Here you will see information on what was covered in class, upcoming quizzes, and solutions to exams

CHECK HERE EVERYDAY !

OLD FINAL EXAMS

FOR SOLUTIONS FOR OLD TESTS from FALL 2010: OLD COURSES

Click on the desired course, then click on UPDATE

FREE online homework website based at Howard for doing practice problems only:

Use practice1 (or practice2 or practice3...) as username and same as password

Instructions to access companion website for texbook (thanks to Dr. Washington)

If you have further questions check out her twitter account

EXAMS WILL BE ANNOUNCED BELOW

If you get 500 or more in 3 tests + quizzes you will be exempted from final exam.

REVIEW MONDAY DEC 9 FROM 2 TO 4PM, ASB-B 213 (near my office).

If you wish to discuss your grade please do so BEFORE final exam.

Try the following problems before coming to the review on monday:

Page 355: 21,23,43,49,53,59

Page 414: 7, 11, 15,17,19,21,23,25,27,29

Page 442: 15,23,25,41,43

page 507: 1,3,5,7,9,11,29,31,33,37,41,45,47,53,63,65

page 624: 19,23,25,27,29,31,35,37,41,43,47, 57,63,65,67

page 673: 9,11,12,13,15,17,23,29,33,35,43,45,47,51,53

I will answer questions you might have about these problems and also work out some old final exams during the review

There is a link for old final exams above

According to university website and their email final exams will go on as scheduled.

Please keep checking university website and their emails.

Today review will happen as scheduled at 2pm in ASB-B 213 near my office.

I will be in office from 11 am onwards.

Today we discussed conic sections.

Quiz 23 SOLUTIONS

I have put up review problems for final exam above

Today we discussed graphing curves whose equation is given in polar co-ordinates.

For wednesday's quiz please study 11.3,11.4 and 11.5

We will go over this material (11.3 to 11.5) tomorrow.

11.3: 3,5,9,11,13,17,21, 33,35,45, 55,59,61,65

11.4: 1,5,7,9,22,24

11.5: 1,2,3

Also try problems from the set "polar coordinates"

Quiz 22 SOLUTIONS

Please study 11.1 and 11.2 (see previous updates below for review problems).

Also do the webwork sets "parametric-equations."

TEST 3 SOLUTIONS

Try test 3 with solutions from Spring 09

Try quiz 6, quiz 7, quiz 8, quiz 9 (first two problems) and test 3 (all except first and last problems) from here: Update page of Spring 2010.

Today we discussed polar equations.

Please try following review problems from 11.3:

3,5,9,11,13,17,21, 33,35,45

Solutions and comments for Quiz 21 from today

Also try the webwork set "polar-equations".

Monday: No Quiz! We will review chapter 10 for test.

Today we discussed finding derivative, length of arc, area, etc., using parametric equations.

Please try following review problems from 11.2:

3,5,13,21,25,27,31,33

Also try the webwork set "parametric-equations".

Friday we will do 11.3 and have a quiz on Taylor series (10.8 and 10.9).

Today we discussed finding radius and interval of convergence of power series, and also started on parametric equations.

Please try following review problems from 11.1:

3,5,9,11,13,17,21, 23,33,35, 39

Solutions and comments for Quiz 20 from today

Also try the webwork set "parametric-equations".

Tomorrow we will continue with 11.1 and 11.2.

Today we discussed Taylor series and Taylor polynomials.

Please try following review problems from 10.8 and 10.9:

10.8: 1,3,7,13,17

10.9: 3,7,11,13,29,35

Also try the webwork set "Taylor-series".

Tomorrow we will discuss Taylor series a little more and then start 11.1.

Tomorrow's quiz will be on power series -- finding radius and interval of convergence.

MONDAY WE WILL HAVE PROBLEM SESSION AS USUAL AT 3.30 IN MY OFFICE.

Today we continued discussing power series.

We discussed absolute and conditional convergence and finding radius of convergence, and also term by term differentiation and integration.

Please try following review problems from 10.7:

3,5,7,9,11,13,17,23,33,39

Solutions and comments for Quiz 19 from today

Also try the webwork set "power-series".

Monday we will discuss Taylor series of a function.

Today we continued and finished discussing alternating series test.

We discussed absolute and conditional convergence.

Please try review problems from 10.6 listed below.

Solutions and comments for Quiz 18 from today

Also try the webwork set "more-series".

Tomorrow we will discuss absolute convergence test and start on power series.

Quiz on tuesday will be on 10.4 and 10.5 (comparison, ratio and root tests).

Please do the following review problems for 10.6:

1,3,5,7,9,13,51,53

Also try the webwork sets "more-series."

