Zvezdelina Entcheva Stankova

Visiting Associate Professor

Office:

713 Evans Hall

Department of Mathematics

University of California at Berkeley

Berkeley, CA 94720-3840

Tel:(510) 642-3768

Fax: (510) 642-8204

Email: stankova@math.berkeley.edu

Webpage: http://math.berkeley.edu/~stankova

Office hours (subject to change):

Fall'07: Tue 2pm-3:30pm, Thur 11am-12:30pm

Teaching Fall'07: Calculus 16A

TTh 12:30-2:00pm, 100 Lewis -- moves to 105 Stanley on Sept 4, 2007

Course Syllabus Postscript format , PDF format

Homework assignments

Notes: If not specified odd or even exercises, it is assumed only even exercises, e.g. #2-8 means 2,4,6,8. Asterick * usually means that the problem is hard/tricky.

HW1, Aug. 28, From 0.1. Functions and Their Graphs. #10,20,22,25,26,30,56; bonus: #50,58. From 0.2. Some Important Functions. #8,12,16,32; bonus: #18,20.

Aug. 30, From 0.3. The Algebra of Functions #24,28,32,34,42; bonus: #36,38. From 0.4. Some Important Functions. #8,10,20,28,34; bonus: #38,40.

HW2, Sep. 4, From 0.5. Exponents and Power Functions. #30,48,50,66,68,70,72,86,90,92,94; bonus: #74,96. From 0.6. Functions and Graphs in Applications. 10,16,18,22,24,37-40; bonus: #46,48,50.

Sep. 6, From 1.1. The Slope of a Straight Line. #6,8,10,16,20,24,26,52; bonus: #32,58. From 1.2. The Slope of a Curve at a Point. #12-18,24,28; bonus: #32,36,38.

Announcements, Sep. 3:

1. The lectures will move to 105 Stanley Hall, starting Sep. 4.

2. For changes in rooms for workshops, please, follow the telebears.

3. Felice Le's office hours will be in Evans 868, on Tuesdays 10:15am-12:15pm.

4. HW solutions will normally appear by Tuesday morning. Please, do not bug your GSI's to post the solutions earlier. The reason that I do NOT want students to look at the solutions before Tuesday is to give you ample opportunity to try to solve them on your own. Otherwise, one starts depending on the solutions, and often gives up in trying to solve the problems when encountering difficulties -- looking instead at the solutions doesn't teach you much problem-solving, unfortunately. So, psychologically, it is a good reason not to have the solutions lying around while solving the HW - just like on exams. Finally, students who really need an answer key can do first the odd "twin" problems (most even-numbered problems are preceeded by a very similar odd-numbered problem) and compare their answers with the textbook answers. The difficulty of the odd-numbered exercises will be about the same as in the even-numbered HW exercises. After that, students can attack the even HW problems without any answer key. We shall not discuss this issue anymore, so try to do your best with the HW's on your own or working together with your friends, and then you can look at the solutions on Tuesday mornings.

5. Please, read the syllabus carefully and follow the instructions there for asking various questions. I have received several e-mails asking me to place students in various sections and help them get off the waitlist for the class, and in addition math questions have arrived on e-mail. If you do send such questions on e-mail, this shows that you have not read the syllabus carefully or that you are ignoring it, and in both cases your answers will be unnecessarily delayed. Use my and the GSIs office hours effectively - these are golden opportunities for you to get all your math questions answered. Be organized and set aside free time to visit office hours. I shall not address these questions in the future.

6. The HW1 solutions were corrected by the GSI and a new version was posted this morning.

7. In general, if a HW problem asks for a calculator (as in the "technology exercises") but a solution can be produced WITHOUT a calculator, students should attempt to solve the problem without a calculator (as much as possible). It is hard to do, for instance, #42 from 0.3 without a calculator, but certain parts of it, e.g. calculating the compositions f(g(x)) and g(f(x)) CAN and should be performed WITHOUT a calculator. Such exercises will be rare in the HW assignments, they will be primarily in the "Technology exercises" section, and often such problems are solvable WITHOUT a calculator. Keep in mind that neither quizzes nor exams will contain problems requiring the use of calculators - instead you will need to perform all calculations by hand.

