Calculus B, Math 10360 (formerly 120), Fall 2005

• Frederico Xavier - Room: 214 Hayes Healy. Office Hours: Mon.,Wed, 3:00-4:00 pm
• William Kirwin - Room: 248 Hayes Healy. Office Hours: Mon., Wed., Fri.s 9:30-11:30 am. or by appointment.

• Ion Dinca - Room 221 Hayes Healy. Office Hours: Tues. 2-3 and 4-5 pm or by appointment.
• Fang Qi - Room 237 Hayes Healy. Office Hours: TBA

There will be three examinations during the semester and one final examination; the dates, times, and rooms are given below. Each exam given during the semester will last 75 minutes and will be worth 100 points. The final exam is a two-hour exam and will be worth 150 points. The final exam will cover all the material of the course. There will be a total of 25 points for the quizzes (which will be given most weeks by the TA's during the tutorial sessions) and other activities in the tutorials. There will also be a total of 25 points for the homework. In all there are 500 possible points for the semester, and your grade will be based on the number of points you receive. However, you will receive a letter grade on each of the three exams administered during the term in order to give you a general sense of where you stand in relation to the other students taking the course.

Homework will be collected at your tutorial session and returned at the tutorial session the following week. Usually three assignments will be due each week; the specific assignments due in any particular week will depend on the material covered during the lectures leading up to the tutorial. Because it may happen that you have trouble with some homework problems and want another shot at them after you see the TA, we will accept homework as late as 4PM of the day following the tutorial (Friday for Thursday tutorials, Wednesday for Tuesday tutorials). If you do not turn your homework in at the tutorial, you have to come to the Mathematics Department and deliver it personally to the TA's office in HHH. You should make arrangements with your TA for doing this.

The purpose of collecting and returning homework is to let you know whether or not you are doing the problems correctly. The homework grade is designed to reward effort. Each problem is graded either 0 (if the problem is missing or there is not much evidence of effort) or 1 (for any honest attempt). The total number of points on any assignment is simply the number of problems honestly attempted.

All examinations and homework are conducted under the honor code. While cooperation in doing homework is permitted (and encouraged), copying is not. Exams are closed book and are to be done completely on your own with no help from others. NO calculators are allowed on the exams. No Palms or laptops either!

A student who misses an examination will receive zero points for that exam unless he or she has a written excuse from the Dean of the First Year of Studies. The Dean will rarely issue an excuse if the request is presented after the exam takes place. Please be aware that the Dean does not consider a travel difficulty to be a valid rationale for missing an exam. Plan your travel for the semester break and the Easter holidays well in advance!

There are 42 class days, 14 Mondays, 15 Wednesdays, and 13 Fridays. They are listed below, together with an indication of when the exams are given.

Exam 1 (8AM Tuesday, 9/20): Homeworks 1-12.

Math 10360-01, EART 102, 8:00 am - 9:15 am
Math 10360-02, DBRT 140, 8:00 am - 9:15 am

Exam 2 (8AM Thursday, 10/27): Homeworks 13-20.

10360-01 (Kirwin) DBRT 126 8am-9:15am
10360-02 (Xavier) DBRT 140 8am-9:15am

Review Session on 10/26 (w/ I. Dinca)
Hayes-Healy 127 7pm-9pm

Exam 3 (8AM Tuesday, 11/29): Homeworks 20-29.

10360-01 (Kirwin) EART 102 8am - 9:15am
10360-02 (Xavier) DBRT 140 8am - 9:15am

Review Session on 11/28
Hayes-Healy 127, 7pm-9 pm

Final Exam (1:45PM Friday, 12/16, NIEU 127): All homework assignments (1-29).

Sample of Exam I .

Answers to Exam I sample:

Multiple Choice: all answers (a), SKIP #9
Partial Credit - Outlined solutions. Not enough detail for full credit; just an indication of the technique.
13. Set the equations equal to solve for the endpoints; you should get x=plus/minus 1. Then integrate (1-x2)-(x2-1) from -1 to 1.
14. Factor out the 3 in the bottom. Then do a substitution with u=(x-2)/sqrt(3). Integrate using the arctan rule, and plug in the endpoints.
15. First solve c0/2=c0 e^{r 24000) for r. Next, solve 2=c0 e^{r 1000} for c0 using your value for r. Finally, compute c=c0 e^{r 10000} with your values of r and c0.
16. SKIP

Sample of Exam II .

Answers to Exam II sample:

Multiple Choice: all answers (a)
Partial Credit - Outlined solutions. Not enough detail for full credit; just an indication of the technique.
13. First set the equations equal to find where they intersect (you should get x=sqrt(6)). The volume is:
2pi times the integral from 0 to sqrt(6) of x (8-(x^2-2)) dx = 18 pi.
14. Skip (it is a trig substitution problem).
15. Use the centroid formulas. You get xbar=2/5 and ybar=1/2.
16. Integration by Parts : u=ln(2x) and dv=1/x^2 dx. You get (-1/x) ln(2x) -1/x + C.

Sample of Exam III .

Answers to Exam III sample:

  1 c)
  2 e)
  3 d)
  4 a)
  5 e)
  6 c)
  7 a)
  8 c)
  9 d)
10 e)
11 a)
12 b)

Outlined solutions. Not enough detail for
full credit; just an indication of the technique.

13. Substitute x = sin t:
End up having to  integrate sin^3(t) cos^2(t) dt

14. First series n-th root test: L=4/6<1 converges.
Second series: ratio test L=0<1 converges

15. Do the indefinite integral by parts:
-xe^{-x}-e^{-x}+C.
By the definition of the improper integral, you need to calculate limit as t->infinity
of -te^{-t} - e^{-t} which is 0.
The first summand is a l'Hopital, the second
is one of the basic limits.
Final answer is 1.

16. x=.424242...
100x =42.424242.... = 42+x.
x=42/99=14/33

Sample of Final Exam .

Revised sample of Final Exam , with many misprints fixed.

Quick answers for first sample of the final exam (the one with
the misprints)

1c, 2b, 3d, 4e, 5a, 6b, 7c, 8c, 9c, 
10b (except that +C is
missing, and that sqrt should be on all of the denominator),
11a, 12e (should be y^2), 13a, 14d, 15, 16a, 
17 : answer is 8 \pi/3, 
18: answer is sin^3x/3 - sin^5x /5 +C, 
19c,  20a, 21e, 22c, 
23: answer is \infty (change to (1+3x)^{1/x} to get a), 
24b, 25e, 26b, 27e.
On the partial credit problems:
1. y=2e^{5 \sqrt{x^2-9}}.
2. x{3^x}/\ln 3 - 3^x/(ln 3)^2 + C
3. 72 \pi/5
4. 9844/9900
5. a) diverges by nth term test; b) converges by ratio test

Quick answers for the revised sample of the final exam:

1c, 2d, 3d, 4a, 5e, 6c, 7b, 8a, 9(e) except it should have "dx";
10c, 11d, 12a, 13a, 14a, 15a, 16a, 17e, 18c, 19b, 20b, 21e, 22b

Review for Exam I: Sept. 19, 2005, from 7-9 pm - HAYE 127

Review for Exam II:

Review for Exam III:

Review for Final Exam:

Additional Help

In case extra help is needed, you are encouraged to attend the Calculus Help Room: MTWH 7:00-9:00 pm in room 215 Hayes-Healy Hall.