Course: Math 231/Math 249, Honors
Calculus II, Section D1H/P1H
Time: MWF 11:00--11:50am
Location: 145 Atlgeld Hall
Instructor: Prof. Leininger
Phone: 265-6763
Email: clein (at) math.uiuc.edu
Office: 366 Altgeld Hall
Office hours (my office): Wednesday 10:00--11:00, Thursday 11--11:50
and by appointment.
Text: Stewart, Calculus: Early Transcendentals, 6th edition
About the honors course: Although the official syllabus for this class is the same as the usual Math 231, we will be delving deeper into certain aspects of the material. In particular, we will be doing some proofs. This semester the recurring theme will be the complex numbers.
I will be pushing many of you to your limitations in the hopes that you will gain a better understanding of calculus. If you are not willing to put in the extra effort required to succeed, I strongly urge you to switch to one of the regular sections of Math 231. On the other hand, you will not be punished for enrolling in the honors section, and I will be reasonable when it comes to grading more difficult problems.
Grades: Grades for Math 231 will be based on quizzes [20%], three midterm exams [20%,10%,20% each], and a final exam [30%]. Notice the change from 2 to 3 midterms!
The grade for the one credit hour Math 249 will be assigned based on your completion of the ``honors problems'' (I expect there to be between 5 and 7 of these). These are assignments made throughout the
semester that will investigate some topics outside the regular course material. These will be collected and graded.
I will curve an exam score if absolutely necessary (e.g. the problems were legitimately too difficult or the exam
was too long). The final grades will be assigned on the usual scale: 90--100 A, 80--90 B, 70--80 C, 60--70 D,
below 60 Failing.
Homework and quizzes: I will be assigning homework daily in addition to the honors problems, but it will not be collected. Instead, I will have two quizzes per
week which will be similar to (or the same as) what is in the homework (one will be about 10 minutes, the other longer, about 20 or 25 minutes). These will not always
be on the same day each week, and some weeks we may only have one quiz. In general, these will take place at the beginning of class.
I encourage you to work together on homework. The best approach is to attempt all the problems on your own before discussing it with your classmates.
Missed exams/quizzes: I will drop the lowest 4 quiz grades for the semester, so don't come to class when you're sick (although an email letting me know you won't make it is always appreciated). A missed exam will count as ZERO, unless there is a valid excuse. Make-up exams for the midterms will not be given, and a make-up for the final will occur only under extreme circumstances. In the situation that there is a valid reason to miss an exam (my discretion), I expect prior notification of the absence if it is humanly possible. In the case of a midterm, the average of the other exam score and the final exam will be used to replace the missing score. Honors problems will not be accepted late under any circumstances.
Attendance: The quizzes serve the secondary purpose of providing a basic attendance record. This could be relevant in making grade decisions for borderline cases.
Exams: The two midterm exams will be 50 minutes each, during class. It was unreasonable to find a time during the evenings.
Midterm 1: Wednesday, February 16, in class.
Midterm 2: Wednesday, March 16, in class.
Midterm 3: Wednesday, April 27, in class.
Final Exam: Friday, May 13, 8:00--11:00 usual classroom.
Assignments and more:
- Wednesday 1/19: Lecture notes. Homework: §5.5 problems 7, 11, 13, 17, 19, 23, 29, 39, 43; §10.3 problems 1--6.
- Honors problem 1, due Monday 1/31.
Please send any typos/errors to me as soon as possible. A typo was found: the reference to part (h) in part (j) should have been a reference to part (g) and the definition of the integral. This has been fixed in the current version here. Some solutions and notes.
- Friday 1/21: Lecture notes. Homework: §7.1 problems 3, 9, 11, 21, 23, 29, 43, 57, 65. Quiz.
- Monday 1/24: Lecture notes. Homework: §7.2 problems 5, 9, 17, 19, 23,
25, 35, 45. (note the correction to 7.2 rather than 7.1)
- Wednesday 1/26: Lecture notes. Homework: §7.3 problems 7, 15, 17, 19, 25, 31 (for this last, see solution 2 example 5 from this section). Quiz.
- Friday 1/28: Lecture
notes. Homework: §7.4 problems 7, 9, 11, 15, 17, 21, 25, 29, 31,
35. Quiz.
- Monday 1/31: Lecture notes. These also contain my "solutions" to the integrals on the worksheet (good luck reading them---your best bet is to try to get hints from my scribbles). Homework: §7.5, all odd problems. I don't expect you to have done all of these by next class, but you should do 4 or 5 every day for practice. When you finish these, practice with the odd integrals from the previous chapters, too.