HW3, Sep. 11, From 1.3. The Derivative. #8,14,16,18,24,26,30,36,46,48; bonus: #52,54,56. From 1.4. Limits and the Derivative. #10,12,14,18,20,34,36; bonus: #40,42,44.

Sep. 13, From 1.5. Differentiability and Continuity. #1-12 (all exercises),16,18,20,22,26 bonus: #28,32,34.

HW 4, Sep. 18, From 1.6. Some Rules for Differentiation. #4,8,20,24,28,30,34,36,38,44,48,54,56; bonus: #40,42,44. From 1.7. More About Derivatives. #8,10,14,22,24,28,30; bonus: #32,34.

Sep. 20, From 1.8. The Derivative as a Rate of Change. #4,6,10,12,16,18,20,26,28 bonus: #24,32.

Announcements, Sep. 17:

1. Review for Midterm 1: PDF format; PS format. The material for Midterm 1 will encompass everything through section 1.7 (inclusive). Midterm 1 will NOT include the material from section 1.8, which will be covered this Thursday. Midterm 1 will NOT include concepts #27-30 on the Review handout. These concepts will be deferred to Midterm 2.

2. Instructions for Midterm 1: PDF format; PS format. Read these instructions carefully, so that you don't spend time during the exam reading them.

3. DSP students: So far only one student has provided me with a hard copy of a DSP official letter, asking for special accommodations. I have not received any other DSP letters, whether through e-mail or other means. According to the class syllabus and as we discussed so thoroughly in lecture, to receive special accommodations, students must present me with the DSP official letters at least 10 days prior to the exam to make arrangements. At the current moment, I am going to assume that there is only one DSP student and make arrangements for only one student. Please, be aware that there is no way for us to make quick arrangements for special accommodations on a short notice, and there is no way to allow for such accommodations without having received the DSP notice prior to and well in advance of the exam. Promises of "future DSP letters" will NOT be honored - please, don't ask for exception to this policy.

4. The student who gave me the DSP letter must contact me immediately via e-mail to finalize arrangements for the midterm 1 .

Announcements, Sep. 19:

Extra Office Hours: Koushik (one of the GSIs) is offering extra office hours this Friday and Monday from 1-4 pm, in addition to his regular hours.

Announcements, Sep. 20:

Extra Office Hours: Jae-Young (one of the GSIs) is offering extra office hours this Thursday 5-6pm and Friday 4-6pm, in addition to his regular hours.

Announcements, Sep. 23:

Come early to Midterm 1: Come 10 minutes early for the Midterm 1 on Tuesday, Sep. 25, so that everyone is settled down and ready to start exactly at 12:40pm.

Read midterm instructions: Please, read the class syllabus, midterm review and the midterm instructions, BEFORE sending me e-mails on questions that are already answered there. As the students who ignored this found out, I do not answer such questions in e-mails. Be responsible and follow the directions, which are so clearly spelled out in your review materials and class syllabus.

HW 5, Sep. 27, From 2.1. Describing Graphs of Functions #6,8,10,12,14,16,18,22,24,30,35,38,39; bonus: #32,34,40.

Announcements, Sep. 27:

If you have a complaint about your midterm grading: you return your midterm to your GSI in section after the 10 minutes of midterm viewing, and come to my office hours within a week, the latest by Thursday, Oct. 4. No exams will be reconsidered after that date. Check out my office hours from the course syllabus.

HW 6, Oct. 2, From 2.2. The First and Second Derivative Rules. #2,4,6,12,18,20,24,40,44; bonus: #36,38,42. From 2.3. The First and Second Derivative Tests and Curve Sketching. #6,12,18,24,26,34,38,42 bonus: #40,44.

Oct. 4, From 2.4. Curve Sketching. #7,8,16,20,26,28,31,32 bonus: #30,38(skip 38(a)). From 2.5. Optimization Problems. #2,4,6,8,10,13,16; bonus: #22,26,30.

Announcements, Oct. 2:

Last time in lecture we agreed on the following conventions:

A function f(x) is increasing on [a,b] if f(x)<=f(y) for any x < y in [a,b]. The function f(x) is strictly increasing on [a,b] if f(x) < f(y) for any x < y in [a,b]. Similarly for decreasing and strictly decreasing . Thus, for instance, a constant function is both increasing and decreasing, but not strictly increasing and not strictly decreasing. On the other hand, the function y=x is strictly increasing on all of R , and it is also true that y=x is (just) increasing on R .

Announcements, Oct. 9:

The following problems will be relevant to the upcoming quiz this Thursday, Oct. 11: from HW6, everything from Sections 2.2, 2.3, 2.4, and from Section 2.5: only problems #2 and #4. The remaining HW6 problems, #6-8-10-13-16 from Section 2.5, shall be fair material for the quiz on Thursday, Oct. 18, along with anything else from HW7.

Let's agree on the following conventions: a concave up function is one whose tangent slopes strictly increase, and similarly, a concave down function is one whose tangent slopes strictly decrease. Thus, a line doesn't qualify as either concave up or concave down (as its tangent slopes remain constant throughout), and hence we agree that a line has no inflection points.

Recall that a constant function, on the other hand, is both increasing and decreasing, but not strictly increasing and not strictly decreasing. Every point on a constant function is a local maximum and a local minimum (except for endpoints); and every point on a constant function (including endpoints) is an absolute maximum and an absolute minimum.

HW 7, Oct. 9-11, From 2.6. Further Optimization Problems. #2,4,6,10,11,12,14,16,18,20,22,26,27,28; bonus: #8,24,29,30. Plus: review HW6 problems #6-8-10-13-16 from Section 2.5. Any of these problems may be tested on the quiz on Oct. 18.

HW 8, Oct. 16, From 2.7. Applications of Derivatives to Business and Economics. #2,4,6,10,12,14,18; bonus: #20,22. From 3.1. The Product and Quotient Rules. #4,8,10,14,18,24,28,30,34,36 bonus: #42,44,62.

Oct. 18, From 3.2. The Chain Rule and the General Power Rule. #2,4,8,16,20,24,30,36,40,41,46,50 bonus: #58,64.

Announcements, Oct. 21: The GSI who wrote the solutions to HW7 has made some minor corrections to two problems there. The revised solutions were posted above.

Announcements, Oct. 22: Note that there are two drawings in the Review materials: they will appear only in the PS file. However, one of the drawings refers to the class problem of the circular flower and square vegetable gardens, so you have this drawing in your notes. The other drawing refers to a problem whose statement is written in the review materials: you can easily draw it yourself.

2. Midterm 2 will include: everything on the Review handout for Midterm 2, except for concepts #19 (exponential function) and #20 (differential equation) in the Definitions and anything related to them later on. In addition, as written above, concepts #27-30 on the Review handout for Midterm 1 can also be covered by Midterm 2, so study that previous review handout too.

3. Come early to Midterm 2: Come 10 minutes early for the Midterm 2 on Tuesday, Oct. 30, so that everyone is settled down and ready to start exactly at 12:40pm.

4. If you are a DSP student who has given me the official document but have not yet e-mailed me to arrange accommodations for Midterm 2, please, e-mail me ASAP. All DSP students who have e-mailed me to arrange for accommodations for Midterm 2, must come the latest by 12 noon on Oct. 30 to my office (Evans 713): late arrivals will miss the GSIs who will take the DSP students to specially reserved rooms.

5. Koushik, one of the GSIs, has been hospitalized after a sports accident. He will be operated on his leg tomorrow. He is feeling OK, under the circumstances, but he will need a couple of weeks to recover from the operation.

The Math Department has put in a request for larger rooms for the next two weeks, so we can temporarily merge Koushik's 8-9:30am, 11-12:30am and 3:30-5pm sections with the corresponding sections of Farmer(8-9:30am), Jae-Young(11-12:30am) and Jae Young(3:30-5pm).

Please, everyone look Wed evening on this class website: for updates on the room assignments for your sections. Be aware that even if you are not in Koushik's sections, the room for your section may be changed. We plan for all quizzes (including for Koushik's students) to proceed as normal, proctored by the other 3 GSIs, so make sure you continue going to your sections and check out the website for updates on room changes.

HW 9, Oct. 23, From 3.3. Implicit Differentiation and Related Rates. #2,4,8,12,14,16,18,22,24,26,28,30,36,38,42,46; bonus: #40,44. Note: Material from this HW will be relevant to Midterm 2 and possibly the Final exam.

Oct. 25, From 4.1. Exponential Functions. #4,8,14,16,24,30,42 bonus: #28,40. From 4.2. The Exponential Function e^x. #2,6,10,21,36,40 bonus: #42,46. From 4.3. Differentiation of Exponential Functions. #4,10,14,16,18,20,24,26,32(+graph!),34,36,40 bonus: #44,48. Note: Material from this HW will be relevant to the Final exam.

Announcements, Oct. 23: The room arrangements for sections for the next two weeks, Thursdays 10/25/07 and 11/01/07, are as follows.

1. All 8am-9:30am sections (Koushik's and Farmer's) will be held in EVANS 70. To be taught by Farmer.

2. All 11am-12:30pm sections (Koushik's and Jae-Young's) will be held in WURSTER 101. To be taught by Jae-Young.

3. All 3:30pm-5:00pm sections (Koushik's and Jae-Young's) will be held in EVANS 9. To be taught by Jae-Young. Note that this is the original room for Jae-Young's 3:30-5pm section.

4. All remaining sections meet at their usual places.

Note that all sections will have quizzes so make sure you know ahead of time where your section's room is.

HW 10, Nov. 1, From 4.4. The Natural Logarithm Function. # 4,6,10,28,31,38,40,48; bonus: #44,46. From 4.5. The Derivative of ln(x). #6,8,18,20,24,26,30,34, bonus: #32,36. From 4.6. Properties of the Natural Logarithmic Function. #2,4,6,8,10,12,14,22,36,46, bonus: #50,52,54.

HW 11, Nov. 6, From 5.1. Exponential Growth and Decay. #2,4,6,10,14,16,22,28,31; bonus: #27,30. Nov. 8, From 5.2. Compound Interest. #2,4,8,10,18,20,24,26,28; bonus: #16,22. From 5.3. Applications of the Natural Logarithm Function to Economics. (up to Elasticity of demand) #2,4,6,8,10,12; bonus: #9,11.

Announcements, Nov. 6:

If you have a complaint about your Midterm 2 grading: you return your midterm to your GSI in section after the 10 minutes of midterm viewing, and come to my office hours within a week, the latest by Thursday, Nov. 8 No exams will be reconsidered after that date. Check out my office hours from the course syllabus.

The room arrangements for sections for this week, Thursday 11/08/07, are the same as for the past 2 weeks since Koushik hasn't recovered completely yet. I have listed again the same room arrangements, but I am waiting for confirmation from the scheduling services.

1. All 8am-9:30am sections (Koushik's and Farmer's) will be held in EVANS 70. To be taught by Farmer.

2. All 11am-12:30pm sections (Koushik's and Jae-Young's) will be held in WURSTER 101. To be taught by Jae-Young.

3. All 3:30pm-5:00pm sections (Koushik's and Jae-Young's) will be held in EVANS 9. To be taught by Jae-Young. Note that this is the original room for Jae-Young's 3:30-5pm section.

4. All remaining sections meet at their usual places.

Note that all sections will have quizzes so make sure you know ahead of time where your section's room is.

Announcements, Nov. 7: No files of old HWs shall be sent out to individual students. Please, don't ask the instructor or the GSIs about old HWs: there won't be any exceptions regardless of what reasons you give. You are responsiblie for taking each HW solution off the web within a week while it is posted, for printing it out, saving it on your computer, etc. -- whatever you do. If you computer or software crashes, if you lose the HWs, or whatever else happens, ask your classmates to xerox their old HW solutions.

HW 12, Nov. 13, From 6.1. Antiderivatives. #2-36(all even exercises),42; bonus: #48,54,56. ( Note : don't fall in the "trap" set for you in #12; #16 will involve some guessing, some functions in #2-24 must first be rewritten in a different equivalent form for you to be able to find their antiderivatives; #26-36 are actually easier: they give you the form of the antiderivative on the RHS, you should take the derivative of this RHS and set it equal to the function on the LHS, then solve for k .) Nov. 15, From 6.2. Areas and Riemann Sums. #4-24(all even exercises); bonus: #19,21.

