Table of topics and assignments -- Calculus II - Spring 2013

For the complete solution manual (9th edition) you can click here (requires username and password which I'll give in class). For tutoring services (including online), check this page.

Learning Assistant:  John Tenenholtz [jtene001"at"fiu.edu] -- He will help you in class during the problem solving hour and he will also conduct review sessions before exams. These will be announced later.

The structure of the exams will be roughly as follows: about 80% is at the level of  standard suggested problems, 10% at the level of more difficult suggested problems or theoretical topics (proofs that you will be asked to know), while the rest of 10% may test your creativity and capacity to reason. In the suggested assignment below, the more challenging problems are denoted with a star. You should do enough of the suggested problems to be sure you understand the technique and/or idea behind them. If you have troubles with the suggested problems, particularly the standard ones, be sure to ask for help (my office hours, the tutoring services, colleagues, the LA).

We will be occasionally using in class the free version of the WolframAlpha computer software system . You can use this system at home to check your work, but it is essential that you learn the Calculus material not just rely on the software package. For your exams you will not be allowed any kind of electronic devices.  Your mini-projects will likely involve computer/calculator work.

Date Topics covered Suggested Assignment Comments
Jan. 8 5.4 Area
1-19odd, 10, 21-23all, 35, 37, 41, 43, 51, 53, 57-61all
Worksheet 1
Read also section 5.1.
Proof of Theorem 5.4.2 is a possible theoretical exam topic. See your notes.
Jan.10 5.5 The Definite Integral
5.6 Fundam. Thm. of Calculus
9-29odd, 37, 41
1-39odd, 45-51odd, 55-63odd, 69, 70, 72*
Possible theoretical exam topic: Proof of Thm. 5.6.3 (FTC - part 2)
Quiz 1 on Thursday, Jan.17, covers sections 5.4, 5.5, 5.6.
Jan. 15 5.7 Rectilinear motion
5.8 Average value of a function

1, 4, 11, 14, 31
1-11odd, 25-18all
Worksheet 2

 
Jan. 17 5.9 Substitution Method
Quiz 1
1-47odd, 54*, 63*, 65*

Office hour for Friday, Jan. 18 is cancelled.
It is replaced with 12:00-13:20 on Wed. Jan. 23.
Jan. 22 5.10 Logs & other functions
6.1 Area between curves
15, 17, 25, 28*, 31, 43
1-9odd, 11-14all, 35, 36
Worksheet 3
Quiz 2 on Thursday, Jan. 24, covers sections 5.9, 5.10, 6.1
Jan. 24 6.2 Volumes by slicing
6.3 Volumes by cyl. shells
Quiz 2
1-15odd, 19, 23, 25, 39-42all, 49*, 50*, 60*
1-4all, 5-15odd, 27-29all, 34*
 
Jan. 29 Review for Exam 1 For your practice, here is the Exam 1 given last semester. It covered more material,
so problems 6 and 7 you cannot do at this point. Be aware that your exam is likely to
be quite different;
just working on the problems from last year is not enough practice.
Exam 1 on Thursday, Jan. 31, covers all sections done up to and including 6.2
(but not 6.3).
Office hours on Wednesday, Jan. 30, 12:00-13:20. John Tenenholtz will be also
available for questions from 13:30 to 15:30 outside (or inside) DM 409A.
Jan. 31 Exam 1    
Feb 5 6.4 Arclength 3-5all, 27-31odd  
Feb. 7 6.5 Surface Area
6.6 Work
1-7odd, 23, 26*, 27*, 33, 36, 37
7-9all, 14-18all, 21, 22, 25
Quiz 3 on Thursday, Feb. 14 covers sections 6.3, 6.4, 6.5.
Feb. 12 7.1 More int. by substitution
7.2 Integration by Parts
1-15odd, 24, 25, 28, 29
1-29odd, 55, 57, 60*, 61a, 62b, 63*, 64*, 68*
Worksheet 4
Here is your mini-project for the course. It is worth 50 points.
Deadline to turn it in: Thursday, March 21.