- Friday 2/4: Lecture notes.
Homework: § 7.7 problems 7, 11, 13, 15, 19, 21.
Quiz.
- Honors problem 2, due Monday 2/14.
Please send any typos/errors to me as soon as possible. To clarify: the gamma function here is taken to be a function defined on the positive real numbers. Solutions.
- Monday 2/7: Lecture notes. Homework: §7.8 problems 5, 11, 19, 25, 29 (compare example 7 from the book), 49, 51, 53.
- Wednesday 2/9: Lecture notes. Homework: §8.1 problems 3, 5, 7, 9, 13, 17, 35, 37. Quiz
- Friday 2/11: Lecture notes. Homework: §8.2 problems 7, 9, 13, 15, 25, 29, 31.
- Midterm review problems (see also homework 1/31 above): Chapter 7 review problems 1--49 odd, 63, 65, 69, 71, 73. Make sure you know how to compute arc length and surface area for surfaces of revolution. Study complex numbers and complex valued functions as in the first honors problem.
- Another practice problem: Suppose L is the line through the origin making an angle θ with the positive x-axis (with 0 < θ < π/2) and suppose f(x) is a function on the interval [a,b] whose graph is above this line. This means that f(x) > tan(θ) x. Find the surface area of the surface obtained by revolving the graph y=f(x) around the line L.
- Monday 2/14: Lecture notes. Homework: §8.3 problems 1, 7, 13, 21, 23, 25, 31.
- Wednesday 2/16: Midterm 1!! Solutions. (sorry, I got distracted so it took a little longer than 10 minutes.)
- Friday 2/18: Returned midterm 1 today, went over solutions, answered questions. Very briefly mentioned sequences and indicated their importance in what follows.
- Monday 2/21: Lecture notes. Homework: §11.1 problems 3, 5, 7, 9, 11, 13, 15. For each of the sequences below, decide whether it converges, and prove it (so, for a given ε find the require N...):
A. {n/(3n+3)} B. {n^{2}/(300n+2n^{-1})} C. {(-1)^{n}n/(n^{2}+n + 5)} D. {2^{n}/n!}
- Wednesday 2/23: Lecture notes. Homework: §11.1 problems 17--45 odd, 57, 61, 63, 65, 77. Quiz.
- Honors problem 3: §11.2 problems 64, 73, 76. Solutions.
- Friday 2/25: Lecture
notes. Homework: §11.2 problems 11, 17, 21, 25, 35, 39, 41, 43, 55. (for 41, 43 see example 4 from book). Quiz.
- Monday 2/28: Lecture
notes. Homework: §11.3 problems 3, 7, 15, 19, 23, 25, 27, 35.
Quiz.
- Wednesday 3/2: Lecture notes. Homework: § 11.4 problems 3--31 odd, 37, 43. Quiz.
- Friday 3/4: Lecture notes. Homework: §11.5 problems 1--19 odd.
- Monday 3/7: Lecture notes. Homework: §11.6 problems 1--19 odd, 29, 31
- Wednesday 3/9: Lecture notes. Homework: §11.6 problems 21--27 odd; §11.7 problems 1-38 (lots of practice for the test next week). Quiz. Series Worksheet solutions.
- In preparation for midterm 2:
- Make sure you understand the definition of the limit of a sequence. Given ε make sure you can find N (for practice, try this for §11.1 problems 18, 19, 25, 29, and 35 for example (45 diverges, so don't do that one)). Be able to compute using limit laws, too.
- Know geometric series, when they converge, what their sums are, and how to find sums via algebraic manipulation (e.g. sums and differences; telescoping series).
- Make sure you know how all the tests work, what the hypotheses are, and be able to use them effectively.
- Go through §11.2--11.7 and decide convergence/divergence for every series in the problem sets, as well as absolute versus conditional convergence if the series converges.
- Be able to estimate the sum of a series which converges by applying the integral test, and how to get an estimate with a certain accuracy (see pages 700--702 and § 11.3 problems 32--38).
- Be able to detect a geometric series in a geometric problem (as in honors problem 3).
- Friday 3/11: Quiz.
