Homework

Math 102

Prof. Donnay

Fall 2006

* denotes challenge problems.

Wk	Due	Section	Problems: Recommended	To be Handed In
1	Wed 9/6			review sheet with basics of differential and integral calculus.
	Mon 9/11			Sect 3.1 (p. 133)#31; Sect 3.6 (p. 181) #4, 17, 26, 34; Sect 7.1 # 5, 6, 23, 25; Sect 7.2 #2ab, 7, 8, 13, 17, 24, 29, 30, 34, 35, 38.
	Mon 9/11			Quiz 1 You have 15 minutes to do this quiz. You may not use any books or notes while you do the quiz nor discuss the quiz with anyone. There is one page to the quiz.
2	Wed 9/ 13			Sect 7.2 #71, 72, 73, 76; Sect 7.3 #3, 4, 7, 10, 14, 15, 23, 24, 45*, 57
	Mon 9/18			Sect 7.2 #55ab, 61(also determine when f is increasing/decreasing and make a sketch of f), 75, 78, 79(include sketch), Sect. 7.3 #25, 27, 28, 29, 30, 43, 44, 47*, 49 Sect. 7.4 #2, 4, 8, 13, 21, 23, 25, 30, 36, 65, 66, 68, 70, 71, 74, 78(make a sketch).
	Mon 9/18			Quiz 2. You have 20 minutes to do this quiz. You may not use any books or notes while you do the quiz nor discuss the quiz with anyone. You may use a calculator only on problem 3b. There are two pages to the quiz. Show your work clearly.
3	Wed 9/20			Worksheet with area of boxes using right hand endpoints. Sect. 5.1 #3, Summation problems. Sect. 7.4 #24, 57 (in addition to what is asked, find when f is increasing/decreasing and graph f).
	Mon 9/25			Sect 7.4 #6, 27, 36, 39, 40, 43, 58 (in addition to what is asked, find when f is increasing/decreasing and graph f; give all relevant information about f), 79. Sect. 6.2 #1, 3, 5*, 41, 47*(lay the cone sideways centered along the x axis). Do the volume in a cup problem. To bring to class for group work; keep separate from other homework: Review sheet for trig Quiz 2: you should use your calculator for this quiz.
4	Wed 9/27			Mathematica 2 assignment due.
	Wed 9/27			Sect. 7.5 #3, 6, 7, 11*,22, 23, 25, 31, 36, 59, 60, 61, 62
	Mon 10/2			Sect. 7.5 #9, 17, 20, 49*, 64, 70, 71 Sect. 8.8 #supplemental questions, 3, 6, 8, 9, 21. You may want to make a photocopy of your work that you can check against an answer key that I will put in the library. Quiz 4: no calculator. Quiz 4 Feedback
5	Mon 10/9			Sect 7.7 #16, 18, 23, 28, 34 Sect 8.1 #1, 4, 6, 22, 34 Sect 8.8 #19, 47b, 49, 50; for these last three do not find the value of the integral, simplify determine if it is finite or infinite by comparison. Quiz 5
				Mathematica 3 assignment (Mathematica, worksheet) due Wed. Oct 25^th.
	Tues 10/10			Worksheet on convergence/divergence from class and worksheet on graphing area under curve. Class survey
	(Wed 10/11) Now due Friday 10/13 instead at 5pm Due outside Prof. Donnay’s office by 5pm			Sect 8.1# 16, 36, 41, 42(ab) Sect. 8.6 #2, 6, 10, 22 – for these problems, you will often have to make an initial u, du substitution to make your integral look like one in the tables.
	Friday 10/13 5pm at Prof. Donnay’s office.			Mid-term rewrites (instructions).
6	Mon 10/23			Length of curve worksheet. Other homework problems. Sect 8.8 #51, 52, 54 Quiz 6
	Wed 10/25			Sect. 7.5 # 72 – do not use integral tables on this. Convert into arctan form by factoring, substitution. Sect 7.7 #1, 2 Determine the length of the curve y = x^2 with x in the interval [0,4]. Sect 9.1 #2 - Also: draw this curve. It is part of a circle. What is the radius of this circle? Repeat the problem for the function y = (R^2-x^2)^1/2. Use your answer to derive the formula for the circumference of a circle of radius R. Sect 9.1 #17.
	Friday 10/27 5pm			Who Does Which Problem, Discovery Assignment. Step 1
7	Mon 10/30			Sect 7.7 #37, 41, 49 (Hint: factor out x). Sect 8.6 #10, 22 (do again from earlier homework if you had trouble with the problems), Sect 8.7 #5 – do this example with Midpoint and Trapezoid rules (not with Simpson’s rule), 31a. Redo: Find the length of the curve given by the function y = (R^2-x^2)^1/2with x in the interval [0 , R ]. Use your answer to derive the formula for the circumference of a circle of radius R. Quiz 7 Instructions for quiz: You may have 30 minutes to do this quiz. You will need to use your integral tables. Other than that, you should not use any books or notes while you do the quiz nor discuss the quiz with anyone. You may not use your calculator.