Announcements, Nov. 12:

Sections this Thursday, Nov. 15: Koushik is back, not yet 100% recovered but moving OK, and will be able to teach his 8am-9:30am and 11am-12:30pm sections. Jae-Young will still take over the two 3:30-5:00pm sections in Evans 9. Thus, this Thursday:

1. All sections are back to normal (as originally assigned with your own GSI), except :

2. Koushik's 3:30-5pm section: this section will still be in Evans 9, grouped together with Jae-Young's section and taught by Jae-Young.

3. Everyone, make sure you know which room your section is meeting (original room, or Evans 9 for 3:30-5pm), so that you arrive on time. Quizzes will be given as usual.

Koushik's office hours for this week will be only on Thursday, Nov. 15, 9:45-10:45am.

Instructor's office hours on Tuesday, Nov. 13 are split between 11:30-12:30pm and 2-2:30pm. Due to a medical procedure, the instructor's office hours on Thursday, Nov. 15 are cancelled. However, lectures this week, Nov. 13-15 proceed as usual. There will a substitute instructor on Thursday.

Quizzes this week, Thursday, Nov. 15 will cover the material only from 5.1 and 5.2 (excluding Present Value: p. 291) -- this adjustment is done because of the shortened lecture last week due to the fire alarm.

However, the remaining material from 5.2 and 5.3 (covered on HW 11) will be relevant for future quizzes and the final exam, so make sure you learn that material too (i.e. present value, relative rates of change and logarithmic derivative; but elasticity of demand in 5.3 is not mandatory).

HW 13, Nov. 20, From 6.3. Definite Integrals and the Fundamental Theorem of Calculus. #2,6,10,12,24,26,30,36,40,42; bonus: #46,48,50.

Happy Thanksgiving! A healthy balance of food and math over the holidays might be a really good idea! :)

HW 14, Nov. 27, From 6.4. Areas in the xy-Plane. #2,4,6,8,10,12,14,20,22; bonus: #24,26,28. Nov. 29, From 6.5. Applications of the Definite Integrals (average value, volumes of solids of revolution). #1-10,30-36(all exercises).

Announcements, Nov. 27:

Sections this week, Thursdays Nov.29: are back to normal. Koushik will be teaching all of his sections at the regular rooms.

Koushik has office hours this week: Thursday, Nov. 29, 2-3:15pm.

HW 15, Dec. 4, From 6.5. Applications of the Definite Integrals. All odd and even exercises: #15-20 and #37-42; bonus: #27,28.

Announcements, Dec. 5:

1. Don't forget about quizzes this week in the last section meetings, Thursday, Dec. 6.

2. Review materials for Final Exam: PDF format.

3. The last lecture on Thursday, Dec. 6 will be dedicated to reviewing for Final Exam.

4. The extra material covered in lecture on Tuesday, Dec. 4: can appear as bonus problems on the Final Exam . Read the review for the final carefully.

Announcements, Dec. 11:

Final Exam in 16A: Wednesday, Dec 19, 2007; 12:30pm-3:30pm; 2050 Valley LSB.

Please, do NOT e-mail me with questions where Valley LSB is: check the campus map. The exam will start at 12:40pm sharp, so be seated in the auditorium at least 5 minutes early.

Felice, one of the GSIs, will be holding extra office hours this Wednesday, 12/12, 4:30-5:30pm, and next Monday, 12/17, 2-4pm in the Free Speech Movement Cafe in the Moffitt Library. She will also hold her regular office hours this week and next week: Tuesday 10:15-12:15 in Evans 866. Everyone is welcome to attend her office hours.

As discussed in lecture, the same rules apply for the final as for the midterms, including the one-sided cheat sheet, no calculators or other aids, etc... No e-mails shall be answered regarding these rules. Please, do NOT bother the GSIs with questions related to the rules for the final in hopes that the rules will be relaxed: the rules for final exam will be exactly the same as for the midterms. No questions on the number, topic or difficulty of the exam problems will be answered. So, instead of wasting your time asking such questions, do your best in studying for the final. Is the final comprehensive? Whoever asks this question has not read the class syllabus and has not paid attention to discussions in class.

