Math 104-007, Fall 2007

Announcements:

 

  • December 10. First midterm (which was erased by mistake) is now available from this webpage.
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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. I prepared an extended answer key to Fall06Makeup with some hints and comments (though not full solutions!).
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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.)
  • December 7. My recommendation for preparation to the final exam is as follows: repeat the material and prepare the cheat sheet (you can use reviews on the bottom of this page, homework and core problems), then solve few old final exams (I especially recommend Fall06Makeup and Spring07). We can discuss these two exams 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, 11am-1pm at DRL A6.
  • December 6. The location of the final exam is Huntsman/G06.
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  • December 5. A solution for the sample midterm has been posted.
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  • December 4. The syllabus for the midterm is as follows: sections 12.1—12.10 but without the remainders (I do not promise anything regarding the bonus problem 11). In addition to the sample (which is rather similar to the midterm) I also posted a list of recommended problems for your practice (only on the new material: 12.9 and 12.10).
  • December 4. I posted a sample midterm, see the HW section below.
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  • December 3. I scheduled a review session on Wednesday, December 5, 6:30-8:00, DRL A8. Prepare your questions!
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  • November 20. It was a relatively typical mistake in this midterm to circle a wrong answer (with a correct answer written in the work). I cannot accept those answers as correct ones, but I decided to keep the information about such cases in a separate column in the gradebook (it is called “incorrect circling”). These points will not be added to the total curve, but I’ll take them into account when deciding about the final cutoffs. If you want me to update this column in your gradebook, you should show me such a mistake (just a wrong circle) in any of the midterms.
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  • November 20. The results of midterm3 were better than the results of midterm2. This time rough cutoffs are AB – 80, BC – 60, CD – 40.
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  • November 20. I posted a new HW and a review on sequence and series (it covers all material we’ll study).
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  • November 13. I scheduled a review session on Wednesday, November 14th, from 7:15-8:30 in DRL A5 (on the first floor). Also, I posted a solution to the sample midterm.
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  • November 12. I posted a brief review on chapters 9 and 11 (on the bottom of the webpage). Also, I’d like to clarify: in section 9.5 we cover only the definition of the probability density function and of the mean value; specific distributions (e.g. normal) were not covered.
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  • November 9. The third midterm will cover sections 9/1,2,5 and 11/1,2,3,4. I posted a sample midterm in the HW section below.
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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 22. Solutions for the sample midterms and a brief review on methods of integration were posted onto the webpage (on the bottom of the page).
  • October 22. The midterm on Thursday will cover sections 1,2,3,4,5 and 8 from chapter 8.
  • October 22. I’ll be holding a review session on Wednesday, October 24, 5-6:30pm in DRL A1, and my office hour is shifted to 4-5pm.
  • October 22. Wednesday workshops are relocated as follows: 3C4 in DRL from 5:30-7pm. There is no workshop this Wednesday!
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  • October 9. The midterms II and III are shifted by a weak. In particular, the next midterm is on Thursday, October 25.
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  • October 5. Math104 workshops will be held at the following time/location: Monday, from 5-6:30pm at Williams 218; and Wednesday from 5:30-7pm at DRL 4E19. It will basically be a review of materials and assistance on any HW questions you might have.
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  • October 5. My office hour on Tuesday, October 9th will be from 4-5pm instead of the usual time from 5-6pm (from 5-6pm I’ll hold a review in my math114 class).
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  • September 27. The first midterm will be held in class on Tuesday, October 2. The material which we cover is chapters 6,7 excluding sections 6.4 and 7.6. Even if your recitation is on Wednesday, you may attend a Monday recitation on October 1. Also, I’ll hold a review before the midterm on Monday, October 1, 6-7:30pm, DRL A2. Prepare your questions towards the review!
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  • September 25. Putnam Competition will be held this year on Saturday, December 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 18. I was informed that the tentative date of the first midterm (September 27) has a “schedule conflict” with the Sukkot holiday. It forces me to reschedule the midterm for Tuesday, October 2.
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  • September 13. I posted a new homework and I’ll try to assign homework on Thursdays in the future (the reason is that our recitation days are Mondays and Wednesdays). Also, I posted a review of the material on areas and volumes (see the Review notes section below).
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  • September 12. The answer key to the diagnostic test is here, but the link will be disabled soon. It is ok to score 10 or above for part I and 15 or above for part II.
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  • September 11. The days of the recitation groups 265-268 were misprinted on this webpage. The correct days are Monday for sections 265 and 266 and Wednesday for sections 267 and 268.
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  • Welcome to Math 104!

