Math 231 E1H, Honors version, Spring 2009
Homework
assignments Score Reports Solution of Quiz2 Solution of Ex1(average
45.6/50) Free
tutoring Solution of Quiz6(average 13.9/20) Solution of Ex3(average 39/50) Solution
of final(average 88/100)
Check “ex0” under score
report for your overall grade. 10=A+, 9=A, 8=A-, 7=B+…. Wish you a good break.
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Lectures: MWF 1:00-1:50 in 243 Altgeld Hall
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Instructor: Tao Mei, mei@math.uiuc.edu
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Course homepage: www.math.uiuc.edu/~mei/231.html
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Office & Telephone: ALTGELD Hall 109, 217-244-2478
. Office Hours: 5:10-6:10pm Monday and Tuesday or by appointment.
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Textbook (required):
Calculus, 3rd edition: (written by) R. Smith, R, Minton, ISBN: 978-0-07-287029-9.
Course Description:
Differences to the standard Math 231: The course
covers the same material as the regular 231 sections, but deeper. It is more
challenging and more labor-intensive, but also intellectually more rewarding
than the standard version of 231. For example, we will cover theoretical
material that in standard sections would often be skipped, we will do some
proofs, and the homework assignments will include more difficult, "honors
level" (but doable) problems.
Tentative exam dates: There will be three hour-long exams during the semester and a final exam.
Exam #1 -7:00-8:00pm, Wednesday, Feb. 18th in Altgeld 143.
Exam1 covers sections 6.1-6.4, 6.6 and 7.1.
Exam #2 -7:00-8:00pm, Wednesday, Mar. 18th in Altgeld 143.
Exam 2 covers sections 8.1-8.5. A good understanding of review Probs #1-52 on page 710 will be enough for a grade of 45+ on Exam2 (totally 50pts).
Exam #3 -7:00-8:00pm, Wednesday, April 29th in Altgeld 143.
Exam 3
covers sections 8.6-8.8, 9.1-9.5.
Final Exam- 1:30-4:30 PM, Tuesday, May 12 in our regular classroom 243 Altgeld. Please arrange any travel, etc., so that you can take the
final on this date. As a "non-combined"
course, there will be no conflict exam given except for those few
individuals who meet the official university criteria given here in the student code.
The Final will have 6-8 probs in total. First one will be on
no procedure-questions, including convergence interval of power series,
converge/diverge of sequences/series, existing/non-existing of improper
integrations. The second one will be on chapter 6, including integral by part,
trig-tech, and partial fraction, etc. Next 2-3 problems will be on Chapter 8,
one of them will be on
Homework and
Quiz: Practice is essential
for this course. I will assign a few homework problems after each class. You
should check the assignment at the class webpage. Problems in part (b) are
required to be handed in weekly. Handed-in homework is due at the beginning of
class on the due date. Assignments dropped off in mailboxes will not be
accepted; however, you can turn in an assignment, in person in my office any
time before the class hour in which it is due. We will also have practicing
quizzes during the week before/of the exams. 3 poorest grades of Hws and
quizzes will be dropped from the final score in the class. As a result, HW
extension or make-up quizzes will not be allowed.
Homework Rules: (1) Print your name, section at the top of the
paper. (2) Staple the papers together if your homework takes more than one
page. (3) Work out the problems, grading will be based not only on the
correctness of the solution, but also on the quality of the write-up and the
work shown; in particular, an answer alone (like the answers to odd-numbered
problems given in the back of the book), without justification, won't earn
credit.. (4)Be neat and legible.
You will be able to
check your homework and exam grades at Score Reports, which
is the Math Department's gradebook program. This will be available
beginning a few weeks into the semester. All your hw, quiz and exam
grades will be posted there. You will be prompted for your NetID and NetID
password after following the Score Reports
link. Please check score reports regularly to make sure your grades have been
correctly reported and tell me promptly about any errors. You are
responsible for keeping all of your graded homework and exams so that any
discrepancies in recorded grades can be settled.
