AnswerPSet_2010_02

AnswerPSet_2010_02 - Answers P-Set Number 2 18.385j/2.036j...

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Unformatted text preview: Answers P-Set Number 2, 18.385j/2.036j MIT (Fall 2010) Rodolfo R. Rosales (MIT, Math. Dept., room 2-337, Cambridge, MA 02139) October 1, 2010 Course TA: Jan Molacek, MIT, Math. Dept. room 2-331, Cambridge, MA 02139. Email: [email protected] Contents 1 Problem 2.2.13 - Strogatz (Skydiving). 2 1.1 Problem 2.2.13 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Problem 2.2.13 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Problem 2.4.09 - Strogatz (Stat. Mech. and the critical slowing-down). 7 2.1 Problem 2.4.09 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 Problem 2.4.09 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Problem 3.4.06 - Strogatz (Find and classify bifurcations). 8 3.1 Problem 3.4.06 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Problem 3.4.06 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Problem 3.4.15 - Strogatz (First-order phase transition). 10 4.1 Problem 3.4.15 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Problem 3.4.15 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5 Problem 3.5.4R - (Bead on horizontal rotating wire). 13 5.1 Problem 3.5.4R statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.2 Problem 3.5.4R answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 6 Problem 3.5.06 - Strogatz (Model problem about singular limits). 18 6.1 Problem 3.5.06 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 6.2 Problem 3.5.06 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 7 Problem 4.1.08 - Strogatz (Potentials for vector fields on the circle). 21 7.1 Problem 4.1.08 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 7.2 Problem 4.1.08 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8 Problem 4.5.03 - Strogatz (Excitable systems). 22 8.1 Problem 4.5.03 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 8.2 Problem 4.5.03 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1 2 9 Problem 5.2.11 - Strogatz (Single eigenspace matrix). 25 9.1 Problem 5.2.11 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 9.2 Problem 5.2.11 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 10 Problem 6.1.11 - Strogatz (Computer generated phase portrait). 26 10.1 Problem 6.1.11 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 10.2 Problem 6.1.11 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 11 Problem 6.2.02 - Strogatz (A trapped solution). 27 11.1 Problem 6.2.02 statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 11.2 Problem 6.2.02 answer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .11....
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This note was uploaded on 02/28/2011 for the course MATH 18.385j taught by Professor R. during the Fall '10 term at MIT.

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AnswerPSet_2010_02 - Answers P-Set Number 2 18.385j/2.036j...

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