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MA 1002 Worksheet 8 Due Date: November 4, 2009 Print Name: Signature: ID #: Instructor/Section: Instructions: Explain each step using the conventions from class. Please mark solutions clearly. You will not receive full credit for a correct answer without explanation. 1. (50 points) Draw the direction field of the autonomous system of differential equa- tions: x 1 = x 2 ( t ) x 2 = - 0 . 2 x 2 ( t ) - x 1 ( t ) using matlab or by hand. Indicate the trajectory of a solution that starts at the point [0 . 8 , 0 . 8]. What will happen to the solution eventually? 2. (50 points) Download and install (1) MikT E X and (2) T E Xmaker (or a similar editor, like T E XnikCenter) on your computer. Then use a tutorial, say on
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Unformatted text preview: http://www.math.uiuc.edu/ ˜ hildebr/tex/course/intro1.html to learn how to create a simple document containing a math formula. (a) Use L A T E X to encode the following problem from an UIUC Math Contest (2000): Problem 5 Evaluate the inFnite series 1 2 1-2 − 1 + 1 2 2-2 − 2 + 1 2 4-2 − 4 + 1 2 8-2 − 8 + · · · (b) Encode your favorite Math formula in L A T E X. Hand in a printout of the code and of the output. 3. (extra) Solve the problem above. Please bring a computer to class next Wednesday!!!...
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