Math 114-003, Fall 2007

Announcements:

  • December 10. True/false answers were added to the answer key for Spring05 final exam.
  • December 10. I post the link for an answer key for the sample final exam with some hints and comments on the solutions.
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  • December 9. I received very few e-mails about schedule conflicts with the review, so I do not plan to organize a special makeup review session. However, I’ll be available during Tuesday, so you can just schedule an appointment for Tuesday.
  • December 9. It seems that the answer key for Spring05 final exam is unavailable, so I prepared an answer key of my own with some hints and comments (not full solutions!). An answer key for the sample will be posted tomorrow.
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  • December 7. Please do not forget to bring your Penn ID to the final exam, you might be asked to show it. (It is a general policy of the department.)
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  • December 6. You can find here a sample final exam. It is slightly lengthier than the final (by a problem or two), but has a similar structure. The material not covered by the midterms (16.8,16.9, and chapters 10,18) is emphasized (half of the sample exam). It is impossible to cover everything, for example, there are no problems on exponential decay, Euler method and boundary value problems, but I hope that the sample can give you an idea of what can be asked in the final. An answer key with some hints and comments will be posted on Monday. My recommendation is as follows: repeat the material and prepare the cheat sheet, solve few old final exams (I especially recommend Spring04 and Spring05), and then solve the sample using your cheat sheet only. We can discuss the sample on the review session on Monday. If you want me to discuss any other problem, please send me an e-mail with your request.
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  • December 6. I scheduled a review on Monday, December 10, 3-5pm at DRL A7.
  • December 6. The location of the final exam is Logan Hall 17. To help you to prepare to the exam I’ll post a sample final exam soon (hopefully, tonight or tomorrow).
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  • November 30. You can find here a link to the final exam syllabus. Roughly, the exam covers chapters 13-16,10 and 18, excluding sections 13.6, 16.5, 10.5, 10.7, but there are few exceptions. So, read the above syllabus carefully.
  • November 30. On the two last lectures we will cover sections 18/2,3,4. The theoretical part will not be larger than usually, but as you will see, typical problems will require much more time to solve. Since I still want to discuss few problems of different types, I need you cooperation: please READ section 18.2 before the lecture on Tuesday and section 18.4 before the lecture on Thursday. (You can also use the review on ODE’s on the bottom of this page).
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  • November 20. A new HW is posted. Also, I posted a review on ODE’s including the material we’ll study.
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  • November 16. A solution for the second midterm is now available (on the bottom of this page).
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  • November 13. The scores for the midterm are available via gradebook. The results are much better than on the first midterm (the average is about 42 this time). An informal estimate for grades cutoff is as follows: AB cutoff is 48, BC cutoff is 38, CD is 28 and DF is 18 (this is a rough estimate only).
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  • November 10. I post here my answer to an e-mail regarding problems 8 and 9 in the sample midterm2 (I received few more questions about those problems).
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  • November 9. I posted the answers to the second sample midterm (see the HW section below).
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  • November 8. I’ll hold a review before the exam. Time and location are as follows: Friday, November 9th, from 6-7:30pm, DRL A5. Please prepare your questions before the review. I want to recall that in order to attend the make up exam you should register for it. Here is the list of students registered for the make up so far.
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  • November 7. I posted a review on multivariable calculus (on the bottom of this webpage). Two last sections concern with the material not covered by the midterm. Also, I posted two sample midterms as a part of new homework. Probably, it is worth to postpone solving them until the lecture on Thursday.
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  • November 6. Now, it is final: the second midterm covers chapter 15 and sections 16/1,2,3,4,6,7. We will study 16/6,7 on Thursday, but look through 16.7 before the class. I plan to devote half an hour to your questions, so prepare them before the next lecture. The make up will be held at 8pm; as earlier, you should register for the make up if you plan to attend it. You can find some word and tricky problems on the math114 webpage of Prof. Pemantle, and I recommend to solve at least part of those problems (some of them are easy, but there are rather difficult ones). Here are the links for your convenience:  word problems;  tricky problems; solutions for tricky problems.