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 12-1:30pm DRL A4

Teaching Assistants:

·  Andrew Silberman (215-898-5066)

·  E-mail: sandrewmath.upenn.edu

·  Office: DRL 4N33

·  Office Hours:  Mon 1:30-2:30, Wed 3-4

·  Recitations:

  • 104-261: M 9:00-10:00    DRL 2C6
  • 104-262: M 10:00-11:00  DRL 2C6   
  • 104-263: W 8:00-9:00      DRL 3C4   
  • 104-264: W 9:00-10:00    DRL 3C4

 

·  Sridevi Narayanan

·  E-mail: srideviseas.upenn.edu

·  Office: DRL 4N11

·  Office Hours: Mon 11-12, Wed 10-11

·  Recitations:

  • 104-265: M 9:00-10:00     DRL 4E19
  • 104-266: M 10:00-11:00   DRL 4E19
  • 104-267: W 8:00-9:00       DRL 4C8
  • 104-268: W 9:00-10:00     DRL 4C8

Texts:

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

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

Evaluation:

·  Midterm I;   Thursday, September 27  (Chapters 6 and 7)                              15%  The midterm is rescheduled for Tuesday, October 2 (to avoid time conflict with the Sukkot holiday) !!!

·  Midterm II;  Thursday, October 18      (Chapter 8)                                         15%  The midterm is rescheduled for Thursday, October 25.   

·  Midterm III;  Tuesday, November 13   (Chapters 9 and 11)                            15%  The midterm is rescheduled for Thursday, November 15.

·  Midterm IV;  Thursday, December 6     (Chapter 12)                                      15%  

·  Final Exam; Wednesday, December 12  9-11am    at   Huntsman/G06            40%

All grades will be posted on the Blackboard. The midterm exams will be held at class; their dates are tentative.

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 104 homepage of Math Department. It contains syllabus, core problems, old final exams, etc.

The course can be divided to four parts (accordingly to midterms): I applications of integration and inverse functions (chapters 6 and 7), II techniques of integration (chapter 8), III lengths, areas, parametric and polar curves (chapter 9 and 11), IV series (chapters 12).

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 Thursdays on this webpage. The homework is not obligatory, but I strongly recommend to do it in full details.

Ways to get help:

  • Sunday night reviews: on Sundays, from 7-9pm at DRL A1.
  • Math and Maple Centers – see the link.
  • The Tutoring Center - check out their (free!) "Satellite Centers", and
  • Math 104 Workshops: Monday, from 5-6:30m at Williams 218; Wednesday, from 5:30-7pm at DRL 3C4.

Homework Assignments:

More difficult problems are marked with * (work on them if it is interesting to you).