Grading:
three
midterms (15% each), final exam (30%), Home-works & Quizzes
(25%).
Remember that this is an
honors level course, aimed at the best and brightest of our students. As such,
it is more challenging and labor-intensive as a regular calculus course, and it
requires a significant level of commitment and work - probably more so than any
of your other classes. To do well in this class, you must:
- Attend
the lectures.
- Read
the text.
- Do
the reading right before/after the lecture (or the same day), when the
lecture is still fresh in your mind. Don't wait with the reading till the
homework is due. A 5-minutes review of old text and pre-reading of the
new text will be very helpful.
- Read
each section in linear order, from beginning to end, as you would read a
novel. The material in the text is usually arranged in a logical order,
with each concept building naturally on the previous one. You get the
most out of it if you read the section in this order. Resist the
temptation to treat the text as a dictionary/encyclopedia, looking up
concepts and formulas only when you need them in a homework problem!
- Don't
neglect the pictures. A picture can often explain a concept better than a
passage of prose.
- While
the bulk of the reading should be done after I have covered the section
in class, it is useful to read, or at least skim, the text of the upcoming
section ahead of each lecture. This will help you in understanding the
lecture, and it may uncover any difficult points in the material that I
should go over in the lecture.
- Take
the homework seriously. The homework, both the non-graded and the
graded variety, is an essential part of this course, and requires a
substantial investment of time. If you skip the non-graded homework, or
blindly copy someone else's homework without really understanding what's
going on, you'll be in trouble during exams.
- Come to office hours and get help from
your classmates.
Homework
Assignments
Assignment
#1 (due by the beginning of the class on Jan. 28, Wednesday)
(a) Review exercise of Chapter 4, # 3, 9, 18, 20, 27, 41, 55, Sec 6.2 #2, 45.
(b) Sec 6.1 #29, 41, 44, Let f(x)=\int_0^{x^3}sint dt, find the derivative of f(x), Sec 6.2 #16, 35, 40,46.
Assignment #2
(due by the beginning of the class on Feb. 4, Wednesday)
(a) Read Example 3.3, Sec 6.3 #9, 15, 25, 33, Sec 6.4 #31.
(b) Sec 6.3 #2,10,12,18,30, 34(c), Sec 6.4 #12,18, 34, Let P(x)=a_0x+b_0, Q(x)=(a_1x+b_1)(a_2x+b_2), assume that neither “a_1x+b_1” nor “a_2x+b_2” is a multiplication of the other. Prove that P(x)/Q(x) can always be written as c_1/(a_1x+b_1)+ c_2/(a_2x+b_2) for some real numbers c_1, c_2. Here a_0,a_1,a_2,b_0,b_1,b_2 denotes for arbitrary real numbers.
Assignment #3
(due by the beginning of the class on Feb. 11, Wednesday)
(a) Read Sec 6.5, Ex6.6, #49, 53-56, 75.
(b) Ex 6.6 #7,8,10,20,24,32,42, 46,50, 76 (P(x>a)= ∫[a,∞) f(x)dx, work on #75 first).
Assignment #4 (due by the
beginning of the class on Feb. 18, Wednesday)
(a) Read, Ex 7.1 # 5,17, Ex 8.1, 33-42,
(b) Ex 7.1 # 4,12,29, Ex8.1, #8(a)(b), Even number probs from #14-26 (no procedure needed), #32, 54, 58 (prove it converges first then identify the limit as an integration), Let a_n be the integration of (sinx)^n from 0 to π/2. Prove that a_n converges. Let b_n=a_{2n+1}/a_{2n}. Prove that b_n converges to1. (hint for b_n, use integration by part to show a_n/a_{n-2}=(n-1)/n, then use squeeze theorem to prove the desired assertion.)
Assignment #5 (due by the
beginning of the class on Mar. 4, Wednesday)
(a) Read, Ex8.2 #33, 37, 41, 47,48, 51, 53.
