Here are your Final Exam scores. (Also your midterm scores, which hopefiully you've checked before).

The final exam scores ranged from 0 to 138 (both across all sections and across my sections; my students had both the low and the high scores).

I think there were some issues with the exam, and I tried to adapt the grading scales so those issues wouldn't hurt you too much. On the other hand, a surpringly large number of you didn't get basic easy problems like the derivative of the base-8 logarithm; I couldn't drop the cutoffs too much.

If you have any questions about your grade: I don't discuss grades in detail over email, though if you've found a mistake in the way one of the midterms was recorded or really want me to change a D to an F I can probably deal with that by email. You can make an appointment to see your final or discuss your grade once the new semester begins.

As usual, I've posted my teaching evaluations. If you are curious what your classmates thought of the class, have a look. Thank you for your feedback on WebWork, I will definitely take it into account in future classes.


Office Hours

T-Th 10:30-12:00, PSB 319

Other tmes by appointment

TA Hours:

Mondays and Wednesdays from 2:30 - 4:00 pm

Tutorial Room

Where: Learning Emporium, Bilger Addition 209

When: See http://www.hawaii.edu/natsci/math.php

Assigned Assignment Handouts
Aug 22 Class: Discuss class policies; start inverse functions (7.1)

"Pre"quiz on Calc I (doesn't count!)

HW: Review Chapter 5 (FTC and Integration)
5.4/11, 15, 23, 27b, 33
5.5/7, 21, 23, 42

Due: Aug 24 (don't turn in!)
Quiz on Aug 29 problems taken from this homework

Aug 24 Class: 7.1, Section 7.2

7.1/11b,13,17,22,25, 31, 38, 45
7.2/3, 7, 9, 23, 30, 39, 45,57, 61, 65, 70, 71(tricky!),75

Quiz on 7.1-2 on Aug 31

Inverse Functions
Aug 29 Quiz today on review problems (Ch. 5)

Class: 7.3

7.3/5, 9, 15, 17, 23, 25, 29, 35, 41, 47, 55, 57, 63, 73, 87, 90, 99, 105, 113, 115, 121

Exponentials and Logarithms
Aug 31

Quiz today on 7.1-2, possibly 7.3

7.4/21, 29, 33, 39 <- Quiz on Sep. 7 will cover this

7.4/43, 47, 51, 61, 71, 73, 79, 89, 97, 99, 104, 107 <- Quiz on Sep. 14 will cover this
(You might also want to do 1-19 odd just as review of inverse trig)

Solution to Quiz 1

Solution to Quiz 2

Sep 5 Continuing 7.4
Sep 7

Quiz on 7.3, 1st part of 7.4

Start 7.6

7.6/3,5,17,23,25,27,33,35,41,45,53,66b (quiz on these September 14)

Sep 12 More 7.6 examples; start Chapter 8 (Techniques of integration)


Handout: Integration By Parts
Sep 14 Quiz on 7.4, 7.6

Continue Ch. 8


Handout: Integration of trig functions

Handout: Integral of cos^12(x) the "easy" way (using the reduction rule)

Handout: Integral of cos^12(x) the "hard" way (using the reduction rule)

Sep 19 Continue 8.2
Sep 21 Quiz on 8.1

8.3 (Trig substitution)

8.3/3,5,11,13,15, 22, 23, 31

Solutions to quizzes 3-5
Sep 26 Review

If time: hyperbolic trig (optional/extra credit section)

Sep 28 Midterm Exam I

Covers through 8.3

(OK, exam will only cover through 8.2)


Also, TRY THESE TRIG INTEGRALS (the circled ones)



A128, B90, C75, D55

S28-O3 WebWork: This is a FREE FOR YOU online homework system. I will be giving some supplementary assignments using it, including some extra credit and "techniques of integration" practice. It isn't hard to use, and will even let you check correctness of your answers before submitting them.

I would like everyone to try the first assignment, which is called "Demo", before 4:00PM next Tuesday Oct 3 (but preferably before class so you can ask questions in class if you have problems). These are some simple problems you should all be able to do, but will give you practice working the interface.

VIDEO TUTORIAL (best viewed in fullscreen mode; use controls to pause or single step):

(Note: no sound in these videos, sorry)

To log in to WebWork, go to


Your login should be either your UH email address, or the part of that address before the @ sign. For example, if your UH email is myname@hawaii.edu, your login should be myname

Your initial password is your 8 digit UH ID number.

Oct 3 Finish Trig Sub; Start Partial Fractions (8.4)

Your first attempt at WebWork should be made before 4pm today!

Partial fractions Handout 1
Oct 5 Quiz on 8.3; Finish Partial Fractions

8.4/7, 11, 15, 25, 33, 39, 45

Partial Fractions Handout 2
Oct 10

Miscellaneous substitutions and tables of integration

8.5/3,9,15,25,29,31,47,48 <---these are "table" problems. You can use the table to the right to get some practice with it ---->


Oct 12 Quiz on 8.4 (only)

Improper integrals (8.7)

8.7/37, 41, 55, 57,74

Oct 17 Surprise quiz on sequence video

Finish improper integrals


9.1/3, 5, 7, 9, 17,23,27 (for these sequences [3-27] try to determine whether they are increasing/decreasing, bounded, etc.) 33,41,45,59, 65, 79, 85, 98

Harder but interesting:


Video on sequences.

Another version, might be more phone-friendly.

(video slightly corrected 10/15)

Watch this BEFORE Tuesday, Oct 17. Don't forget to make it full screen. It moves very quickly, so look for the pause control in your viewer.

Handout on sequences

Oct 19 Quiz on 8.5, 8.7

Start series (9.2)


You might want to review 5.2 (Sigma notation), and try 5.2/10-18

Grade Prediction Tool

Handout on series

Video: intro to infinite series.