Tuesday we will discuss absolute and conditional convergence and start on power series.

Applications of series

Today we discussed, ratio and root tests.

We discussed the divergence test and how the integral test can be used.

Please try the following from 10.5:

1,3,7,9,11,13, 17,19,27, 31,33,41,43,45,51

Solutions and comments for Quiz 17 from today

Also try the webwork set "more-series" ( for now only ratio test, though).

Quiz tomorrow will be on 10.3 and 10.4

Please do the following review problems for 10.4:

1,3,5,7,9,13,15

Also try the webwork sets "sequences" and "series."

Tomorrow we will discuss ratio and root tests.

We discussed various series and the tests and theorems that can be used to check for convergence and find the sum.

Please do the review problems for 10.1 to 10.3 below.

Also try the webwork sets "sequences" and "series."

Tomorrow we will discuss integral test and comparison test.

We discussed the divergence test and how the integral test can be used.

Please try the following from 10.3:

3,7,9,11,13,19,23,25,33,37,55

Solutions and comments for Quiz 16 from today

Also try the webwork set "series"

We discussed sums of geometric series, telescoping series and the test for divergence.

Please try the following from 10.2:

3,5,7,11,15,19,27,31,33,35,41,45,49,53,55,65

Friday's quiz will involve 10.2

Today we finished 10.1 and started 10.2 by talking about geometric series.

10.1: 69, 71, 75, 78, 85, 87, 93,97

For 93 and 97 you start by letting limit = L and come up with an equation for L and then solve it.

Solutions and comments for Quiz 15 from today

Some paradoxes dealing with infinity

Today we covered more of 10.1, talking about how to find the limit of a sequence using the sandwich (squeeze) theorem and other techniques.

In addition to problems from friday please try webwork set "sequences"

We will finish 10.1 and start 10.2 tomorrow

Quiz tomorrow will be based on what we did friday and today.

We discussed how to identify the patterns in sequences and write formulae for them

Please try 1,5,13,15,19,23,27,31,37,43,47,49

Solutions and comments for Test II from today

TEST II ON WEDNESDAY OCT 23 ON ALL OF CHAPTER 8 EXCEPT 8.5

REVIEW IN CLASS TUESDAY

Please study class notes for chapter 8 except 8.5

Try these old tests: fall2010test2 (all except prob 1) and spring2009test2

You can also see solutions to quizzes from old courses by going through the update page for that course:

Click on OLD COURSES then click on desired course then scroll down and click on UPDATE

Please also go through review problems for 8.1,8.2,8.3,8.4,8.6,8.7 listed below

Also try Webwork problems for these sections listed below.

I have sent out an email about your MIDTERM GRADES and what you can do to IMPROVE YOUR GRADES.

Please let me know if you didn't get it.

See above for what to study for the test on wednesday.

TODAY PROBLEM SESSION STARTING 3.30 PM. MEET IN MY OFFICE 219 ASB-B

Today we finished 8.7, integration of improper integrals.

Please try problems 1,3,13,21,25 from 8.7

I circulated a handout about the class in general. Please read it

Learning Math : What is it about?

MONDAY PROBLEM SESSION STARTING 3.30 PM. MEET IN MY OFFICE 219 ASB-B

Today we started 8.7, integration of improper integrals.

Please try problems 1,17 from 8.7

Solutions and comments for Quiz 14 today

I have also put up solution for quiz13 below, under 10/15/2013

Sorry I forgot to put it up on tuesday

Today we finished 8.6, numerical integration.

Please do problems 3,5,23,37

Quiz on friday will be on 8.4, integration by partial fractions

Today we finished 8.4, integration using partial fractions.

Please try from 8.4 problems 19,21,25,35,39 also

Please try the webwork problem set "integration-partial fractions"

Solutions and comments for Quiz 13 today

WEDNESDAY PROBLEM SESSION STARTING 3.30 PM. MEET IN MY OFFICE 219 ASB-B

Today we started 8.4, integration using partial fractions.

Please do problems 11,13,15,17

Quiz on tuesday will be on 8.3, integration by trigonometric substitution

Please also try the webwork problem set "integration-partial fractions"

Solutions and comments for Quiz 12 today

Today we did 8.3, integration using trigonometric substitution.

We ran out of time for Quiz on 8.2. It has been postponed to friday

Please do review problems listed below (under 10/7/2013) for 8.2.

Please also try the webwork problem set "trig-integrals"

For 8.3 try 3,7,11,15,25,35,45,53,55,57

I have added some trig substitution problems to the webwork set "trig-integrals."

Today we finished 8.2, integration of trigonometric expressions.