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  • November 1. It is the time to start to think about the forthcoming midterm. I ask the students with a schedule conflict to e-mail me about that. The midterm syllabus has not been finalized yet, but most probably it will cover chapter 15 and sections 16/1,2,3,4,6,7. Note that section 16/5 is not in the syllabus (both for the midterm and for the final exam). My plan is to cover sections 16/4,6 on Tuesday, and to spent about half an hour to answering your questions on Thursday.
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  • October 30. A Penn Undergraduate Mathematics Colloquium will take place on Wednesday October 31 at 3:00PM in Chem 102. The speaker is Hendrik Lenstra from the Math Institute of the University of Leiden in the Netherlands. His title is, "ESCHER AND THE DROSTE EFFECT".  Professor Lenstra will give a mathematical analysis of one of Escher's prints, by means of a quite dazzling series of computer animations. The talk will be followed by tea and refreshments at 4 PM in DRL 4E17.
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  • October 23. My office hour on Wednesday, October 24 will be from 4-5pm (I’ll be holding a review in another class from 5-6:30).
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  • October 12. A solution to the midterm is posted on the bottom of this page. Also I posted a new homework, which will serve as the basis for the next quiz.
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  • October 6. It is a common policy on math114, that the students should have their penn id with them during the exam. So, do not forget to bring it!
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  • October 6. You can find here two examples of old midterms from Prof. Pemantle’s course page. The first one is here, it is from Spring2007 and contains solutions by Prof. Galvin. The second one is here, but its syllabus is slightly different (includes areas in polar coordinates, for example).
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  • October 5. I posted a review on vectors and vector functions (the material of chapters 13 and 14). See the review notes section below.
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  • October 5. I’ll hold a review before the exam. Time and location are as follows: Tuesday, October 9th, from 5-6:30pm, DRL A1. My office hour on Tuesday will be from 4-5. Also, there will be regular Sunday review sessions during the fall term from 7-9pm at DRL A2 (including this Sunday).
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  • October 5. I’d like to remind that the midterm on Wednesday covers chapters 13 and 14, except section 13.6. The regular midterm will be held at CHEM 102, from 7-8:30. The make up will be held from 8-9:30. I would like to inform you that there will be a chemistry make up around noon. So, it may happen that you will prefer to take the chemistry make up and the regular math114 midterm (in such case you enjoy a larger break between the exams). You can find here the list of students registered for the make up. If you plan to attend the make up, but are not in the list, please inform me urgently. On Tuesday or Wednesday morning, I’ll inform the students from the list about the location of the make up.
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  • October 2. Starting with Wednesday, October 3, there is going to be held a workshop for our math114 class. It may be an excellent opportunity to improve your skill of solving practical problems. The time and place are Wednesdays, from 6:30-8pm, Williams Hall, room 006.
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  • September 25. Putnam Competition will be held this year on Saturday, Dec. 1st, and it consists of two 3 hour sections during which the students have to solve 12 (rather difficult) problems. Besides the fun of solving math problems, there is also a financial incentive: the top 25 contestants nationwide receive monetary prizes, and there are also prizes for the top school teams. This year we are planning to organize weekly problem sessions before
    the exam. Any student who would like to participate or ask questions about the competition, should email apopa    math.upenn.edu.
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  • September 17. I corrected the duration of the midterms on the webpage (it is an hour and half). To avoid schedule conflict with a chemistry midterm, we plan (not a final decision yet) to hold a makeup for the first midterm at October 10th, 8-9:30pm. Please inform me urgently if the alternative time does not fit your schedule too.
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  • There is no quiz this week! (Rosh hashana holiday.)
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  • It was decided that all math 114 classes will have two common midterms, so I updated the relevant information on the webpage. This decision forces a change in the grading policy which was previously announced on the webpage; see the Evaluation section for the new policy.
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  • Welcome to Math 114!

 

General Info:

Instructor:

Michael Temkin

E-mail: temkinsas.upenn.edu (or temkinmath.upenn.edu).

Office: DRL 4N61 (215 - 573 - 1029)

Office Hours:  Tue 5-6, Wed 5:30-6:30

Lectures:  TR 9:00-10:30 DRL A1

Teaching Assistants:

Tamaz Brelidze

E-mail: brelidzesas.upenn.edu

Office:  DRL 3W8

Office Hours: Tue 11-12, Thu 11-12

Recitations:

  • 114-221: W 8:00-9:00 DRL 4E9        
  • 114-222: W 9:00-10:00 DRL 4N30
  • 114-223: F 9:00-10:00 DRL 3C8
  • 114-224: F 10:00-11:00 DRL 3C8

 

Mohammed Shaik Hussain Ali

E-mail: mohammedseas.upenn.edu

Webpage: www.seas.upenn.edu/~mohammed/Math114

Office:  DRL 4N11

Office Hours: Thu 3-4, Fri 3-4.

Recitations:

  • 114-225: W 8:00-9:00   Towne 307
  • 114-226: W 9:00-10:00 Towne 307
  • 114-227: F 9:00-10:00   DRL 3C2
  • 114-228: F 10:00-11:00 DRL 3C2

Texts:

James Stewart, Calculus. Brooks/Cole, fifth edition, 2003.

Maple/Calculus Lab Manual for Math 103/104/114/115.

Evaluation:

TA's grade                                                                                                           20%

Midterm I;   Wednesday, October 10  7-8:30pm at CHEM 102                         20%       

Midterm II;  Monday, November 12  7-8:30pm at CHEM 102                          20%

Final Exam; Wednesday, December 12  9-11am at Logan Hall 17                    40%        

All grades will be posted on the Blackboard. The midterm and the final exams are common for all math114 sections.

At the end of the semester, everyone who has not withdrawn from the class will get a grade. Incompletes will not be given to avoid F's.

Course description:

Here is math 114 homepage of Math Department. It contains syllabus, core problems, old final exams, etc.

The course can be divided to four parts: I vectors and vector functions (chapters 13 and 14), II partial derivatives (chapter 15), III multiple integrals (chapter 16), IV differential equations (chapters 10 and 18).

Maple is an optional tool which can turn out to be helpful in your studies. It can also be used in lecture demonstrations.

Exams:

All exams are without books and calculators. You may bring one handwritten cheating sheet of size 11.5"x8" (both sides).

Homework:

The exercises are assigned on Fridays on this webpage. The homework is not obligatory, but I strongly recommend to do its regular part (without *) in full details.

Ways to get help:

  • Sunday night reviews: on Sundays, from 7-9pm at DRL A2.
  • Math and Maple Centers – see the link.
  • The Tutoring Center - check out their (free!) "Satellite Centers", and
  • Math 114 Workshops: Wednesdays, from 6:30-8pm, Williams Hall, room 006.

Homework Assignments:

More difficult supplementary problems are marked with *; work on them if it is interesting to you. The problems with * are not obligatory (will not show up in quizzes) but may be helpful for a deeper understanding of the course.