This will be the only mini-project (not two as I initially announced in the syllabus).
Feb. 14 7.3 Trigonometric integrals
Quiz 3
1-11odd, 17, 25, 29, 33, 39, 40, 68*, 70*
I have to cancel office hours both for Friday, Feb. 15, and Monday
February 18. I will have office hours on Wed. Feb. 20 from 11:00am to 1:00pm.
Sorry for the inconvenience.
Feb. 19 7.4 Trig. subs 1-29 odd, 31-35 all, 37, 39
Worksheet 5
 
Feb. 21 7.5. Partial fractions 1-8 all, 9-33 odd, 49, 50 Exam 2 on Thu. Feb. 28 covers sections
6.3, 6.4, 6.5, 6.6, 7.1, 7.2, 7.3, 7.4, 7.5
Possible theoretical exam questions: The work-energy relationship
(proof of formula (6) in section 6.6) and the proof of int. by parts formula.
Feb. 26 Review for Exam 2
7.6 Numerical Approx. of integrals
Here is Exam 2 given last semester. We did not cover yet the material for Pb. 3 and 4(a).
For 4(a), you can compute the integral from e to e^2. You can now do Pbs. 6 and 7 from
the last semester Exam 1.
Additional office hours on Wed. Feb. 27, 12:00-1:20.
(Regular office hours on Mon. Feb. 25, 1:00-2:30)
Feb. 28 Exam 2    
Mar. 5 7.8 Improper Integrals 1, 2, 3-39 odd, 45-51 odd, 55 Here is your Quiz 4. It is a take home quiz, with due date Thu. Mar. 21.
Thus, you'll not have a in class quiz right after Spring break. But you should
finish your mini-project, do this quiz and also work on section 9.1 during  the break.
Mar. 7 9.1 Sequences 1-4all, 5-29odd, 31-34all, 42*, 43, 46*  
Mar. 11-16 Spring break Have a good Spring Break!  
Mar. 19 9.2 Monotone Sequences

1-25odd, (27-31)* all
Worksheet 03/19
Starting this week, until the end of the semester my office hours will be:
Mondays 1:00pm-2:30pm, Wednesdays 12:00noon-1:20pm.
I will no longer have office hours on Fridays.
Mar 21 9.3 Definition of Series 1-14all, 17-24all, 27-30all, 35-37all  
Mar. 26 9.4 Convergence tests
1-8all, 9-25odd
Worksheet/Take home quiz 03/26
The worksheet/take home quiz on the left is due on Thursday, Mar. 28.
Mar. 28 9.5 Comparison & ratio tests
1-4all, 5-15odd, 22, 23, 25-49odd, 51*, 54*  
Apr. 2 9.6 Alt. series; Abs. & conditional conv.
9.8 Power series, interval of convergence
1-27 odd, 31, 32*, 37, 39, 43, 48*, 51*, 52*
29-47 odd
Worksheet/Take home quiz --Due 04/04
The worksheet/take home quiz on the left is due on Thursday, Apr. 04.
Apr.4 9.7 Taylor polys
9.8 Taylor series
9.10 Operations with Taylor series
7-12all, 17, 21, 23
1-6all, 11-27odd
1, 2, 5, 6, 27, 28, 36*, 37, 40
These are some nice links showing the approximation accuracy of Taylor polynomials
of increasing degree: Link 1 Link 2
Apr. 9 9.9 Convergence of Taylor series/
Review for Exam 3
1, 3, 5, 9, 10
Here is Exam 3 given last semester.
 
Apr. 11 10.2 Polar coordinates
10.3 Area in polar coords.
3, 6, 9, 11, 17-49 odd
25, 29-39 odd
Exam 3 is rescheduled for Tuesday, Apr. 16. The topics remain the same,
section 7.8 and the whole Chapter 9 (no polar coordinates on exam 3).
Possible theoretical topics: Thms. 9.3.3, 9.4.1, 9.5.1, Examples 1 or 2 in 9.9 .
Apr. 16 Exam 3    
Apr. 18 Review for final Here are blank copies of your three midterms
Exam 1
Exam 2
Exam 3
The final exam is comprehensive. Expect about 1/3 or maybe a bit more
of the final to be from series. The rest will be on integration and its applications.
One problem will be from  polar coords. sections 10.2, 10.3. Review the three exams and the worksheets. 

If you have time to review section by section (this would be best), 
try to understand what are the central ideas in each section and do a couple of problems from each. 
Apr. 23 Final Exam 9:30am-11:45am regular room Office hours for final: Friday and Monday 10:00am-12:00noon, 1:00pm-2:30pm
       
    Here are the results. In second column is your score
on the final exam (out of 150 pts), in the last column is your grade
for the class.
Have a good Summer and good luck with your further studies!