CALCULUS II SECTION 4 SPRING 2018 UPDATE PAGE
SITARAMAN
Here you will see information on what was covered in class, upcoming quizzes, and solutions to exams
CHECK HERE EVERYDAY !
SCROLL DOWN BELOW TO SEE SOLUTIONS OF TESTS AND QUIZZES FROM THIS COURSE
COURSE PAGE WITH GENERAL INFORMATION (GRADING, ETC)
Tentative schedule of daily topics (SYLLABUS)
TESTS AND QUIZZES FROM FALL 2013
OLD
FINAL EXAMS
FOR SOLUTIONS FOR OLD TESTS from FALL 2010, SPRING 2009 ETC., go to
OLD COURSES.
Click on the desired course, then click on UPDATE.
You can get into the online homework website Webassign
using the class key:
howard 7760 2130
QUICK START INSTRUCTION to see how to get started.
Look under "SELF-ENROLMENT" OPTION
You will need an access code that came with the ebook or in the textbook at the time of purchase.
TUTORIAL LAB everyday 9am-6pm in ASB-B room 109
EXAMS WILL BE ANNOUNCED BELOW
FINAL EXAM MAY 1 TUESDAY 3.30 TO 5.30PM.
ROOM CHB 305 (Chemistry Bldg down the steps past Rankin chapel).
FINAL EXAM
REVIEW Monday April 30, Room 213,ASB-B (behind Locke hall, near my office) starting 1pm.
4/27/2018
Today we had Test III. Solutions are below.
Monday we will do a review for final (see above).
We will go over FINAL AND OTHER TESTS FROM FALL 2013
Fall 2013 final exam
Final exams from other semesters
TEST III
TEST III SOLUTIONS
For test 3 study the following (apart from class notes,
practice problems and quiz solutions (all quizzes after test 2)).
Test 3 will cover 10.3 to 10.5 and 11.1 to 11.10.
Quizzes 9,10,11 and all but problem 1 of Test 3 from
fall 2010 Calculus
Quizzes 15 to 23 and Test 3 from
Fall 2013 Calculus 2.
LAST QUIZ IN CLASS IN THREE PARTS: Friday (20), Monday(23) and Wednesday(25).
No make-ups for this one.
Will give one problem at end of each class that can be done if you pay attention to what we do in class.
GRADUATING SENIORS CONTACT ME ASAP TO TAKE FINAL.
FINAL MUST BE TAKEN BEFORE 27TH.
ALL PENDING WORK MUST BE FINISHED BY Thursday 26TH.
ABSOLUTELY NO OVERDUE WORK WILL BE ACCEPTED AFTER THAT.
4/26/2018, Thursday
FINAL EXAM MAY 1 TUESDAY 3.30 TO 5.30PM.
ROOM CHB 305 (Chemistry Bldg down the steps past Rankin chapel).
We did a review for test 3 today. Test 3 will be tomorrow.
Page 1 (length of arc in polar coordinates).
Page 2 (continuation of page 1, equation of ellipse).
Page 3 (slope of tangent in polar coordinates).
Page 4 (Review of convergence tests).
Page 5 (Telecoping series).
4/25/2018, Wednesday
We discussed 11.10 (Taylor and MacLaurin series) and 11.9 today.
Updated Notes (Taylor and Maclaurin series of functions)from monday and today.
Tomorrow (Thursday) we will do some review problems for test 3.
4/23/2018, Monday
We discussed 11.10 (Taylor and MacLaurin series) today.
Notes (Taylor and Maclaurin series of functions)from today.
Wednesday we will do the practice problem in the notes above as well as one
more from list below.
If time permits we will also review some problems from earlier sections.
Please try problems 5,7,11, 13,27,31,49 from 11.10.
4/20/2018, Friday
We discussed 11.9 (term by term differentiation/integration of power series) today.
Notes (differentiation /integration of power series)from today.
Please try problems 5,7, 13,15,25,39 from 11.9.
4/19/2018
Quiz 10 from today
Quiz 10 solutions
4/18/2018, Wednesday
QUIZ 10 will be tomorrow (thursday), on 11.5,11.6, 11.7 and 11.8.
We discussed 11.7,11.8(miscellaneous series and power series) today.
Notes (power series)from today.
Please try problems 5,7, 15, 23 from 11.8.
I have also updated monday's notes with a lot of problems(below).
You may need to refresh your browser.
EXTRA CREDIT 10 POINTS
PROBLEMS 33,34,44 FROM 11.3.
PLEASE DISCUSS THEM WITH ME IN OFFICE BY WEDNESDAY, 4/18, 3PM.
4/16/2018, Monday
QUIZ 10 will be (thursday), on 11.5,11.6, 11.7 and 11.8.
We discussed 11.6(ratio and root tests) today.
Notes (ratio and root tests)from today.