- Monday 3/14: Lecture notes. I will be here from 1--3 so you can pick up your quiz.. sorry for the confusion.
- Tuesday 3/15: You can come ask me questions 8:10--9:30.
- Wednesday 3/16: Midterm 2. Solutions. Office hours for the rest of the
week are cancelled because of the exam.
- Friday 3/18: No class today. Have a great break!
- Monday 3/28, Wednesday 3/30, Friday 4/1: Circumstances beyond
my control have forced me to be away this week. Professor Kapovich will
be filling in for me while I am gone. There will be quizzes this week. I
will do my best to have the midterms graded soon. I will post here when
that happens, and you can email me for your scores.
- the exams are graded. The scores were very good. You can email
me for the scores. The average was in the high 80's, and there will
be no curve.
- Wednesday 3/30: The assignment for today §11.9 problems 3, 7,
14, 15, 20, 24, 27.
- Friday 4/1: §11.10 problems
2, 3, 7, 8, 11, 13, 16.
- Honors problem 4, due Monday 4/11.
- Monday 4/4: Lecture notes. §11.10 problems 17, 19, 21, 23, 25, 27.
- Wednesday 4/6: Lecture notes. § 11.10 problems 29, 31, 35, 45, and take a look at 70: this is the function I was refering to on Monday. Quiz.
- Friday 4/8: Lecture notes.
§11.10 problems 43, 47, 51, 63, 65; §11.11 problems 15a,b,
17, 27, 35a,b (you only need to compute the first couple terms of the
Maclaurin series for tanh for this, and you may assume it converges to
tanh on some interval about 0; see Section 3.11 for more on hyperbolic
functions).
Quiz.
- Honors problem 5, due Monday 4/18. This
is even easier than the fourth problem... but still it's a pretty
application of what we've learned. The typo should be fixed now.
- Monday 4/11: Lecture notes. §10.1 problems 1, 5, 9, 15, 17 (see section 3.11 for more on hyperbolic trig functions), 19, 24.
- Wednesday 4/13: Lecture
notes. §10.2 problems 3, 5, 17, 19, 25, 27, 29.
- Friday 4/15: NO CLASS!!!!
- Monday 4/18: Lecture notes. §10.2 problems 33, 36, 39, 43, 61, 65. Quiz.
- Wednesday 4/20: Lecture
notes. §10.3 problems 15, 21, 29, 33, 35, 37, 39, 45, 57, 59, 61,
63; §10.4 problems 9, 13, 17, 19, 21, 23, 27, 29, 31, 45. There are
a lot of problems here and I do not expect you to have done them all
before class Friday.
- I misread the course syllabus, so we are essentially done with the material for this semester. The next midterm will be on the second half of chapter 11 and Sections 10.1--10.4.
- Friday 4/22: Lecture notes. No additional problems (though I will soon post practice problems for the third midterm).
- Honors 241 registration: If you would like to register for
the honors section of Math 241 you should email mathadvising@illinois.edu
and ask them to give you permission.
- In addition to the problems listed above for sections 10.3 and 10.4,
here are some more practice problems for the next midterm. There is
overlap with the assignments from earlier, too. §11.8 problems 3-33
odd, 37, 39; §11.9 problems 3-31 odd, 37; §11.10 problems 5-19
odd (try to show that the function equals the power series), 25--37 odd,
43, 47, 49, 63, 65, 67; §11.11 problems 3-9 odd, 13-21 odd, 25, 27,
29; §10.1 problems 1-27 odd, 33, 41; §10.2 problems 1-9 odd,
17, 21, 25-33 odd, 41-47 odd, 57-63 odd; §10.3 problems 7-25 odd.
- Monday
4/25: Review for Midterm 3.
- Wednesday 4/27: Midterm 3.
- If you would like to take the final exam before the regular time, I need to know by WEDNESDAY, APRIL 27. The early exam time will be May 2, time and place TBA.
- Wednesday 4/27: Here are the solutions to Midterm 3.
- Reviewing for the final exams: The best strategy for
preparing for the final exam is to rework as many of the old
homework/quiz/midterm problems as you can. These are all on the webpage
here, so I will not repeat them. Here are just a few more problems from
§8.3: 9, 15, 27, 29, 33, 39, 41.
- Monday 5/2: Lecture notes.
- Here are solutions to honors problems 4 and 5.
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