exam1_review - Exam 1 Review MAP 2302 Disclaimer: This...

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Exam 1 Review MAP 2302 Disclaimer: This review is by no means complete. Please study the homework as well as the lecture notes. These questions are just an outline of the material. 1. Chapter 1 KNOW: definition of differential equation, difference between explicit and implicit so- lution, initial value conditions, how to sketch a graph, isocline, given a direction field sketch the approximate solution. (a) Solve dy dx = ln( x ) with P = (1 , 1). (b) Let dy dx = r 2 π sin( x 2 ). Where is the solution monotonic? What symmetry (if any) does y ( x ) have? 2. Chapter 2 KNOW: autonomous first order differential equation, equilibrium solutions, stable, unsta- ble and semistable solutions, phase line, Existence-Uniqueness theorem, applications like Malthus Models (simple exponential growth), and Logistic Models. (a) Determine the behavior of the equilibria for dy dx = y ( y - 1) 2 . (b) Let dy dx = y 1 / 3 through the point (0 , 0). What does the Existence-Uniqueness theorem state? What about the solution
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This note was uploaded on 07/18/2011 for the course MAP 2302 taught by Professor Tuncer during the Summer '08 term at University of Florida.

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