Please try problems 7, 13, 17, 23, 25, 29,45 from 11.6.
Also try problems 1,3,5,7,13,21,27,35,37 from 11.7.
I have also updated friday's notes (below).
You may need to refresh your browser.
4/13/2018
QUIZ 10 will be (thursday), on 11.5,11.6, 11.7 and 11.8.
We discussed 11.5(alternating series test) today.
Notes (alternating series test)from today.
Please try problems 7, 11, 17, 23, 27,35 from 11.5.
4/12/2018
We WILL HAVE CLASS tomorrow but will finish early.
Quiz 9 from today
Quiz 9 solutions
As mentioned in email, the next two quizzes will be worth 40 points just as this one.
4/11/2018
QUIZ 9 will be tomorrow (thursday), on 11.2,11.3 and 11.4.
We discussed 11.4 (comparison test) today.
Notes (comparison test)from today.
Also reloaded notes from monday (below). Please refresh your browser.
Please try problems 7, 13, 17, 27, 29,31,37,41 from 11.4.
4/10/2018
QUIZ 9 will be on thursday, on 11.2,11.3 and 11.4.
4/9/2018
We discussed 11.3 (integral test) today.
Notes (integral test)from today.
Please try problems 7, 13, 17, 27, 29,37,39 from 11.3.
4/6/2018
We discussed 11.2 (series) today.
Notes (geometric series, telescoping series, divergence test)from today.
Please try problems 15,17,23,25,27,29, 37,39, 43,51,81,82 from 11.2.
The last two problems are really just to challenge your understanding.
4/5/2018
Quiz 8 from today
Quiz 8 solutions
As mentioned in email, the next two quizzes will be worth 40 points just as this one.
We will also have an extra credit assignment soon.
The last test (Test 3) will be on the last day of classes.
4/2/2018
QUIZ 8 tomorrow Thursday, 10.3 to 10.5 and 11.1
NOTE THAT 10.6 IS NOT INCLUDED.
We started with 11.1 (sequences) today and it will be in quiz.
Notes from today.
Please try problems 15,17,23,25,35,,27,37,47,73 from 11.1.
4/2/2018
QUIZ 8 on Thursday, 10.3 to 10.6.
Today we discussed conic sections (10.5).
We also reviewd polar coordinates from friday.
Notes from today.
Please try problems 5,15,19,27,37 from 10.5.
3/30/2018
I didn't know school was closed at 3, so we had class.
Today we discussed polar coordinates (10.3 and 10.4).
These are easy to study from the notes.
If you have questions we can discuss on monday.
Notes from today.
Please try problems 15,17,23,25, 39,57 from 10.3 and
1,17, 21, 45, 47 from 10.4.
3/29/2018
Today we had Test II. Solutions are below.
Tomorrow we will start with 10.3, polar equations.
TEST II
TEST II SOLUTIONS
Due to school closure on 21st, I have moved Quiz 7 to Monday, 26th.
Test 2 will still be next thursday.
TEST 2 Thursday March 29 ; 7.7,7.8, 8.1 to 8.5, 10.1,10.2.
REVIEW IN CLASS WEDNESDAY MAR 28.
PLEASE STUDY CLASS NOTES, PRACTICE PROBLEMS, QUIZ SOLUTIONS AFTER TEST 1
Review problems for Test 2 SOLUTIONS BELOW
These are IN ADDITION to class notes, quiz solutions and practice problems.
Wed, 3/29/2018
Review problem solutions
These are IN ADDITION to class notes, quiz solutions and practice problems.
3/26/2018
Quiz 7 from today
Quiz 7 solutions
Review problems for Test 2 SOLUTIONS ABOVE
These are IN ADDITION to class notes, quiz solutions and practice problems.
We will go over these on wednesday.
3/23/2018
QUIZ 7 Monday, March 26, 8.5,10.1,10.2.
Today we discussed derivatives and integrals of parametric equations of curves (10.2).
We saw how to calculate area, length of arc and surface area using parametric equations.
Notes from today (Parametric equations--area, length of arc, surface area).
Please try problems 5,7,11,29,33,41,43,51,61,63 from 10.2.
3/22/2018
QUIZ 7 Monday, March 26, 8.5,10.1,10.2.
Today we discussed parametric equations of curves (10.1).
Notes from today (Parametric equations).
Please try problems 5,9,33,46 from 10.1.
EXTRA CREDIT 20 POINTS:
Do problems 73,74 and 75 from 7.8 and answer questions in my office.
It will be like a small oral test and the questions will be on or related to
these three problems.
You must do this by 3pm on the 22nd of this month.
3/19/2018
QUIZ 7 Monday, March 26, 8.5,10.1,10.2.
Today we discussed applications of integration to probability theory (8.5).
Notes from today (Probability).
Please try problems 1,3,7,9,13,17 from 8.5.