  • September 8. HW 1. 13.1/11,15,16,36; 13.2/8,14,17,22,24.
  • September 14. HW 2. 13.3/1,8,12,13,24,26,32,40,41*,50*,53*; 13.4/4,9,11,12,18,24,25,32,34 (problems 32,34 use triple scalar product, which will be discussed in class on Tuesday),39*,40*,41*,42*,43*,44*,45*. There are many problems this time, but most regular problems (without *) are easy.
  • September 21. HW 3. 13.5/1,8,14,16,18,22,30,37,42,46,49,54,65,69,72.
  • September 28. HW 4. 13.7/4,19,24,38,43,50; 14.1/6,12,16,39,41*; 14.2/6,10,18,25,31 (find cos(alpha) only),37,51,50*.
  • October 5. HW 5. There is no quiz next week. The homework is comprehensive, and it should help you to prepare to the midterm. Check your knowledge on true-false quizzes on pages 881 (chapter 13) and 918 (chapter 14). I’ll post the answers to even problems after the weekend. Chapter 13, review exercises (page 881) 7,11,17,19,21,39,41,43,45,47. Chapter 14, review exercises (page 918) 5,9,11,15,17,19.
  • October 12. HW6. 15.1/17,30,31,32,35,53-58,62; 15.2/10,11,19,31; 15.3/17,37,44,57,82,85,91*.
  • October 19. HW7. 15.4/3,6,15,28,32,37,41*,42*; 15.5/5,10,14,22,32,36,41,42,48*,53* (some exercises are based on the material of  section 15.5 which will be studied on Tuesday).
  • October 26. HW8. 15.6/4,9,19,24,29,34,36,37*,52,54,63*; 15.7/3,7,10,28,35*,49,53*,54*,(read the proof of theorem 3 from section 15.7)*.
  • November 1. HW9. 15.8/5,21,23,39(two constraints),48; 16.1/6; 16.2/19,22,33; 16.3/13,14,15,19,25,26,43,46,48,49.  15.8/43*,44*, 16.2/35*,36*.
  • November 7. HW10, part I. You can find here two examples of old midterms from Prof. Pemantle’s course page. The first one is here, it is from Spring2007 and contains solutions by Prof. Galvin (questions 8 and 9 are not covered by our midterm syllabus). The second one is here, it is a multiple choice exam and the answer key will be available later. I strongly recommend to use these exams for a real simulation of an exam: no coffee breaks, no calculators, no discussions, etc. Probably, it is a good idea to first fully prepare for the exam, including your cheat sheet, and to then check your knowledge on the sample exams.
  • November 8. HW10, part II. 16.4/7,17,21,25,36*; 16.6/9,12,23*,24*;16.7/3,13,17,27,31,33,49. Also, I recommend to solve true-false quizzes after chapters 15 and 16 (in chapter 16 solve only problems 1,2,3,4,5,6), and you can check your theoretical knowledge on concept checks questions (in chapter 16 the relevant questions are 1,2,3,6,7).
  • November 9. The answer key  to the second sample midterm (please, let me know if you find wrong answers).
  • November 16. HW11. 16.8/2,3,5,6,11,21,33,35; 16.9/3,5,8,9,13,15.
  • November 20. HW12. 10.1/1,3,5,9,11; 10.2/2,3,4,5,6,21,23(calc); 10.3/2,4,12,20,37,41,42,44*.
  • November 29. HW13. 10.4/3,9,13,19(use a calculator),22; 10.6/1,3,15,19,23*,25*; 18.1/1,5,9,13,17,19,23. Also, study the asymptotic behavior of the solutions for the differential equations 10.3/19,20. Here is a link for a nice online slope calculator (it requires Java), use it (or maple) to plot few solutions. If you need to practice more on word problems I can recommend to solve also the following problems: 10.4/11,15 and problems 25,26,28 from the list of word problems (another link is on the top of this page).

Lectures:

Each lecture's title is followed by relevant core problems. Make sure you can solve them (you can skip the details if the problem is easy for you). More difficult supplementary problems are marked with *.

