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Math 20B: Winter 2006: Calculus for Scientists and Engineers

# Math 20b: Virtual Office Hours

## Email me a question!

Since I post the answers here, everyone benefits.

 > hi prof. stein, im in your math 20b class, > how would you recommend us to study for the math final? I'll lay out a strategy in class on Wednesday. I'd tell you something now, but I'm not the only person writing the final and it doesn't exist yet. The profs teaching 20b are meeting Tuesday to discuss the final, so by Wednesday I'll know what we're expecting to test with the final. That said, I think that basically the final will test your ability to solve problems similar to the ones on the homework for the whole course. So you could go back through the listed homework problems and do some of them again, do variations on them, and do similar ones from the book. -- William  > Hi again Professor Stein, > > I was wondering if there'd be a way to find out the solutions & the > manner to solve the problems on the practice midterm before class on > Wednesday. I just spent 5 minutes punching all but the first one into SAGE, and have logged the session here for you. I don't certify correctness of any of the answers, but they are very likely to be correct. I hope you find this useful.  On Saturday 25 February 2006 17:08, you wrote: > I believe that if you post up the answers to the supplement questions > with step by step explanations it would dramatically help students, > including myself, in class. You are an excellent teacher and clearly > saavy with computers as can be seen through your website, so I don't > see why this should be a problem. Thanks so much for the help if you > do it :) Check out the new link I just added at http://modular.math.washington.edu/20b/ namely to http://modular.math.washington.edu/20b/supplement.pdf.  More solutions from the TA: From 4.6: 2. 1/(x-1)^2 + 1/3(x-1) - 1/3(x+2) 4. 1/2x - (2x+1)/3(x^2+1) + (x+8)/6(x^2+4) 5. 5/12(x-2) - 1/2(x+1) + 1/2x - 1/6(x+1) - 1/4(x+2)  On Thursday 16 February 2006 20:54, you wrote: > Hello there Professor Stein, this is Chris Stollar from your Calc 20b > class, and I was wondering if you had the answers to Supplement 4.6 > questions 2, 4, 5. That would be greatly appreciated if you could get > those for me. Thank you in advanced, see you tomorrow in class. Bye - > Chris Stollar If you paste this into the online SAGE calculator (http://modular.math.washington.edu/calc/) and click the "SAGE" button you'll get the partial fraction out: maxima('(2*x+1)/( (x-1)^2 * (x+2))').partfrac('x').display2d() You can change what's in the quotes to any rational function in x. William  The TA has some more remarks about the homework problems in the supplement: We say r(x) has a pole at 'a' if lim_{x->a} r(x)= +/-infinity. For example: 1/(x-2) has a pole at 2 1/(x-3) has a pole at 3 x/(x-2) has a pole at 2 Multiplicity is basically the power of the denominator: 1/(x-2) has a pole at 2 of multiplicity 1 1/(x-2)^10 has a pole at 2 of multiplicity 10 A pole at infinity means lim_{x->infinity} r(x)= +/-infinity x^2 has a pole at infinity of multiplicity 2 x^2/x-2 has a pole at infinity of multiplicity 1 (x-7)^10/(x-6)^4 has a pole at infinity of multiplicity 6 For 3a, the pole is at -1. How do you do this: 1. factor the denominator and get (6+x+x^3)=(x+1)(5x^2-5x+6) 2. note that lim_{x->-1} 3/((x+1)(5x^2-5x+6)) = infinity. By definition, this means there is a pole there. Does it have a pole at infinity? No. lim_{x->infinity} 3/((x+1)(5x^2-5x+6)) not= infinity. By definition, this means there is not a pole there. For 3b, it has a pole at 2 by the logic above. It has multiplicity 1 basically because the power of (x-2) in the denominator is 1. If the equation were (3-2x)/((x-2)^10(x^2+5x+7)), then it'd have a pole at 2 of multiplicity 10. A caveat: (2-x)/((x-2)(x^2+5x+7)) does NOT have a pole at 2 since the (x-2) term cancels. Likewise, (2-x)/((x-2)^10(x^2+5x+7)) has a pole at 2 of order 9. The roots of (x^2+5x+7) are complex numbers, so there are no real poles from that factor. Let me know if this helps.  