3/9/2018
Today we had Quiz 6. Solutions are below.
Monday the 19th we will start 8.5 (Probability).
QUIZ VI
QUIZ VI SOLUTIONS
3/8/2018
QUIZ 5 Friday, March 9, 8.2,8.3,8.4.
Today we discussed applications of integration to economics and biology(consumer surplus, population growth, growth of an investment, etc.,) (8.4).
Notes from today.
Please try problems 5,9,12,15,16,22 from 8.4.
I also showed how to find the surface area of the prolate ellipsoid.
This is Problem 8.2.27.
3/7/2018
Today we discussed applications of integration (pressure on dam, center of mass) (8.3).
Notes from today.
Please try problems 7,9,12,27,30,31 from 8.3.
I have also uploaded notes from monday with solution to problem 27 of 8.2.
It shows that "Gabriel's horn" has infinite surface area.
Earlier we showed it has infinite area (from which it is obtained by rotating)
and finite volume.
Reload the link below.
3/5/2018
Today we discussed surface area (8.2).
Notes from today.
Please try problems 7,11,17,27,31 from 8.2.
3/2/2018
Today we had Quiz 5. Solutions are below.
Monday we will start 8.2 (SURFACE AREA USING INTEGRATION).
QUIZ V
QUIZ V SOLUTIONS
3/1/2018
QUIZ 5 Friday, March 2, 7.7,7.8,8.1.
Today we discussed arc length (8.1).
Notes from today.
Please try problems 9,13,15,19,21,39 from 8.1.
2/28/2018
QUIZ 5 Friday, March 2, 7.7,7.8,8.1.
Today we discussed more about improper integrals (7.8).
Tomorrow we will do 8.1.
Notes from today.
Please try problems 1,5,7,11,13,15,21,29,31,39,51,49,63 from 7.8.
39 is actually done on the bottom of last page of wednesday's notes, but with different limits of integration.
2/26/2018
QUIZ 5 Friday, March 2, 7.7,7.8,8.1.
Today we discussed improper integrals (7.8).
Wednesday we will finish it.
Notes from today.
Please try problems 1,5,7,11,13,15,21,29,39,63 from 7.8.
39 is actually done on the bottom of last page of today's notes, but with different limits of integration.
2/23/2018
Today we continued with approximate (numerical) integration (7.7).
Monday we will start 7.8.
UPDATED Notes for approximate integrals (7.7)(MAY NEED TO REFRESH YOUR BROWSER)
Please try problems 5,7,11,15,17,29,35 from 7.7.
2/22/2018
Today we discussed approximate (numerical) integration (7.7).
Tomorrow we will continue with 7.7.
Notes for approximate integrals (7.7)
Please try problems 5,7,11,15,17,29,35.
2/21/2018
Today we had Test I. Solutions are below.
Tomorrow we will start with 7.7, approximation of integrals.
TEST I
TEST I SOLUTIONS
TEST I ON WED FEB 21. 6.1-6.5 and 7.1-7.5.
REVIEW IN CLASS FRIDAY FEB 16.
PLEASE STUDY CLASS NOTES, PRACTICE PROBLEMS, QUIZ SOLUTIONS AND THE FOLLOWING OLD PROBLEMS:
ALL problems EXCEPT 4 and 5 in BOTH Fall 2013 test 1
and
Fall 2010 Test I.
Problems 1,2,3,4 in Fall 2013 test 2
and all EXCEPT 1,2a,7 in Fall 2010 Test 2
2/16/2018
Today we did a review for test 1. See above for details.
Here is one problem we did in class:
The volume of a solid of revolution using cylindrical shells.
NOTE: In the picture it should also say: "When y = 9, x = 6."
This is problem 6.2.5. We did this in class on 1-22 (see notes) but using slicing method.
Usually one method works better than the other but for this one both are about the same.
2/15/2018
Today we had Quiz 4. Solutions are below.
Tomorrow we will do a review for test 1. See above for details.
QUIZ IV
QUIZ IV SOLUTIONS
2/14/2018
QUIZ 4 ON THURSDAY, ON 7.4 AND 7.5 ONLY
Study class notes and practice problems.
Today we finished discussing integration using partial fractions(7.4).
We also did some problems from 7.5.
Updated notes for partial fractions with problems added from 7.5.
Please try 8,10,15,19,21,23 from 7.5.
2/8/2018
Today we discussed integration using partial fractions(7.4).
Notes for partial fractions.
Please try the problems in the notes that were not done in class.
We will do them wednesday.
Please also try problems 11,17,23,31,37,43,47 from 7.4.
2/9/2018
Today we had Quiz 3. Solutions are below.
Monday we will start 7.4 (PARTIAL FRACTIONS).
QUIZ III
QUIZ III SOLUTIONS
2/8/2018
Apology for delayed posting.
