Signal Processing and Linear Systems-B.P.Lathi copy

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Unformatted text preview: aveling off into space in a straight line; • T he f irst t o posit t hat a n electrical charge would increase in mass as its velocity increases; a n a nticipation of an aspect of Einstein's special theory of relativity.7 He also forecast t he possibility of superconductivity. Heaviside was a self-made, self-educated m an w ith only a n e lementary school education, w ho eventually became a pragmatically successful mathematical physicist. He b egan his career as a t elegrapher, b ut increasing deafness forced him to 6.2 Some Properties of t he Laplace Transform 381 r etire a t t he age of 24. He t hen devoted himself t o t he s tudy of electricity. His creative work was disdained by many professional mathematicians because of his lack of formal education a nd his unorthodox methods. Heaviside's misfortune was t hat he was criticized b oth by mathematicians, who faulted him for lack of rigor, a nd by men of practice, who faulted him for using t oo m uch mathematics a nd t hereby confusing students. Many mathematicians, trying t o find solutions t o t he distortionless transmission line, failed because no rigorous tools were available a t t he time. Heaviside succeeded because he used mathematics not with rigor, b ut w ith insight a nd i ntuition. Using his much-maligned operational method. Heaviside successfully attacked problems t hat t he rigid mathematicians could n ot solve: problems such as t he flow of h eat in a b ody of spatially varying conductivity. Heaviside brilliantly used this method in 1895 t o d emonstrate a fatal flaw in Lord Kelvin's determination of t he geological age of t he e arth by secular cooling; he used t he s ame flow of heat theory as for his cable analysis. Yet t he m athematicians of the Royal Society remained unmoved a nd were not t he least impressed by the fact t hat Heaviside had found t he answer to problems no one else could solve. Many mathematicians who examined his work dismissed i t w ith contempt, asserting t hat his methods were either complete nonsense or a rehash of already-known ideas. 5 Sir William Preece, t he chief engineer of t he B ritish P ost Office, a savage critic of Heaviside, ridiculed Heaviside's work as too theoretical and, therefore, leading t o faulty conclusions. Heaviside's work on transmission lines a nd loading was dismissed by t he B ritish P ost Office; this work might have remained hidden, had not Lord Kelvin himself publicly expressed admiration for it. 5 Heaviside's operational calculus may be formally inaccurate, b ut in fact it anticipated t he c urrent operational methods developed in more recent years. s Although his method was not fully understood, it provided correct results. When Heaviside was attacked for t he vague meaning of his operational calculus, his pragmatic reply was, "Shall I refuse my dinner because I do not fully u nderstand t he process of digestion ?" Heaviside lived as a bachelor hermit, often in near-squalid conditions, a nd died largely unnoticed, in poverty. His life demonstrates the arrogance a nd snobbishness of t he intellectual establishment, which does n ot respect creativity unless it is presented in t...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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