Calculus

     Hi everyone. My topic for the mathematics part of the challenge program is calculus. There are two forms of calculus, Differential and Integral calculus. The topic calculus seems interesting to me because it doesn't just focus on one thing, it focuses on different fields in this area. Here are some questions that I will be answering for my research:

Who invented calculus?

What was calculus used to solve?

When was calculus invented?

What is the difference between Differential and Integral calculus?

                                                   Differential Calculus

     Differential calculus a sub-field of calculus.Differential calculus is basically the study of the rates at which quantities change. It is one of the two traditional divisions of calculus. The derivative of a function are the primary objects of study on Differential calculus. The derivative of a function is a chosen input value that describes the rate of change of the function near the input value. Derivatives of function are usually used to find the maxima and minima of a function. The maxima is the largest value of a function. The minima is the smallest value of a function. Derivatives and their generalizations appear in many mathematic fields-complex analysis, function analysis, differential geometry, measure theory, and abstract algebra.

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A Differential calculus graph function:

                             Integral Calculus

      Integral calculus is the use of functions as tools used with Differential calculus. Integral calculus is the second traditional division of calculus. Given a function,f, of a real variable,x, and a interval,(a,b), of the real line, the definite integral is defined to be the net signed region in the xy-plane bounded by the graph of f, the x-axis and the vertical lines where x=a and x=b also. The example of this integral calculus equation is shown below. Through the fundamental theorem of calculus, which specifies the relationship between the operations of calculus, integration is connected with differentiation.

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Pictures of what the equation would look like when written: 

                                                       Inventors Of Calculus

     The inventor of calculus was an English physicist and mathematician Isaac Newton (1642-1727) and German mathematician Gottfried Leibniz (1646-1716) are credited with the invention of calculus. They developed calculus as a means of explaining the laws of physics with mathematical symbols. Newton devised his methods before Leibniz started his work, but Newton did not publish his results quickly enough. Leibniz's theories were published in 1684 and Newton's did not follow until 1693, thus causing much tension between the two esteemed scientists.They both, however, came to the same conclusions using different symbols and notations.Calculus is generally used to solve problems with motion and with variation.

Isaac Newton, one of the two inventors of calculus:

Gottfried Leibniz the second inventor of calculus: