Welcome.

Here you will see info about what we did in class, upcoming exams, solutions for past exams, etc.,

CHECK AT LEAST ONCE A WEEK!!

SYLLABUS

COURSE PAGE

Started 8/15/2018

UPDATE PAGE from Fall 2017 Calculus I with

You can get into the online homework website Webassign using the class key: howard 2324 4616

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

Please do the diagnostic test in the textbook (just before "Preview of calculus") to make sure you are prepared for course.

SCROLL DOWN TO THE BOTTOM FOR MORE MATERIAL TO HELP YOU PREPARE FOR CLASS

SEE YOU IN CLASS MONDAY!

PLEASE USE ebook for Stewart's Calculus 8th edition

Monday, 12/3/2018.

BRIEF SOLUTIONS FOR FINAL EXAM ABOVE

BRIEF SOLUTIONS FOR SPRING 2016 FINAL EXAM

(Spring 2016)some review problems for final

SOLUTIONS FOR FALL 2015 FINAL EXAM

TUTORING AVAILABLE IN TUTORING CENTER ASB-B GROUND FLOOR MON 9-4 AND TUE 11-1.

Friday, 11/30/18.

FINAL EXAM REVIEW MONDAY DEC 3, 11 AM TO 1PM ROOM 213, ASB-B.

Solutions for Test 3.

Please try Test 3 problems.

The Fall 2018 COAS Course Evaluations extended through Tuesday, December 4, 2018:

Please check your email for link to evaluation.

Wednesday,11/28.

I have updated the solutions (specifically problems 3 and 12) for the test 3 review problems from Fall 2015 below.

Please also study all class notes given below as well as quiz problems.

TEST 3 ON NOV 29: REVIEW WED NOV 28.

It will cover 4.5,4.7,4.9,and 5.1 to 5.5.

Topics: Curve sketching, Maxima minima problems, Basics of Integration, Substitution method.

TRY PROBLEMS FIRST BEFORE LOOKING AT ANSWERS.

IGNORE PROBLEMS ON L'HOSPITAL'S RULE AND ROLLE'S AND MEAN VALUE THEOREM IN TESTS BELOW.

Fall 2015 test 3 review problems; Fall 2015 test 3 review problem solutions; Fall 2017 test 3 solutions;

PLEASE USE ebook for Stewart's Calculus 8th edition

Monday, 11/26/18.

Please read Integration by Substitution

Practice problems for 5.5: 13,21,25,35,45,59,66,69,79,84.

(for 66 use the fact that sine is an odd function. Look at example 11).

Please try Quiz 10 problems.

This will help you prepare for test 3.

After trying them, please read Solutions for Quiz 10.

Thursday, 11/22/18.

Happy thanksgiving!

On monday we went over the Chapter 4 (questions 7 to 21) and Chapter 5 (all) True-False questions.

The true false questions are at the end of the file. Chapter 4 questions 1 to 6 were done earlier.

Please try them yourself and then look at the Solutions for the chapter 4 and 5 true false questions.

This will help you prepare for test 3.

On monday we will go over 5.5.

Friday, 11/16/18.

QUIZ 10 will help you prepare for test 3!

QUIZ 10 TO COVER 4.9, 5.1, 5.2,5.3, 5.4.

Tuesday I am in my office until 3pm and then tomorrow I will be here 10 to 12pm.

I have updated the Notes on integration (Definite integrals, Fundamental theorem...).

You may need to refresh your browser.

Practice problems for 5.3 and 5.4:

5.4: 5,9,15,31, 37,43,49,61,63,67,71.

5.3: 3,9,13,21,29,31,37,45,59,63,72.

Extra credit work (10 points): APPLIED PROJECT: PLANES AND BIRDS.

Page 344, end of section 4.7.

Explain your answers to me in office. by wednesday, 11/28.

Thursday, 11/15/18.

I have updated the notes on integration (see below).

You may need to refresh your browser.

Practice problems for 5.2: 3, 5,7,9,19,23,33,49,57,58,63.

Wednesday, 11/14/18.

Please read Notes from today (Approximating area using rectangles).

Practice problems for 5.1: 1,3,13,17.

Friday, 11/9/18.

ONLY ABOUT A MONTH TO GO!

VERY IMPORTANT TO DO WELL IN QUIZZES

THEY WILL HELP YOU DO WELL IN TESTS AND FINAL.

GRADES TEND TO GO DOWN AFTER FINAL, ON AVERAGE.

Please read Notes from today (Antiderivatives).

Overview of integration.

Practice problems for 4.9: 7,9,15,23,25,27,33,41,67,75.

Thursday, 11/8.

Please read Solutions for Quiz 9.

We will talk about integration and antiderivatives (4.9) friday in class.

Quiz 9 problems.