  • September 8. HW 1. 6.5/1,3,5,7; 6.1/9,15,17,23.  
  • September 13. HW 2. Chapter 6, review exercises on pages 406-407: 1,3,5,9,10,12,15,16,23,24,30,26*.
  • September 20. HW 3. 7.1/33,37,39,43,48*; 7.2/27,29,39,71,73, 85*,86*,87**; 7.3/8,15,25,33,51,63,47*; 7.4/11,25,67,73. (There are many problems this time, but most of regular problems (without *) are easy and short.)
  • September 27. HW 4. 7.5/7,20,25,43,62,65;7.7/15,19,25,29,59,47*. The second part of the homework is given in the form of a sample midterm, and you can find it here. Do not expect to find exactly the same problems in the midterm, but it should give you a good practice. The recommended time is 5 minutes per problem. I’ll post the answer key on Sunday evening and a handwritten solution on Monday evening.
  • October 5. HW 5. 8.1/ 3,5,9,13,23,29,33,41*,43*,44*,65*;8.2/1,3,5,17,39.
  • October 12. HW 6. 8.2/23,27,31; 8.3/3,5,7,11,13,21,29; 8.4/3a,4a,7,11,13,17.
  • October 18. HW 7. 8.5/7,4,15,19,23,29,47,54. The second part of the homework is given in the form of two sample midterm: sample2, sample2b. The recommended time is 5 minutes per problem. The following problems involve improper integrals from section 8.8: sample2/3,4,5,7,10; sample2b/1,3,4. You can either skip them and wait until Tuesday, or read section 8.8 and solve them. Also, you can solve those problems only for indefinite integral. The material covered by midterm is as follows: chapter 8, sections 1-5, 8 (we will study sections 8.5 and 8.8 on Tuesday).
  • November 1. HW8. 8.7/15,27* (requires careful reading of 8.7); 8.8/11,13,15,24,31,36; 9.1/5,7,11,15,14*; 9.2/3,5,7,13,15,25*,35*,36*.
  • November 8. HW9. 11.1/11,13,28; 11.2/5,7,19,30,37,41,57; 11.3/3,5,11,25,35,39,54; 11.4/5,7,17,19,25*,37.
  • November 9. You can find here a short sample midterm. In addition, I recommend to solve the relevant problems in the following two midterms from Spring 2007 (these were common midterms for all math104 sections), midterm2 (problems 8 and 9) and midterm3 (problems 1,2,3,4). These two midterms contain solutions, but read them only after you solve the problems!
  • November 20. HW10. 12.1/5,15,17,23,29,31,33,61*,63*(use monotonic sequence theorem for 61 and 63); 12.2/17,19,25,37,43,65*; 12.3/15,17,19,21,31*(use a calculator for parts a) and b), use the formula for the remainder for part c) ).
  • November 29. HW11. 12.7/1,3,5,7…37. Solve as many odd problems as you can. Also, solve 12.8/3,5,17,25,29. I will post a practice midterm on Tuesday, because we have yet to study Taylor series.
  • December 4. You can find here a sample midterm on chapter 12. The solution will be posted tomorrow night. There is no HW12, but I would also recommend to solve the following problems for an additional practice: 12.9/9,23,25,27; 12.10/27,29,31,39,43,47. Note that the answers in the text are given in the compact form, but it is sufficient for you to solve for the first four terms. If those problems are easy for you, then here are more advanced problems (A or even A+ level): 12.9/39*; 12.10/15*,17*,51*,53*,55*,59*,62*.

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).