The main ingredients are substitution and integration by parts combined with trigonometric identities

Please do review problems listed below. I have added a couple today

Quiz on 8.2 has been postponed to tomorrow

Please also try the webwork problem set "trig-integrals"

Today we discussed 8.2, integration of trigonometric expressions.

The main ingredients are substitution and integration by parts combined with trigonometric identities

Please do problems 3,5,7,11,13,17,19,21,23,25,29,33,35,37,45,51,53,55,69,71

Quiz tomorrow will be on 8.2

Please also try the webwork problem set "trig-integrals"

MONDAY PROBLEM SESSION STARTING 3.30 PM. MEET IN MY OFFICE 219 ASB-B

Today we finished discussing integration by parts.

We did problems involving the following:

Integration by parts repeatedly

Integration by parts combined with substitution and trigonometric identities

Please do problems 5,9,11,13,15,17,19,25,37,39,41,47,51,53,55,57,59

Quiz on friday will be on integration by parts

Please also try the webwork problem set "integration-techniques"

Solutions and comments for Quiz 11 today

Today we discussed integration by parts,further reviewing integration by substitution along the way.

Please do problems 5,9,11,13,15,17,19,25,37,39,41,47,51,53,55,57,59

Quiz on friday will be on integration by parts

Please also try the webwork problem set "integration-techniques"

Solutions and comments for Quiz 10 today

We also started integration by parts.

Please try the following from the book:

5.6 (substitution): 7,9,27,29,39

8.1 (integration by parts): 1,3,5,7,11,13

Please also try the webwork problem set "integration-techniques"

Starting next monday we will have a problem session every monday at 3.30pm. Room TBA.

Please prepare for quizzes just like you would for a test.

Please work with me, with your classmates or in tutorial lab EVERYDAY.

Monday we will start the next chapter (Chapter 8)

Solutions and comments for Test I from today

TEST I WILL BE ON WEDNESDAY SEP 25

TEST WILL BE HARDER THAN QUIZZES, SO PLEASE PREPARE WELL

REVIEW IN CLASS TOMORROW

Today we discussed inverse hyperbolic sine and cosine functions, starting with inverse (usual) sine and cosine and touching on trigonometric substitution along the way.

Solutions and comments for Quiz 9 today

TEST I WILL BE ON WEDNESDAY SEP 25

TEST WILL BE HARDER THAN QUIZZES, SO PLEASE PREPARE WELL

Look above for instructions to access companion website for textbook (thanks to Dr. Washington)

Today we started 7.3, hyperbolic sine and cosine.Will continue on monday

I also talked about basics of differentiating and integrating exponential functions

Please review differentiating and integrating techniques for exponential, trigonometric and logarithmic functions

I have added review problems to the homework set "Hyperbolic-sine-cosine"

Please try section 7.3 problems 1,3,13,17,21,25,31,35,47,53,67,69,71,79,81

Monday's quiz will be on 6.5 only.

TEST I WILL BE ON WEDNESDAY SEP 25, REVIEW TUE 9/24 (BOTH IN CLASS)

TEST WILL BE HARDER THAN QUIZZES, SO PLEASE PREPARE WELL

Today we did problems 1 and 14 from 6.5, applications of integration.

I have added review problems to the homework set "APPLICATIONS-TO-SCIENCE"

Also try problems 3,9,13,31 and 33 from 6.5

Solutions and comments for Quiz 8

TEST I WILL BE ON WEDNESDAY SEP 25

TEST WILL BE HARDER THAN QUIZZES, SO PLEASE PREPARE WELL

Look above for instructions to access companion website for textbook (thanks to Dr. Washington)

Today we finished 6.5, applications of integration.

I have added review problems to the homework set "APPLICATIONS-TO-SCIENCE"

I have corrected the answer for the quiz

(it should be 5 times square root of 5 instead of 25 times square root of 5)

Solutions and comments for Quiz 7

TEST I WILL BE ON WEDNESDAY SEP 25

TEST WILL BE HARDER THAN QUIZZES, SO PLEASE PREPARE WELL

Look above for instructions to access companion website for textbook (thanks to Dr. Washington)

Today we started 6.5, applications of integration.

I have added review problems to the homework set "APPLICATIONS-TO-SCIENCE"

Please do the following :

5.4: 75

6.5: 3,6,9

Solutions and comments for Quiz 7 from today

TEST I WILL BE ON WEDNESDAY SEP 25

Today we finished 6.4, surface area of solids of revolution.

I have added review problems to the homework set "surface-area"

Please do the following from 6.4: 3,11,15,19,29

Quiz monday will be based on 6.4.

Also on monday we will start 6.5, applications to physics & engineering

Solutions and comments for Quiz 6 from today

TEST I WILL BE ON WEDNESDAY SEP 25

Today we went over 6.4, surface area of solids of revolution.