Wednesday, 11/7.

Quiz 9 on 4.5 and 4.7 tomorrow.

I have updated the notes from monday (see below).

Please reload it to see latest version.

Monday, 11/5/18.

Yesterday we discussed 4.7: Optimization problems (Notes).

Practice problems for 4.7: 3,5,9,15,19,20,35,37, 41,45,53,61,74.

Friday, 11/2/18.

Today we discussed 4.5: Curve sketching (Notes).

Practice problems for 4.5: 5,9,15,35,43,55,65.

Monday we'll do 4.7 (Optimization / Application of maxima minima).

Thursday, 11/1.

Please read Solutions for Test 2.

We will talk about curve sketching (4.5) tomorrow.

Test 2 problems.

TEST II THU NOV 1; REVIEW WED OCT 31

It will cover 3.3 TO 3.10 AND 4.1 TO 4.4.

Topics: Chain rule, derivatives of trigonometric functions, implicit differentiation, applications of derivatives, maxima minima, L'Hospital's rule.

Please study these old test problems with solutions:

TRY PROBLEMS FIRST BEFORE LOOKING AT ANSWERS.

Fall 2015 test 2 review problems; Fall 2015 test 2 review problem solutions; Fall 2017 test 2 solutions;

Problem 1 and 3 of Fall 2017 Quiz 8 solutions

Problems 1, 2, 4 of Fall 2017 test 3

PLEASE USE ebook for Stewart's Calculus 8th edition

Wednesday, 10/31/18.

We reviewed some problems fall 2015 test2 today.

Note that solutions are also given above.

We also went over Chapter 4 review (true false problems).

Tuesday, 10/30/18.

Yesterday we discussed 4.4: L'Hospital's rule (Notes).

Practice problems for 4.4: 9,13,17,19,25,27,33,43,47,59,73,78,81.

Tomorrow we'll do a review.

Today we discussed 4.2: Rolle's and mean value theorem(Notes).

Thursday, 10/25.

Please read Solutions for Quiz 8.

We will talk about L'Hospital's rule (4.4) monday in class.

Please try the extra credit problems (below) before coming monday.

Quiz 8 problems.

Wednesday, 10/24/18.

Tomorrow quiz 8 on 4.1 and 4.2

Friday no class but please read Notes on 4.3 (behavior of functions and derivatives)

and do problems 11,17,23,27,55 in 4.3.

If you turn them in by Monday in class you get 5 points extra credit.

Today we discussed 4.2: Rolle's and mean value theorem(Notes).

Practice problems for 4.2 : 5,7,9,11,13,17,21,23,25.

Next monday we will discuss L'Hospital's rule (4.4).

Monday, 10/22/18.

Today we discussed 4.1: Maxima/minima and critical points(Notes).

Practice problems for 4.1 below (see friday):

We also went over Chapter 3 review (true false problems).

I have corrected solution for 9. I misread problem earlier.

Thursday we will have quiz on 4.1 and 4.2.

Friday, 10/19.

Friday, 10/19.

Today we discussed 4.1: Maxima/minima and critical points(Notes).

Practice problems for 4.1:

4.1:1,3,7,19,25,29,35,39,41,49,59,73.

We also watched the video from Hidden figures where she studies the Euler method that involves a bit of differentials.

If you stop at minute 1:11 you can read the lines in the page describing the modified Euler method.

It involves using linear approximation to find a nearby y value and plugging it into the differential equation to find the slope.

Friday, 10/19.

Please read Solutions for Quiz 7.

We will talk about chapter 4 (maxima/minima) today in class.

Quiz 7 problems.

Wednesday, 10/17/18.

QUIZ 7 TOMORROW THURSDAY, on 3.9 and 3.10.

Today we discussed 3.10: Differentials and Linear Approximation(Notes).

Practice problems for 3.10:

3.10: 5,13,23,33,40.

Tuesday 10/16.

Yesterday we covered 3.9 (related rates).

Please read Notes from Monday (Applications of Derivatives-related rates)

Practice problems for 3.9:

3.9: 7,17,20,29,39,43.

Friday, 10/12.

Please read Solutions for Quiz 6.

Monday we will talk about related rates.

Quiz 6 problems.

Quiz 6 tomorrow, Friday, on 3.6,3.7,3.8.

Thursday 10/11.

Today we covered 3.7 and 3.8.

Please read Notes from today (Applications of Derivatives)

Practice problems for today :

(Please also try example problems in the book; Do problem then look at solution)

3.7: 1,9,15,20,23,31.

3.8: 1,3,9,11,15.

Monday, 10/8.

Please read Updated Notes from today (Derivatives of Logarithmic Functions)

You may need to refresh your browser.

This has solutions to problems we went over in class.

Wednesday we will talk about applications of differentiation.