  • September 7. Section 6.5, Ex. 2,5,7. Section 6.1, Ex. 2,7,11. Read sections 6.5 and 6.1; look through section 6.2.
  • September 11. Section 6.1, Ex. 3,4,17. Section 6.2, Ex. 20,21,22,31,32,69*. Read section 6.2; look through section 6.3.
  • September 13. Section 6.3, Ex. 1,2,16,17,46*. Read section 6.3 and repeat chapter 6 (sections 1,2,3,5). Prepare your questions for the recitation. Look through sections 7.2 and 7.1.
  • September 18. Section 7.2, Ex. 1,11,13,16,20(maple),30,38,44,55,72,82. Section 7.1, Ex. 3,9,19,22,26. Read sections 7.1 and 7.2. Look through sections 7.3 and 7.4.
  • September 20. Section 7.3, Ex. 1,2,12,18,24,56,60,66. Section 7.4, Ex. 3,6,10,28,32,37(maple). Read sections 7.3 and 7.4. Look through section 7.5.
  • September 25. Section 7.5, Ex. 3,23,31,46,61,67. Read section 7.5. Look through section 7.7.
  • September 27. Section 7.7, Ex. 1,2,3,4,9,15,29. Section 7.6, Ex. 4,6,9,35,48(maple). Read section 7.7. Look through section 7.6. Repeat chapters 6 and 7 towards the midterm!
  • October 2. Midterm I. You can find a solved midterm here; two other variants just have a different answer key. In problem 2, R is a type I region! Other corrections to the solution are welcome.
  • October 4. Section 8.1, Ex. 3,10,12,34,52,60*. Section 8.2 (odd m or n), Ex. 1,2. Read sections 8.1 and 8.2. Look through section 8.3.
  • October 9. Section 8.2, Ex. 10,14,15. Section 8.3, Ex. 4,5,9. Read sections 8/2,3 and look through section 8.4.
  • October 11. Section 8.4, Ex. 1,4,7,10,12. Read sections 8.4 and 8.5.
  • October 18. Section 8.4, Ex. 5,6,22,28. Read section 8.5, prepare your table of basic integrals and check yourselves on problems 8.5/1-80 (chose few problems at random and try to solve).
  • October 23. Section 8.5, Ex. 5,12,27,31,37,51,60,74,76,81. Section 8.8 (excluding the comparison theorem). Ex. 2,5,6,10,14,17,29.
  • October 25. Midterm II. You can find a solved midterm here.
  • October 30. Section 8.7, Ex. 3(maple),11(maple),21(maple),30. Section 8.8 (comparison theorem), Ex. 49. Section 9.1, Ex. 2,7,24,29. Read sections 8.7,8.8 and 9.1, and look through section 9.2.
  • November 1. Section 9.2, Ex. 2,5,20,25*. Read section 9.2. Look through sections 11.1 and 11.2. Sections 9.3 and 9.4 are not in the exams’ syllabus, however it might be useful to look through them.
  • November 6. Section 9.5, Ex. 1,3,5. Section 11.1, Ex. 2,3,6,11,24,26,28,44. Section 11.2, Ex. 5,8,13(in order to compute the second derivative read Example 1 in the text),43.
  • November 8. Section 11.3, Ex. 9,16,22,29,40,48,54; Section 11.4 (areas), Ex. 3,6,35.
  • November 13. Complements on Sections 11.3 and 11.4 (polar tangents and lengths). Section 12.1. Ex. 2,5,7,9,17,24. Repeat chapters 9 and 11 before the midterm.
  • November 15. Midterm III. You can find a solved midterm here.
  • November 20. Section 12.2. Ex. 1,9,41,43,51,65. Section 12.3. Ex. 3,5,11,28.
  • November 27. Section 12.4. Ex. 1,2,3,6,17,37*. Section 12.5. Ex. 7,8,24*(remainder), 35*(rearrangement). Section 12.6. Ex. 2,3,4,8. Read sections 12.4, 12.5, 12.6 and 12.7. Look through 12.8. Also, read the strategy for testing series from the review on sequences and series (on the bottom of the page). On next lecture we will test many series using that strategy.
  • November 29. Section 12.7. Ex. 2,3,8,37,38*. Section 12.8. Ex. 2,7,12,23,30. Read sections 12.7 and 12.8, and look through sections 12.9 and 12.10.
  • December 4. Section 12.9. Ex. 3,4,9,13,35*. Section 12.10. Ex. 8,11,37,43. Read sections 12.9 and 12.10, and repeat the material of chapter 12.
  • December 6. Midterm IV. You can find a solved midterm here.

Review notes:

  •  A brief review of the material from chapter 6 is here (average value of a function, type I and II regions, areas and volumes). Any comments on (possible) mistakes/inaccuracies are welcome.
  •  A brief review of the material from chapter 7 is here (exponents and logarithms, inverse functions, L’Hospital’s rule). Any comments on (possible) mistakes/inaccuracies are welcome.
  • A brief review of the material from chapter 8 is here (methods of integration and improper integrals). Any comments on (possible) mistakes/inaccuracies are welcome. The review does not contain a table of basic integrals – you should build a table of your own and copy it to your cheating sheet (or memorize it).
  • A brief review of the material from chapters 9 and 11 is here (lengths, surface area, probability density function, parametric and polar curves). Any comments on (possible) mistakes/inaccuracies are welcome.
  • A brief review of the material from chapter 12 is here (sequences, series, power series and Maclaurin/Taylor series). Last update was made on November 26th. Any comments on (possible) mistakes/inaccuracies are welcome.

Solutions:

  •  The solution for the sample midterm 1 is here.
  •  The solutions for the sample midterms 2: sample2, sample2b. The solution for sample2 is accompanied with a list of few typical mistakes.
  • The solutions for the sample midterm 3 is here (the relevant problems are 1-6).
  • The solutions for the sample midterm 4 is here.