Numerical integral Research Paper Example | Topics and Well Written Essays - 500 words

Numerical integral - Research Paper Example Before Cavalieri introduced the system of indivisibles, Archimedes had also been working on the same thing. Archimedes had developed a method of calculating areas and volumes, but he was not willing to reveal his method. Elroy states that â€Å"Cavalieri developed a rational system of the so-called indivisibles and attempted to establish the validity of this approach† (63). Without the formalism of the integral itself, Cavalieri derived a number of basic theorems of integral calculus from his principles. Cavalieri’s method of calculation is accurate for parallelograms and plane figures lying between two parallel lines (Elroy 63). In 1639, Cavalieri obtained the power rule for integration of a polynomial, although the rule had been discovered three years before by Gilles de Roberval and Pierre de Fermat. A method for representing areas, lines, and volumes by indivisibles of a lower dimension than the continuous whole that is made by them, was thus developed by Cavalieri. Sriraman points out that â€Å"in his theory, Cavalieri stated that if two solids have the same height, then their volumes will be proportional to the areas of their bases† (7). The integration of f(X) =Xn was worked out through this method. According to Wolfram Research, Inc, an integral is a mathematical item that can be defined as an area or an abstraction of an area (â€Å"Integral† Wolfram.com). Integration on the other hand is â€Å"the process of computing or obtaining an integral† (â€Å"Integration†). Integrals have been used in a number of ways namely: 1. In calculation of volume, area, mass and length: Integration is basically applied in Physics and Mathematics. With integration, it is possible to describe the curved area of a plane in terms of functions, and area and perimeter, in terms of integrals. Integration is also used to calculate the mass of an

Undergraduate Education by Marty Nemko Assignment

Undergraduate Education by Marty Nemko - Assignment Example Nemko feels that lectures are very unproductive, however, colleges are a big business and use of lectures is the cheapest method to instruct the masses. He further argues that several professors lack the desire to educate undergraduates, but do it anyway since that’s where the cash lies. The rate of graduation at 4-year colleges is about 40%, which would be not acceptable in any other enterprise. Nemko elaborates the statistics used by colleges to make them appear more elite. He has a feeling that colleges misleadingly advertise custom-made experience amongst other things. He then elucidates what he would do to fix the system. Nemko wants colleges to provide reports that have got genuine statistics and that can directly apply to an individual. He claims that this would at least provide a student with a reasonable preview of his/her next 4 years. Nemko favors online interactive lecture and concludes by stating that continued funding of these poor enterprises will yield and chan ge nothing. It is therefore very clear that Marty Nemko presents an effective argument in â€Å"America’s Most Overrated Product: Undergraduate Education†. Nemko is very clear in his presentation as to why a college education is the most overrated product in America. He in no uncertain terms presents his argument using factual data that he has authoritatively researched on. He explains how even the parents who have no money will spare nothing to have their kids get a college education. He calls it mortgaging their future so as to pay for their children’s college education and gives the approximate figures of $200,000 for a 4-year college degree.