Practice problems for today (Please also try the problems in the class notes above):

3.6: 3,5,13,19,41,45.

Friday, 10/5.

Please read Notes from today (Derivatives of Logarithmic Functions)

Monday we will talk about applications of differentiation.

I will also bring the midterm grade sheet.

Practice problems for today (Please also try the problems in the class notes above):

3.6: 3,5,13,19,41,45.

Thursday, 10/4.

Please read Solutions for Quiz 5.

Tomorrow we will talk about logarithmic differentiation.

Quiz 5 problems.

Wednesday, 10/3/18.

QUIZ 5 TOMORROW< THURSDAY, on 3.3, 3.4 and 3.5.

Today we discussed 3.5: Applications of Chain rule --Implicit Differentiation(Notes).

Practice problems for 3.5:

3.5: 5, 13,15,19,25,33,45,51,53,63,67,75,80.

Monday, 10/1/18.

Today we discussed 3.4: Chain rule (Notes).

Updated notes on 3.3: Derivatives of trigonometric functions.

Practice problems for 3.3 and 3.4:

3,3: 3,9,15,17,21,35,37.

3.4: 7,17,23,31,37,53,63,67,75,77.

Thursday, 9/20.

Today we discussed Derivatives of trigonometric functions.

We saw how to differentiate sin x.

For practice, please try to find derivative of cos x.

Proof is very similar, using limit formula.

After that find derivative of tan x, cosec x, cot x, sec x.

For these functions you don't need to use limit formula.

Just use derivatives of sin x and cos x along with quotient rule.

Please read Solutions for Test I.

Test I problems.

It will cover all of chapter 1 and 2 and first two sections of chapter 3.

Topics: Functions, Limits, continuity, basic definition of derivative, derivatives of polynomials and exponential functions, product and quotient rule.

Please study these old test problems with solutions:

Fall 2015 test 1 review problems; Fall 2017 test 1 solutions;

First seven problems of Fall 2010 test I; Fall 2017 Quiz 4 solutions

PLEASE USE ebook for Stewart's Calculus 8th edition

Monday, 9/24/18.

We completed these Notes (Product and quotient rule for derivatives) today.

Practice problems for today:

3.2: 3,7,11,17,21,31,41,43,57,58.

Friday, 9/21/18.

We completed these Notes (Properties of derivatives, derivatives of polynomials and exponentials) today.

We also watched this video on modeling spread of disease using calculus.

Practice problems for today:

3.1: 3,9,11,19,23,32,33,47,45,51,53,55.

Thursday, 9/20.

Please read Solutions for Quiz IV.

Tomorrow we will talk about derivatives of polynomials and exponential functions.

Quiz IV problems.

QUIZ 4 THU Sep 20.

Will cover 2.5 to 2.8.

Wednesday, 9/19/18.

We completed section on derivatives of these Notes (Limit formula for derivatives, Properties of derivatives) today.

Practice problems for today:

2.7: 3,7,15,20,33,47.

2.8: 3,13,23,29,59.

Monday, 9/17/18.

We completed section on limits at infinity of these Updated Notes (Continuity and limits at infinity) today.

You may need to refresh your browser.

Practice problems for today:

2.6: 19,17,21,25,27, 31,61.

I think if you are using ebook for Stewart's Calculus 8th edition

I have been using the plain 8th edition ebook.

Anyway, you should check the topics and the problems to make sure we are looking at the same thing.

Friday, 9/14/18.

We completed upto page 8 (section on continuity) of these Notes (Continuity and limits at infinity) today.

Practice problems for today:

2.5: 3,9,11,19,21,33,41,45,53,55.

2.5 in print book is 1.8 in ebook. Problems are same.

Thursday, 9/13.

Please read Solutions for Quiz III.

Tomorrow we will talk about continuity and limts at infinity.

Quiz III problems.

Please study class notes and do the practice problems from 2.2,2.3,2.4.(Ebook 1.5,1.6,1.7)

It will be about finding limits and the precise definition of limits.

Wednesday, 9/12/18.

We completed these Updated Notes (Methods for finding limits) today.

You may need to refresh your browser.

Practice problems for today:

2.4: 11,13,21,28,31,37.

2.4 in print book is 1.7 in ebook. Problems are same.

Monday, 9/10/18.

We went up to page 19 of these Updated Notes (Methods for finding limits) today.

You may need to refresh your browser.

Practice problems for today:

2.2: 11,31,37,41

Ebook: 1.5: 11,31,37,39.

2.3: 15,17,19,27,29.

2.3 in print book is 1.6 in ebook. Problems are same.

Friday, 9/7/18.

We went up to page 11 of these Notes (Methods for finding limits) today.

We also watched this video Video (Crash course on derivatives). Mainly to show relationship between tangents, secants, and instantaneous velocity.