QUIZ 3 ON FRIDAY, ON 7.2 AND 7.3 ONLY
Study class notes and practice problems.
EXTRA CREDIT (10 POINTS) PROBLEM 7.1 NUMBER 67 AND Problems 67 to 70 in 7.2.
Please discuss it with me in office by next wednesday, 3pm if you wish for the credit.
Today we discussed trigonometric substitution(7.3).
Notes for trigonometric substitution.
We also discussed relationship between trigonometric integration and Fourier analysis.
Fourier analysis is used in signal processing and data compression.
A video on Fourier analysis.
Please try problems 7,13,17,23 from 7.3.
2/7/2018
QUIZ 3 ON FRIDAY, ON 7.2 AND 7.3
EXTRA CREDIT (5 POINTS) PROBLEM 7.1 NUMBER 67
Please discuss it with me in office by next wednesday, 3pm if you wish for the credit.
Today we finished trigonometric integrals (7.2).
Updated Notes for trigonometric integrals
Please try problems 3,9,13,17,19,27, 33,41,45,67,68,69,70 from 7.2.
2/5/2018
Today we discussed trigonometric integrals (7.2).
Notes for trigonometric integrals
Will complete last two problems wednesday but please try them.
Also please try problems 3,9,13,17,19,27 from 7.2.
2/2/2018
Today we had Quiz 2. Solutions are below.
Monday we will start 7.2 (Trig integrals).
QUIZ II
QUIZ II SOLUTIONS
2/1/2018
QUIZ II ON FRIDAY, 2/2 ; SECTIONS 6.4,6.5,7.1.
Today also we discussed integration by parts (7.1).
REVISED Notes for integration by parts (including Thursday's class)
1/31/2018
QUIZ II ON FRIDAY, 2/2 ; SECTIONS 6.4,6.5,7.1.
Today we discussed integration by parts (7.1).
Notes for integration by parts (including Thursday's class)
Tomorrow we will finish what is in notes above.
We will also do additional problems in preparation for Quiz 2 on friday.
Please try problems 3,11,15,17,33,39,47,49,51,61,65,67,69 from 7.1.
1/29/2018
Today we discussed computing average value of a function using integration (6.5).
Notes (average value, using integration)
We also went over Problem 13 in 6.4
Please try problems 5,7,9,13,19,22 from 6.5.
1/26/2018
Today we discussed Quiz 1 (solutions below) and talked about computing "amount of work done" using integration (6.4).
Notes (work done, using integration)
Please try problems 7,9,13,21,33 from 6.4.
1/25/2018
Today we had Quiz 1. Solutions are below.
Tomorrow we will start 6.4.
QUIZ I
QUIZ I SOLUTIONS
QuizI will be on thursday, the 25th.
It will cover 6.1,6.2 and 6.3.
1/24/18
Today we discussed how to find volumes using integration with cylindrical shells.
Notes from today.
Please try problems 3,5,9,13,17,29 from 6.3.
If you have questions on them we can go over them tomorrow.
Some of them might show up in first quiz.
1/22/2018
Today we discussed how to find volumes using integration.
Notes from today.
Please try problems 3,7,9,11,47,55 from 6.2.
If you have questions on them we can go over them on monday.
Some of them might show up in first quiz thursday.
1/19/2018, 7.30pm
Today we discussed area between curves.
Please note that I drew the graph for problem 10 by mistake, when we did problem 6.
Both problem 10 and 6 have sinx and x but in 10 it is x times something.
Having just x makes it much simpler.
I have uploaded the correct graph in the notes below.
Notes from today.
Please try problems 1, 9,11,15,17, 49,53 from 6.1.
If you have questions on them we can go over them on monday.
Some of them might show up in first quiz next week.
1/19/2018
There was a typo in problem 5b of the concept test below.
It should read "if f'(x)=g'(x) then f(x) = g(x)."
The typo has been corrected.
1/17/2018
Sorry for delay in uploading this.
Please do the concept test below. You have upto wednesday 24th.
Notes from class today: Introduction and a bit of history
Powerpoint on basic idea of finding volume using integration
1/9/2018
In the first week we will discuss basic concepts of calculus, from Calculus I, area under curves, and a bit of history: an ancient Egyptian papyrus discussion of the "Rule of Single False Position"--
this can be thought of as a rudimentary form of Newton's method of approximating solutions using tangent and secant lines.
Please do the Calculus review problems by friday the 19th.
Please go over your answers with me by same date to get extra credit.
If you need to review Calculus I material, here are the
TESTS AND QUIZZES FROM FALL 2017 CALCULUS I
Please read this paper, if you are interested, about the ancient Egyptian papyrus discussion of the "Rule of Double False Position."
This can be thought of as a rudimentary form of Newton's method of approximating solutions using tangent and secant lines.
Also read about how Egyptians may have figured out a formula for volume of frustum of a pyramid.