  • September 7. Section 13.1, Ex. 6,18,21,23,25,29,41. Section 13.2, Ex. 1,4,8. Read sections 13.1 and 13.2; look through section 13.3.
  • September 11. Section 13.2, Ex. 18,24. Section 13.3, Ex. 1,2,4,8,11,14,17 (no need to approximate). Read section 13.3; look through section 13.4.
  • September 13. Section 13.3, Ex. 37,41,49*,53*,54*. Section 13.4, Ex. 2,9,12,26. Read section 13.4; look through section 13.5.
  • September 18. Section 13.4 (triple scalar product), Ex. 33,39,45. Section 13.5 (lines), Ex. 3,15,16,17. Read section 13.5; look through sections 13.7 and 13.6.
  • September 20. Section 13.5, Ex. 1,30,38,51,61,73. Read section 13.7; look through section 14.1.
  • September 25. Section 13.7, Ex. 4,10,13,20,28,34,36,50. Section 14.1, Ex. 4,6,9. Read sections 14.1 and 14.2; look through section 14.3.
  • September 27. Section 14.1, Ex. 11,16,19-24,34,39. Section 14.2, Ex. 3,10,17,21,22,29,31,47. Read sections 14.2 and 14.3.
  • October 2. Section 14.3 (arclength and curvature), Ex. 2,7,10,14,17,26. Read sections 14.3. Look through section 14.4.
  • October 4. Section 14.3 (normal and binormal vectors, and osculating plane), Ex. 40,47,49*,50*. Section 14.4, Ex. 1,2,5,21,22,28,33. Read section 14.4. Repeat chapters 13 and 14 towards the midterm. The midterm covers these two chapters except section 13.6 (though it might be useful to look through that section).
  • October 9. Section 15.1, Ex.1,2,6,11,30,32. Section 15.2 (limits), Ex. 7,10,11,37,39. Read sections 15/1,2 and look through sections 15/3,4.
  • October 11. Section 15.2 (polar and spherical substitutions). Section 15.3, Ex. 1,4,5,16,21,51,66,83. Read sections 15.3 and 15.4, look through section 15.5.
  • October 18. Section 15.4, Ex. 2,12,20,24,31. Section 15.5 (chain rule: case 1), Ex. 4,36.
  • October 23. Section 15.5 (chain rule case 2), Ex. 8,16. Section 15.6, Ex. 3,9,15,23,27,36,38. Read sections 15.6 and 15.7.
  • October 25. Section 15.7, Ex. 1,3,5,11,23,37. Read section 15.8 and look through section 16.1.
  • October 30. Section 15.8, Ex. 1,2(maple),4,10,23,25,39. Section 16.1, Ex. 3,6,8,12,17. Section 16.2 (Fubini’s Theorem). Read sections 16.1 and 16.2; look through sections 16.3 and 16.4.
  • November 1. Section 16.2, Ex. 4,5,14. Section 16.3, Ex. 3,10,24,39,43. Read section 16.3, and look through sections 16.4 and 16.6.
  • November 6. Section 16.4, Ex. 1,3,7,10,18,21,33,36*. Read section 16.4. Look through sections 16.6 and 16.7.
  • November 8. Section 16.6, Ex. 4,14. Section 16.7, Ex. 3,8,16,22,26.
  • November 13. Section 16.8, Ex. 3,8,18. Section 16.9, Ex. 2,12,13,14. Read sections 16.8 and 16.9 and look through sections 10.1 and 10.2.
  • November 15. Section 16.9. Repeat chapter 16. Section 10.1. Ex. 1,5,8,9,11,14. Read sections 10.1 and 10.2. Look through section 10.3.
  • November 20. Section 10.2. Ex. 1,2,3,4,5,6,12. Section 10.3. Ex. 4,6,13,22(maple),32,42. Read sections 10.2 and 10.3, and look through section 10.4 and 10.6.
  • November 27. Asymptotic behavior of solutions of separable equations, see an outline  (the material is not in the text!). Section 10.4. Ex. 4,16,22. Section 10.6. Ex. 8,9,15,29. Read sections 10.4 and 10.6, and look through appendix G and section 18.1 (we will study 18/2,3,4 on the next week).
  • November 29. Section 18.1 (excluding boundary value). Ex. 1,2,5,14,15,17. Appendix G (quadratic equations and complex exponentials). Ex. 22,45. I recommend to read the whole appendix for a better understanding of complex numbers. Read sections 18.1 and 18.2, and look through section 18.3.
  • December 4. Section 18.2. Ex. 1,2,3,12,20,26. Read sections 18.3 and 18.4. Section 18.4 is based on power series, so certain familiarity with them is assumed (see sections 12.8, 12.9 and 12.10). You can also use a review on power series (see below) to recall that material.
  • December 6. Section 18.3. Ex. 2,3,5,6. Section 18.4. Ex. 1,3,12. As I promised, I post here an example of solving a linear ode using power series in compact form (the sigma notation).

Review notes:

  • October 7. A brief review of the material from chapters 13 and 14 is here (vectors and vector functions). Any comments on (possible) mistakes/inaccuracies are welcome.
  • November 7. A review of the material from chapters 15 and 16 is here (partial derivatives and multiple integrals). Any comments on (possible) mistakes/inaccuracies are welcome.
  • November 19. A review on material from chapters 10, 18 and appendix G is here (first and second order ODE’s and complex numbers). Last update was made on November 26th. Any comments on (possible) mistakes/inaccuracies are welcome.
  • November 26. Here is a link to two-page notes by Prof. Pemantle. It contains materials on the asymptotical behavior of solutions of separable differential equations. This topic is not covered enough in the text!!
  • December 4. For you convenience I post here a brief review on power and Taylor series. This is a material of math104 which is assumed to be more-less known, since we will use power series to solve ode’s which cannot be solved exactly. This review can serve you to recall what power series are, though you do not have to know all the details.
  • December 7. You can find here an example of solving linear ode with power series.

Solutions:

  • October 13. A solution to the first midterm is here. Any comments on (possible) mistakes/inaccuracies are welcome.
  • October 14. Some comments concerning the solution to the midterm may be found here. The goal of these comments is to describe few typical mistakes and to outline few alternative (usually more straightforward but more laborious) solutions.
  • November 16. A solution to the second midterm by Prof. Pemantle is here.