Please, do not e-mail me asking me for special treatment regarding your final grade, e.g. to drop more of your quizzes, to change the weight of the exams and what-not: no such things will be done. Everyone will be treated exactly in the same way and we shall be equally fair to all students in the class. Please, refer to the class syllabus for exact information on grading policies. Any e-mails to me asking about grading policies shall be ignored. Please, do NOT bother the GSIs about grading policies either.

All DSP students and students requiring special accommodations must have communicated with me via e-mail already. All such students must come the latest by 11:55am on Dec. 19 to Evans 798 (this is Paulo deSouza's office), and Koushik (one of the GSIs) will take them from there to the exam room. I have received confirmation about these arrangements from everyone except one student: please, contact me immediately to confirm these arrangements.

Announcements, Dec. 13:

HW15 solutions: PDF format; PS format; to be taken down after the final exam.

Two typos were corrected in the review for the final. Review materials for Final Exam: PDF format.

Notes after the Final Exam. Final Scores and Grades

1. As a rule, the instructor and the GSIs do NOT mail, e-mail or communicate in any way the final grades to the students. The final grades are distributed to the students through the regular university channels. There will be NO exceptions to this rule regardless of how anxious you are to see your grade, regardless of students' computer problems accessing bearfacts, regardless of students' delinquency in paying bills and hence postponing the posting of their grades on bearfacts, regardless of the fact that students may be registered through UCB Extension and may receive their grades later. Please, do NOT e-mail the instructor or the GSIs asking for your grade: the GSIs are instructed not to communicate any grades, and any such e-mails will be ignored by the instructor.

2. If a student wishes to dispute the final grade, he/she has to e-mail the instructor after January 15, 2008, when the spring semester starts, and before February 15, 2008. However, the student must be aware that

(a) the final scores are calculated by the percentages announced in the course syllabus, and they are calculated for everyone in the same way: just like in the syllabus. Do NOT ask for exceptions to "twitch your score a bit" so as to give you a higher grade: this won't happen. The grading system is created so that it is fair to everyone. And it will stay that way.

(b) a final grade case will be reopened only if a student has a convincing reason that his/her final grade was miscalculated. Final grade cases will NOT be reopened just to check if the final grade was calculated correctly. The assumption is that all final grades are calculated correctly, unless a convincing evidence to the contrary is brought forward.

(c) a final grade case, once opened, will be fully reviewed, and the final score and final grade will be fully recalculated. This means that, if there is an error, the final grade could go down as well as up. If the final grade calculation reduces the grade, I will have no choice but to change the final grade to the new lower grade and there will be no turning back.

3. If a student wishes to know facts about the final exam (e.g. median, etc): this is internal information and we do NOT communicate it to the students. I can only tell you that the final exam was fairly easy with a high median; thus, doing well on the final exam alone is NO guarantee of an increased final grade. No further questions about statistics, level of difficulty and other info about final exam will be distributed, so don't ask for such.

4. If a student wishes to view his/her final exam: the final exams are out of our hands and into the hands of the main office on the 9th floor in Evans Hall. The student must go there and follow the rules for viewing the final exams within the allowed viewing period. The student must also be aware that if he/she wishes to contest the final exam score, the student CANNOT leave the main office with the final exam under any circumstances: the student can view the final only in the presence of the main office staff. Then, if the student wants to contest the final exam score, the student must e-mail the instructor after the spring semester'08 starts, January 15 2008, and before February 15 2008, and I will pull the final exam from the main office. A student CANNOT take the exam from the office and bring it to me: if by any chance this happens, the student will be disqualified from the right to contest his final exam score. No exceptions.

5. If a student didn't take the final exam, he/she gets an automatic F, as announced in the syllabus. If the student has a documented medical or family emergency and wishes to petition for an incomplete, all such petitions will be considered after the spring semester'08 starts, January 15 2008, and before February 15 2008.

There is no need to send me e-mails during the winter break and ask me for your grades, final exams, incomplete, etc. I shall reply only after the spring classes start at UCB. Please, be reasonable and let us have our break, just like you want to have a winter break.

All e-mails on questions addressed above shall be ignored.

Berkeley Math Circle

http://mathcircle.berkeley.edu