ps1[1] - and mathematicians:...

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Applied Mathematics E2101y Introduction to Applied Mathematics Problem Set #1, due Tuesday, 3 February 2009 Chapter 1, § 1.1: Classification of ODEs and Verification of Solutions 1 8 11 14 21 27 (a) 28 (a) 33 Chapter 1, § 1.2: First-order Initial Value Problems 5 14 19 28 Chapter 2, § 2.3: First-order Linear ODEs 6 17 28 37 Historical Research (for credit) a) How old was Isaac Newton (to within a year) when he invented calculus? b) We will spend about three-and-a-half weeks (7 lectures) on the material of chapter 2 R nota- tion by Leibniz in 1686, and runs through seminal contributions by the Bernoullis, Ricatti, Euler, d’Alembert, Lagrange, and their peers, roughly how many decades of the history of mathematics are we spanning during these lectures? You may find the following webpages convenient for historical questions about mathematics
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Unformatted text preview: and mathematicians: http://www-history.mcs.st-and.ac.uk/history/ Other (not for credit) Complete the student survey and turn it in on Tuesday, 27 January. Some statistics will be provided on Thursday, 29 January. Digest the 7-page introductory lecture handout and come primed with questions to lecture. In addition, identify areas of rust since your last mathematics course. Things to review in particular are the complex exponential and the Euler formula, partial fraction expansions, Taylors theorem, Lebiniz rule for dierentiation under an integral, and integration-by-parts. If these are not solid, your reading of the text and your processing of the lectures will be interrupted; please come to the optional review, on Sunday, 25 January at 1:30pm, Pupin 428....
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