	Wed 11/1			Discovery Project: Using the rubric, read through all the papers (these were handed out in class) from your problem and fill in the peer assessement slip for each paper to give your classmates useful feedback. Bring these slips to class on Wed. Be sure to assess your paper too. Sect 8.7 # 30 Introduction to Differential Equations do the problems on the worksheet. You will discuss them with your group on Wed.
	Thur 11/2 3pm			Using the feedback you got from your peers to revise your paper. Hand it in to the bin outside Prof. Donnay’s door by 3pm on Thur. Attach to it your original draft and also the reflection sheet
8	Mon 11/6			Sect 8.7 # 17, 29, 32 (what is the relationship between speed v(t) and distance d(t)?) Sect 10.1 #1, 3(plug sin(kt) into the equation and see what value of k will lead to a solution), 4 (similar: plug exp(kt) into the DE and see what value of k will lead to a solution). Sect. 8.8 #48b, 52 On the course blackboard site in Group Tools; give an example of a differential equation and explain what it is used for – one paragraph write up; include a web link if you can. If you use the Firefox browser, you will should not have any problems (some browsers have trouble with this feature of Blackboard). Quiz 8 (you will need to use a calculator. The quiz is on one of: midpoint, trapezoid, Simpson’s method)
	Wed 11/8			Give oral presentations to your group about your differential equation. Sect 10.4: #3, 4a, 6(ab). For the population example given in class: P(1790) = 3.9 million; P(1800) = 5.3 million: (a.) Calculate how long it takes for the population to double from the level of 1790. (b.) Calculate how long it takes for the population to double from the level of 1800. (c.) What do you notice about these two doubling times? (d.) Make a conjecture about the doubling time for an exponential function. We make a model of the temperature of an object. An object is placed in a room where the temperature is 130 degrees (Celsius). The rate of change of the temperature of the object is proportion to the difference between the temperature of the room and the temperature of the object. Write a differential equation that expresses this statement. State clearly what variables you are using, what the variables represent and give units to the variables.
9	Mon 11/13			Write up a possible question for midterm 2 together with an answer key. List of topics for midterm 2. Homework questions. Solution of cooling equation. Quiz 9 (no calculators).
	Wed 11/15			Mathematica Assignment 4 is due. Study for midterm exam by doing problems from sections you had trouble with. Approximations: Determine the equation of the tangent line to the function y = f(x) = -1/6 + 3x/2 – 3x^2/2 + 7x^3/6 that goes through the point (1, f(1)).
10	Mon 11/20			Midterm exam is due
11	Mon 11/27			Read chapter on Rwanda. Worksheet on population growth and polynomial approximation. Look through Final projects options and think about which you would like to do.
	Wed 11/ 29			Initial project proposal/partner is due. Series worksheet due. Note – if after the 6^th partial sum sn you are not yet sure about the behaviour of sn, you can take more partial sums. Population prediction problem. (We are going over this work in class; do not have to had in to graders).
12	Mon Dec 4			Final project proposal; partner is due. Homework problems due Quiz 10: note – you will be asked to write out the general formula for a Taylor Series and to give the Taylor Series for one of: e^x, sin(x), cos(x). Mathematica Assignment 5 (Mathematica notebook, worksheet) due.
	Wed Dec 6			Sect 12.1 #18, 20, 59 Sect 12.2 #17, 19 – also write out the first few terms in the series. Consider using the integral approach (as we did in class). Do you think this series will converge or diverge?
13	Mon Dec 11			Homework problems due. Quiz11. On your Quiz 10, write out the Taylor Series for cos(x) using the summation notation – hence you will need to find the formula for the kth term – and resubmit. Last chance to ask Prof. Donnay questions about project is 4pm.
	Wed Dec 13			Last class: Final projects are due. Rubric for final project. Final Project Reflection sheet is also due.
				Final Hw: Not to be handed in. Answer key in library. Sect 12.8 #30, Sect. 12.10 #3, 4, 40, 42 (for these last two, first write out the Taylor Series for sin(x) and e^x; then simplify; then integrate).