Calculus is the study of change which focuses on limits, functions, derivaties, integrals, and infinite series. There are two main branches of calculus: differential calculus and integral calculus, which are connected by the fundamental theorem of calculus. It was discovered by two different men in the seventeenth century. Gottfried Wilhelm Leibniz – a self taught German mathematician – and Isaac Newton - an English scientist - both developed calculus in the 1680s. Calculus is used in a wide variety of careers, from credit card companies to a physicist use calculus in their work. In general, it is a form of mathematics which was developed from algebra and geometry. Integration and differentiation are an important concept in mathematics, and are the two main operations in calculus. Differential calculus is a subfield of calculus which concentrates over the study of how functions change when their inputs are changed. The main focus in a differential calculus is the derivative which can be thought of as how much one quantity is changing in response to changes in some other quantity. The process to find the derivative is called differentiation, the fundamental theorem of calculus states that the differentiation is the reverse process to integration. Derivatives are mainly applied in physics as it concerns with the way quantities change and evolve over time. The principles of integral were developed through the fundamental theorem if calculus individually by Newton and Leibniz. According to Bernhard Riemann, integral is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs. During the 19th century more notions of integrals began to appear, where the type of the function as well as the domain over which the integration is performs has been generalized. There are many modern concepts of integration but the most common one is based on the abstract mathematical theory known as Lebesgue...
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