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Unformatted text preview: MA 366 Spring 2011 Assignments For Wednesday 1/12: Read 1.21.3. Do: p. 25: 7, 9, 16 p. 360, The answer to Exercise 8 is given in the back of the text. Substi- tute the given functions x 1 and x 2 into the the system to show that they do solve the system. Show that they also satisfy the desired initial conditions stated in the exercise. For Friday 1/14 : Read p. 31-39 Do:Exercises : p. 25: 13, 14 p. 360, The answer to Exercise 10 is given in the back of the text. Substitute the given functions x 1 and x 2 into the the system to show that they do solve the system. Show that they also satisfy the desired initial conditions stated in the exercise. Exercises p. 39: 1(use dfield), 4(use dfield), 13,15, 16 Note: Note: In the dfield problems to determine the behavior as t goes to infinity you need to also draw several of the solutions as the text did in figure 2.1.4 on p. 38 and describe what you see. In part (c) you are asked to prove that your observation is correct. For Wednesday 1/19: Read p. 21, first paragraph, p. 42-47 p. 39: 14,19, 24 (use dfield) p. 24: The differential equation in exercise 4 is not linear. Change one single number to make the equation linear. Do not just change one of the coefficients to zero! p. 47, 1, 7, 10 (use dfield), 23. (Hint: Set y = 0 and solve for x . You dont need to compute y to do this! How can you tell that it is a minimum and not a maximum or a point of inflection?) 1 For Friday 1/21: In all of these problems, do not do the computer part! Read Example 1, p. 52. Then do Exercise 4, p. 60. Only find the concentration prior to the point of overflow. Do not do the parts described in the final two sentences of the problem. p. 48, 22 (This is similar to 23, but now you want y = .),24 (Prove that your value really is a maximum.), 30 (a)-(e) p. 62, 16. For Wednesday 1/26 In all of these problems, do not do the computer part! p. 50, 31(a), (b) p.202, 1 (See the discussion relating to Equation (12) pn p. 195. You will need the technique used in this problem for 5(c) below.) p. 60, 5, 20 Note in some versions of the text the rate in and rate out are given as 3 gal/min. Please use 2 gal/min instead. For Friday , 1/28 p. 100 1, 2, 3, 21 In all of these problems, do not do the computer part! p. 50, 32(a), (b) p. 60, 21(a), (b) p. 77, 27(b) Hint You need to express dy dx in terms of v and dv dx . 1. At time t = 0, a tank of water contains 500gal of water with 50g of salt dissolved in it. Water flows into the tank at 30gal/hr and the well stirred mixture flows out at the same rate. Assume that the concentra- tion of the salt coming in at time t is is 10 e- t lb/gal. Write a differential equation and initial value condition which could be solved to find a for- mula for the amount Q ( t ) of salt in the tank. You need not solve the equation....
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- Spring '08