term "calculus" appeared by 1635 in Gottfried Leibniz's "Ars Magna". It was originally introduced to describe what today are strictly elementary calculations. The names of these first two half-dozen mathematicians are known as the precursors of calculus. These include Isaac Barrow (c. 1630-1677) who provided the first definition of the derivative. In 1692, Sir Isaac Newton published the "Principia" which can be called a foundational document for calculus. Once published, calculus was widely adopted by the scientific community and soon thereafter by mathematics itself. The symbol ∫ f '(' x) dx to represent integration was first used in a 1665 text written by James Gregory who had been a student of Leibniz. Gregorie states that he learned it from his teacher Robert Hermann. Hermann, in turn, had learned it from Jacob Bernoulli whom he had met while studying with Johann Bernoulli in Switzerland in 1683. The integral symbol was used by Bernoulli himself in 1694 and Leonhard Euler adopted it in 1729. Calculus is the study of limits and derivatives which are two key concepts in the subject. The derivative of a function at a point is a measure of the slope of the tangent line to the function at that point. They are used to calculate instantaneous rates of change, maxima, minima, extrema, inflection points etc., in any given function. They are also seen as being able to find areas under curves or find instantaneous velocity or displacement when given an equation. There are different types of derivatives that include:Boundary conditions set up restrictions on different derivatives at certain points. cfa1e77820
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