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KMU255Programming_7thClass_IterationChoosingtheRightTech

# KMU255Programming_7thClass_IterationChoosingtheRightTech -...

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KMU 255 Computer Programming Hacettepe University Department of Chemical Engineering Fall Semester Iterative techniques Selis Önel, PhD

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Writing codes for iterative solutions What are iterative solutions When do we need them What does the solution look like What are we going to learn today?
For a quadratic equation (2 nd order polynomial), Ex: f(x)=x 2 -3 Exact zeros (roots) of f(x) can be found by the quadratic formula. However, no such method exists for most nonlinear functions Formula for finding the zeros of a cubic function is very complicated Niels Henrik Abel (1802-1829): In 1824 Abel proved the impossibility of solving algebraically the general equation of the fifth and higher degrees Exact Zeros of Nonlinear Algebraic Equations

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Norwegian mathematician: Born on August 5, 1802 in a small village in Norway Lived a poor life, caused by large size of his family (6 brothers and father died when he was 18) and difficult economic situation in Norway at that time Died of tuberculosis at the age of 26 after being forced to live in miserable conditions because of his inability to obtain a university post. At age 16, gave a proof of the binomial theorem valid for all numbers, extending Euler's result which had only held for rationals . At age 19, showed there is no general algebraic solution for the roots of a quintic equation, or any general polynomial equation of degree greater than four, in terms of explicit algebraic operations. To do this, invented (independently of Galois) an extremely important branch of mathematics known as group theory, which is invaluable not only in many areas of mathematics, but for much of physics as well. Wrote a monumental work on elliptic functions. However, it was not discovered until after his death. When asked how he developed his mathematical abilities so rapidly, he replied " by studying the masters, not their pupils ." Abel, Niels Henrik (1802-1829)
Abel sent a paper on the unsolvability of the quintic equation to Gauss, who proceeded to discard without a glance what he believed to be the worthless work of a crank. In 1825, the Norwegian government funded Abel on a scholarly visit to France and Germany. Abel then traveled to Paris, where he gave an important paper revealing the double periodicity of the elliptic functions, which Legendre later described to Cauchy as "a monument more lasting than bronze" (borrowing a famous sentence by the Roman poet Horatius). However, Cauchy proceeded

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KMU255Programming_7thClass_IterationChoosingtheRightTech -...

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