dynamical-systems-hw10

dynamical-systems-hw10 - 2 The Problems Section 6.5...

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Instructor: Wayne Hacker Math 550.391-f08 Homework Set 10: ODEs on the real line Grading Scheme for homework problems: Each problem will be graded according to the following scheme: Minor algebra/calculus mistake with a correct approach: 2 out of 3 points given Major algebra/calculus mistake with a correct approach: 1 out of 3 points given Wrong approach: 0 points given The differences between major and minor mistakes will be determined by the instructor, not the student! This algorithm will be strictly enforced. No exceptions! Difficulty Rating Scale: Next to each problem will be the following labels. E = Elementary Level Problem I = Intermediate Level Problem D = Difficult Level Problem
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Math 550.391, Homework Set 10-f08, Hackernotes c ± Wayne Hacker 2008. All rights reserved.
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Unformatted text preview: 2 The Problems: Section 6.5 Problems : Problem 1: (rating = E) Strogatz 6.5.1 Problem 2: (rating = E) Strogatz 6.5.2 Problem 3: (rating = E) Strogatz 6.5.3 (just find a conserved quantity for the system. Do not sketch the phase portrait. Problem 4: (rating = I) Strogatz 6.5.4 Section 6.7 Problems : Problem 5: (rating = E) Strogatz 6.7.1 (You need not sketch the graph. Just verify, via a local analysis, that graph 6.7.7. on page 173 is correct) Section 6.8 Problems : Problem 6: (rating = E) Strogatz 6.8.1 (a) Problem 7: (rating = E) Strogatz 6.8.1 (d) Problem 8: (rating = I) Strogatz 6.8.8. Show that at least one of the fixed points in the region bounded by C 1 , C 2 , and C 3 must, in fact, be a saddle....
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dynamical-systems-hw10 - 2 The Problems Section 6.5...

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