10 Interesting Facts about Calculus


There are some interesting Facts about Calculus.Calculus (from Latincalculus, literally ‘small pebble’, used for counting and calculations, as on an abacus)[1] is the mathematical study of continuous change .It has two major branches, differential calculus (concerning instantaneous rates of change and slopes of curves),[2] and integral calculus(concerning accumulation of quantities and the areas under and between curves)

 

Facts about Calculus 1:Differential Calculus

he primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation.

Facts about Calculus 2: Integral Calculus

                   Integral Calculus

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

Facts about Calculus 3:Newton and Leibniz

The major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz.The theorem demonstrates a connection between integration and differentiation. This connection, combined with the comparative ease of differentiation, can be exploited to calculate integrals.

 

Facts about Calculus 4:Applications of Integral

 

                                     Applications of Integral

 

 

In probability theory, integrals are used to determine the probability of some random variable falling within a certain range. .Integrals can be used for computing the area of a two-dimensional region that has a curved boundary, as well as computing the volume of a three-dimensional object that has a curved boundary.

Facts about Calculus 5:Applications of Derivatives

In an automobile there is always an odometer and a speedometer. These two gauges work in tandem and allow the driver to determine his speed and his distance that he has traveled.In the business world there are many applications for derivatives. One of the most important application is when the data has been charted on graph or data table such as excel.

Facts about Calculus 6:Precision engineering

One of the fundamental principles in precision engineering is that of determinism. System behavior is fully predictable even to nanometer-scale motions. To do the job efficiently and correctly to fit your need via modern machinery.

 

Facts about Calculus 7:  Runge’s phenomenon

In the mathematical field of numerical analysis, Runge’s phenomenon (German: [ˈʁʊŋə]) is a problem of oscillation at the edges of an interval that occurs when using polynomial interpolation with polynomials of high degree over a set of equispaced interpolation points

Facts about Calculus 8:The Lagrange Polynomial

 

       The Lagrange Interpolation

 

Lagrange polynomials are used for polynomial interpolation. For a given set of points  with no two  values equal, the Lagrange polynomial is the polynomial of lowest degree that assumes at each value.The interpolating polynomial of the least degree is unique,

Facts about Calculus 9:Gaussian Quadrature

In numerical analysis, a quadrature rule is an approximation of the definite integral of a function, usually stated as a weighted sum of function values at specified points within the domain of integration.

Facts about Calculus 10: The Risch Algorithm

 

 

 Algebra for Engineering

 

the Risch algorithm is an algorithm for indefinite integration. It is used in some computer algebra systems to find antiderivatives. It is named after the American mathematician Robert Henry Risch, a specialist in computer algebra who developed it in 1968.

So, do you like these10 interesting  Facts about Calculus?


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