I have added review problems to the homework set "surface-area"

Please do the following from 6.4: 3,11,15,19,29

No quiz was given today but Quiz friday will be based on 6.3, arc-lengths.

See below for what to study in 6.3.

TEST I WILL BE ON WEDNESDAY SEP 25

Today we went over 6.3, arc-lengths. Quiz tomorrow will be based on this.

I have added review problems to the homework set "arc-length"

Please do the following from 6.3: 1,3,7,9,13,21

Challenge Problem: try to find the circumference of the circle of radius 1 by taking the limit as n goes to infinity of the perimeter of the inscribed regular n-gons. (regular means all sides are equal). Your answer must be close to 2 times pi.

TEST I WILL BE ON WEDNESDAY SEP 25

Today we reviewed 6.2, including volumes of solids obtained by revolving on axes other than x or y axes.

I have added more review problems to the homework set "volumes by shells"

Please do the following from 6.2: 25, 37, 42

Please also do the following from 6.1: 49, 51, 55

Problems 42, 55 are a tiny bit more challenging

Tomorrow we will start on arc-lengths(6.3) and there will not be a quiz.

Solutions and comments for Quiz 5 from today

TEST I WILL BE ON WEDNESDAY SEP 25

Today I gave a review of all the methods and formulae we have used so far.

We will discuss the volumes of solids of revolutions about axes other than x or y axes on monday.

I have added more review problems to the homework set "volumes by shells"

Please also do the following from 6.2: 15,17,21

Solutions and comments for Quiz 4 from today

TEST I WILL BE ON WEDNESDAY SEP 25

Since a majority of the class did not do well on this one, I plan to have another quiz on the same topic (volume by slicing) on friday. Please review the solutions for the quiz (below) and go over the review problems for 6.1 in the textbook and / or webwork.

We will continue the discussion of volumes using cylidrical shells on friday.

Also, please remember that the quizzes will be based on the PREVIOUS one or two classes. A few tried to do the quiz using cylindrical shells, that we went over today in class. The problem is not suitable for shells method (although it is possible to do it that way as well).

Solutions and comments for Quiz 3 from today

REVIEW PROBLEMS FOR 6.2 (MORE TO BE POSTED FRIDAY): 1,5, 9,11

A few review problems have also been posted in Webwork (do homework set "volumes by shells").

Today we discussed volume of solids using slicing

PRACTICE PROBLEMS FOR VOLUMES BY SLICING POSTED ON WEBWORK

REVIEW PROBLEMS: 6.1 PROBLEMS 5,7,12, 19,23,33,45,47,59

Basic idea is to find volume by "adding up" the volumes of the slices obtained by slicing the solid perpendicular to the x or y axes

For solids that are circular in cross-section (solids of revolution), the slices will look like disks or washers

We did problem 11 (volume of tetrahedron) from book. I also reviewed the calculation of the volume of the cone. It is interesting how both of them are one-third of the volume of the "completed solids" -- the prism and the cylinder -- respectively

Here are two links to visualize why that is so:

TETRAHEDRON AND PRISM

CONE AND CYLINDER

Solutions and comments for Quiz 2 from today

Today(8/30 wed) we continued discussion of area under curves, doing integration along y axis.

Then I showed how to find volume of a cone using integration, by slicing it into cylindrical disks.

Challenge problem: Find formula for volume of frustum of pyramid with square base and top using integration, by cutting it into thin square slabs.

We ended the class with a quiz. See above

On tuesday we will continue with volume integration using cross sections approximated by cylindrical disks. You can start working on some problems from 6.1. Will post some later on.

Solutions and comments for Quiz 1 from yesterday

Yesterday(8/28 wed) we continued discussion of area under curves, doing problems 93 from book. I also clarified an example I gave on monday involving velocity and displacement.

Then I gave a light mostly historical introduction to the approximation of length, area, volume, etc., using rectangles and triangles.

Here is a discussion of the Egyptian method for approximating he volume of a piece of a pyramid:Moscow Mathematical Papyrus

We ended the class with a quiz. See above

PRACTICE PROBLEMS FOR AREA UNDER CURVES POSTED ON WEBWORK

Today we discussed area under curves, doing problems 47 and 57 of Section 5.6 from book

PRACTICE PROBLEMS FOR AREA UNDER CURVES POSTED ON WEBWORK

Also try the following problems from textbook:

5.6: 51,55,63,67,73, 77,93, 97, 103

Yesterday (8/26) we talked about basic concepts of calculus, from Calculus I.

Please do the calculus review problems on webwork.

I also talked about 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

For more information see Papakonstantinou's book, pages 12-15