We will see the limit formula for derivative later.

Practice problems for today:

2.2: 5,9,33,43,44.

Ebook: 1.5: 5,9,31,40 ; problem 43 from print: Find limit of lnx-(1/x^2) as x -> 0.

2.3: 35,37,39.

2.3 in print book is 1.6 in ebook. Problems are same.

Solutions for Quiz II.

Quiz II problems.

Thursday, 9/6/18.

Practice problems for 2.1: 3,5,7.

Wednesday, 9/5/18.

Notes from today (2.1: Introduction to limits and tangents; solution to problem 61 of 1.5).

Note that the sections have been rearranged in ebook -- see below.

I will be in office tomorrow 1 to 3 if you need help.

Friday, 8/31/18.

We just did a few problems on exponential functions and logarithms today because school was closed at 3pm.

Please review the basics properties of exponentials and logarithms from the book.

I have updated the notes from yesterday with what we did today.

Updated Notes from yesterday (1.4: Inverse and 1-1 functions and Logarithms).

(You may need to reload your browser).

On wednesday we will start with tangents and limits.

Note that the sections have been rearranged in ebook -- see below.

Thursday, 8/30/18.

Notes from today (1.4: Inverse and 1-1 functions and Logarithms).

We didn't have time to go over basic properties of exponential and logarithm functions such as multiplication of exponential functions and addition of logarithms but please review them from college algebra or precalculus book if book explanation is not adequate.

practice problems: 1.5: 7,19,25,37,53,61.

ebook: 6.1: 7,21 ; problems 25, 37,63,61 are not in ebook --they are in this handout.

Note: the sections in the ebook are in a different order from the sections in the print book. Also some problems are not in ebook. As much as possible I will give you the problems from textbook here if they are not in ebook.

Notes from wednesday (1.4: Exponential functions).

practice problems: 1.4:3,15,21,30,32.

See handout above if you only have ebook because these problems might not be in ebook.

Solutions for Quiz I.

Quiz I problems.

Friday, 8/24/18.

Please come to office at that time if you need help for quiz.

QUIZ ON MONDAY, 1.1,1.2 and 1.3.

(Another professor will give the quiz, so please come to class).

Practice problems from 1.3: 3,7,11,17,35,53,55.

Quiz problems will be similar to practice problems.

notes from today (1.3: transformation and combination of functions).

EXTRA READING IF INTERESTED:

Fractals can be generated by repeated application of same procedure,

similar to how we can compose a function with itself to get f(f(x)), f(f(f(x)))) etc.,

Video to show how snowflake shape can be obtained this way.

It also shows that if you continue this infinitely, then you get a shape where no matter how small you zoom into it, each part looks like the bigger curve.

Friday, 8/24/18.

I have reloaded the notes from yesterday.

It didn't upload properly before.

Thursday, 8/23/18, 9.50pm.

Today we talked about the definition of a function, domain of function, piecewise defined functions, increasing and decreasing functions, even and odd functions and their relation to symmetry about y axis and origin (0,0) repectively. We also did some problems.

Please read the notes from below and also section 1.2 from book.

Please try the following problems:

1.1: 41,44,51,53,57,65,73,77

Notes for Class today(8/23/18 class notes -- basics of functions)

Notes from fall 2017 on functions and models

Notes from fall 2017 on some common functions and their properties --mainly absolute value function and floor function.

Thursday, 8/23/18, 10.20 am.

Happy to let you know that we have a room assigned for thursdays.

We will meet in

Just Hall is the biology building, right next to chemistry.

On other days (MWF) we will meet in the usual place.

Wednesday, 8/22/2018

Meet at 2.10 in usual room unless otherwise specified.

I will post the room and time here if it is different.

Practice problems from 1.1:

Try 7,9,11,15,31,35,37,38,57,59

Monday, 8/20/2018

Notes for Class today(Introduction)

Chart shown in class today; See notes above

The following are from Spring 2016 but you can work on them to get started on the course:

Supplementary material:

Two more graphs related to climate change, following up on practice problem 11 on p.20:

Graph of CO2 over past 650000 years

Graph of CO2 over past 60 years

You are welcome to check out my fall 2015 course Patterns in Environmental Math if you are interested in learning more.

Youtube video showing how to approximate pi (or area of circle of radius 1 or half the perimeter of same circle) using polygons.

In the first part they show the theory and how to find the perimeter of various polygons (squares, pentagons, hexagons,...) that approximate the circle. Lot of formulae in this part.

In the last part they make a neat spreadsheet with perimeters for the different polygons as you increase the number of sides.

This is a great illustration of the limit process because you can see clearly how the polygons kind of merge with the circle at the same time as their perimeter approaches pi times their "diameter."