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

CHECK HERE EVERYDAY !

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

You will need an access code that came with the ebook or in the textbook at the time of purchase.

TEST 2 Thursday March 29 ; 7.7,7.8, 8.1 to 8.5, 10.1 to 10.4.

More details soon.

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 21st of this month.

3/19/2018

QUIZ 6 Friday, March 23, 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

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.