(b) Ex 8.2 Even number probs from #4-20 (no procedure needed), #31, 29, 42, The alternating harmonic series is the infinite sum of 1/k with alternating +, - sign in front of 1/k. That is ∑1≤k<∞ (-1)^k(1/k). Show that this series converges. (hint, consider the partial sums S_{2n} and S_{2n+1}, show that both of them are bounded and monotonic. So both of them converges. Show they converge to the same number).
Assignment #6 (due by the
beginning of the class on Mar. 11, Wednesday)
(a) Read, Ex8.3, Odd number probs from #9-32, #41-50, #35, 55,56, 66, Ex8.4 #11-24, #45.
(b) Ex 8.3 Even number probs from #9-32, #41-50 (no procedure needed), #36,65, Ex8.4 #40 (we expect an accuracy within (1/4)*10^{-8}).
Assignment #7 (due by the
beginning of the class on April 1, Wednesday)
(a) Ex8.5 Odd number probs from #1-37, #41, Ex8.6 #11-24, #31,41, 44, 47.
(b) Ex 8.5 Even number probs from #20-38 (no procedure needed), #44, Ex8.6 #12, Even number probs from #22-30, #34,36, #38,40.
Assignment #8 (due by the
beginning of the class on April 8, Wednesday)
(a)
Ex 8.7, #1,5, 25,
29,32, 39, 47, Denote by P_n(x) the Taylor polynomial of lnx with degree n.
Denote by Q_n(x) the
(b)
Ex 8.7, #10 (show
the proof of convergence by
Assignment #9 (due by the
beginning of the class on April 15, Wednesday)
(a)
Ex 8.8, #7, 17, 23,34,42,
Ex9.1, #2,8, 25-30, Ex9.2, #35, 37. Let R_n(x) be the
error term as in Taylor’s Theorem. Show that R_n(x)
(b) Ex 8.8, #10, 14, 33,41, Ex 9.1, #34, 38,40, 44, Ex 9.2, #4, 14, 20 (“describe its motion”=``find the direction and speed”), 28, #43 and show that the double derivative of y with respect to x equals to (y’’x’-x’’y’) over the cube of x’ at any t for any differentiable pair (x(t),y(t)). Here y’,x’,y’’ denote the derivatives with respect to t. (Hint, start from dy/dx=y’/x’, then d(dy/dx)/dx=?)
Assignment #10 (due by the
beginning of the class on April 22, Wednesday)
(a)
Ex 9.3, #7, 13,
Ex9.4, #5,11,17, 51-56, Suppose we have a smooth simply closed curve.
Prove the area formula (5.6) of section 9.3 by using (2.5) of section 9.2 (hint,
Suppose r=f(Ө). Then (x,y)=(f(Ө)cosӨ, f(Ө)sinӨ) is a parametric equation of Ө.
The graph is a counterclockwise curve (why?). )
(b) Ex 9.3, #4, 14, 24, 30, Ex 9.4, #26, 29, 60.
Assignment #11 (due by the
beginning of the class on April 29, Wednesday)
(a) Ex9.5, #3, 18, 21, Ex9.6, #5, 17, 23, Let
us consider a fixed point (x,y) on a parabola with directrix y=k. Let L1 be the line tangent to the
hyperbola at (x,y). Let L2 be the line passes the focus and the point (x,k).
Let L3 be the line passes the focus and (x,y). (i) Show that L1 is
perpendicular to L2. (ii) Show that the angel between L1 and L3 equals to the
angle between L1 and y-axis.
(b) Ex9.5, #4, 14, 26, Ex 9.6, #6, 18,24, 29,
38.
Extra points-Hw (20pts to hw/quiz in case your total grade of hw/quiz won’t exceed 280pts after dropping 3 lowest ones, due May 9th 2pm): Last problem of part (a) of Hw 8-11.