The TA has some remarks about the homework problems in the supplement: For 1, just multiply everything out. You should get x^3-6x^2+11x-6 For 3a, the pole is at -1. How do you do this: 1. factor the denominator and get (6+x+x^3)=(x+1)(5x^2-5x+6) 2. note that lim_{x->-1} 3/((x+1)(5x^2-5x+6)) = infinity. By definition, this means there is a pole there. Does it have a pole at infinity? No. lim_{x->infinity} 3/((x+1)(5x^2-5x+6)) not= infinity. By definition, this means there is not a pole there. For 3b, it has a pole at 2 by the logic above. It has multiplicity 1 basically because the power of (x-2) in the denominator is 1. If the equation were (3-2x)/((x-2)^10(x^2+5x+7)), then it'd have a pole at 2 of multiplicity 10. A caveat: (2-x)/((x-2)(x^2+5x+7)) does NOT have a pole at 2 since the (x-2) term cancels. Likewise, (2-x)/((x-2)^10(x^2+5x+7)) has a pole at 2 of order 9. The roots of (x^2+5x+7) are complex numbers, so there are no real poles from that factor. As for your quiz, that is what the spreadsheet says. If your actual quiz has a different score, I'll happily change it. You can pick it up during my office hours.  Professor Stein asked me to reply to this on his behalf. The Math 20B final examination will be held Wednesday of Finals Week from 7:00pm - 10:00pm, as per the announcement above the Math 20B listings in the Winter 2006 Schedule of Classes, which reads as follows: * All Math 20B lectures will have common examinations. The final exam will be Wednesday, March 22, 2006, 7:00-10:00 pm.* This should also be the time listed in your Final Planner; however, it appears that the TritonLink programmers have missed something since other students in Professor Stein's lecture have Tuesday 3:00pm - 6:00pm listed for the time as you apparently do. Thank you for pointing this out. I will work to get it corrected as soon as practicable. John Eggers Math 20B Coordinator  On Thursday 09 February 2006 01:43, you wrote: > What is the TA's email address? It's Dan Budreau: [email protected]  > Do we get to use a cheat-sheet on the midterm? Yes. one 8.5 x 11 double-sided hand-written paper. Enjoy!  > Hi I was wondering if there's a way for us to view the correct answers > and solutions to the practice test. that would be very helpful. Here's a long answer from the course coordinator about solutions for the midterm. I agree with him: "I prefer not to post solutions. This is somewhat controversial: Many faculty prefer to post solutions. My own opinion is that the real reason for posting solutions is to put an end to students asking for them (which, of course, has nothing to do with the question of whether they're helpful or not). In fact, I would suggest that posting solutions is actually harmful because many students will look at them before they have even tried to solve the problems on their own. Then, they will think to themselves "I understand that," put it in their notebook and forget about it, having never even flinched the mental muscle required to solve it on their own. I tell students that it is very important that they face the situation of not having "the solution" readily available in order to develop their own ability to find "the solution" and to check it themselves for correctness. That said -- I'll answer any of your questions on Wednesday.  > I was wondering if we'll have to graph certain polar curves. For > example, one of our homework problems is r = 3cos(theta). Then we have > to find the area that it encloses. Will the graph be provided for us or > do we have to draw one ourselves? If you don't know how to draw graphs, what is provided might be much more difficult for you to make sense out of. But there will be something of a graphical nature provided.  On Tuesday 10 January 2006 19:20: > Hi, I was just wondering if disscussion for math20b is mandatory. Your grade will be completely determined by your quiz scores, midterms, and final. I very strongly recommend that you go, but I won't record whether or not you go and will not take whether or not you went into account in any way when determining your grade.  On Tuesday 10 January 2006 16:01: > Hello, my name is Slim Shady and I am in your MWF 4-4:50 Math 20B > course. I was wondering if the dates of your quizzes are the same ones > posted on the main course webpage? Or in other words, do all of the Math > 20B courses take thier quizzes on the same days? Yes, the dates are the same, i.e., all 20b's do the quizzes on the same day.  On Monday 09 January 2006 18:25: > Is there any homework for math 20b? The homework is listed here: http://www.math.ucsd.edu/~jeggers/math20b/homework.html NOTE: You do not turn the homework in. Instead there will be quiz on Friday, January 20 that will consist of two problems from the homework for Sections 5.3 - 5.5. You can discuss your solutions to the homework problems with the TA (Dan) during the discussion section. You should do every homework problem.