Another version, might be more phone-friendly.

Oct 24

Finish 9.2; start 9.3


Handouts on series convergence tests:

Integral Test

Comparison tests <----new

Root and Ratio test

Oct 26 Finish integral test (9.3)

Start Comparison tests (9.4)

Quiz on 9.1, 1st block of 9.2 problems

9.3/1-19 odd ,23; 35; 42. Look at 41. (Quiz on these Nov. 2)

Oct 31 Finish 9.4 (Comparison tests, see also notes uploaded at right)

Start 9.5 (root/ratio tests)

Finish 9.4

Nov 2 Finish 9.5

9.4/1-21odd, 27,33,39; look at 40

9.5/3,5,7,9,11, 14, 16,19,23,25, 29,32,39,41,43 (last 3 are harder but interesting!), 47 (looks hard, really isn't)

(I will not be quizzing you on 9.4 - 9.5, but these sections will be on the exam.)

9.6 (Alternating series)

Quiz on 9.2 (second block of problem) and 9.3

Nov 7 Exam review; bring questions

I will not be quizzing you on 9.4,9.5, but they are covered on the exam, and I will have a webwork assignment on these sections due on November 10 (so it can help you for review, and you will have motivation to at least try it by Nov 9)

Nov 9 Midterm II

Will cover 8.3-9.5

Some Review Information

Exam 2 solution. (Video, no sound.)

(Might not work on all browsers.)

Extra Credit Homework: the Weierstrass "half-angle" substitution

(Due November 28 - after TG break -but it might be easier for you to do it now, especially as there will probably be other videos to watch over the break.)

First, watch THIS VIDEO on the half-angle substitution. (It is only 5 minutes!)

Next, do THIS PROBLEM SET using the substitution.

You are encouraged to both watch the video and do the problems with classmates, but please do not just copy their answers!

Nov 14 Power Series (9.7)

9.6/5,7,13,15,21,29,33,36, 41,47,48, 51

9.7/7,9,11,19,21,27, also 6 and 18 <--------------covered on quiz next week

9.7/5,13,25,35,39,45 <--------Not covered on this quiz

Nov 16 Start Taylor Series (9.8, 9.9)

As promised, the example from class

9.8/7,11,15,17,21,25, 26,29

Nov 21 Finish Taylor Series (remainders)

Quiz on 9.6, 9.7

9.9/3,6,7,9, 13, 19, 21, 22, 25, 31, 37 (19-25 are practice in error estimates; 31 is an example of one of my favorite applications of series); look at 45

(If time: start numerical integration, 8.6: Trapezoid rule and Simpson's rule)

Lecture notes for Taylor remainders

Video (optional):

Derivation of the Taylor error estimates.

(While this is optional, anyone thinking of majoring in math or physics or EE should definitely watch it, and for anyone else, it is a nice application of IBP.)

Another Extra Credit Assignment: Hyperbolic Trig Functions

1. Watch THIS VIDEO on the hyperbolic fiunctions, Section 7.7

(Here it is in a different format, if the other one didn't work.)

2. Next, do the WEBWORK assignment called HyperbolicFunctions.

You are encouraged to both watch the video and do the problems with classmates, but note that WebWork randomizes problems, so you can't just copy your friend's answers!

Due: Last day of class (Dec. 7)Day after the final exam: 10AM, Dec 14

The remainder of the semester will mainly be on Ordinary Differential Differential Equations (ODEs), which appear in Chapter 16/17 of the text. If your copy of the text does not have Chapter 16, don't worry; Chapter 16/17 of the text is available online here (click) as a pdf.

So that I can focus class time on examples, I am uploading some videos that supplant my lectures. YOU SHOULD WATCH THESE VIDEOS BEFORE WE GET TO THE DISCUSSION IN CLASS. (In fact, you might just want to watch all the videos over TG break.)

Viewing these videos is not optional, and I might quiz you on them at the beginning of the corresponding class.

Nov 28 Finish numerical integration (8.6)

Exponential Growth (8.5) and Separation of variables

Start: General ODEs (16.1)


7.5/21, 23, 25 (these are on exponential growth/decay)

7.5/1c, 3, 7, 9-17 odd (these are general ODE problems)


You should read 7.5, also at least skim 16.1 (up to around Page 5)


1. Introduction to ODEs

(Here's a more cellphone-friendly version)

This video introduces the terms: Ordinary differential equation, Initial value problem, Initial condition, order of a differential equation, particular solution, general solution

2. Separation of Variables

Don't forget to go to full screen video when viewing these.

You should watch these before class on Nov 28!

Nov 30 Finish: General ODEs. Do: 1st order linear ODEs

Read 16.2 (see worked examples, through top of page 13)


16.2/All of 1-19 odd are appropriate, but I would start with 1,9,17,19

Problems on Trap rule/Simpson's rule:

8.6/Iab, IIab for 3 and 7; also do 19 <----added Nov 30:


1st order Linear ODEs

Dec 5 2nd Order homogeneous linear ODEs with constant coefficients (17.1)

Quiz on 9.9 (last "real" quiz!)


17.1/ All of 1-60 are appropriate (and shouldn't take more than a minute or two each!), but start with 1, 5, 13, 25, 49<----mainly done on Nov. 30

Bring questions on HW from 7.5, 8.6, 16.1, 2<----note

Dec 7 Ketchup/questions and problems
Dec 13 Final Exam, 12-2, room ART 101

Extra office hours: Me: Tuesday 1-4. Jamal: Monday afternoon until around 5

Here is the Common Final from Fall, 2015

Here is the Common Final from Spring, 2016

Here is the Common Final from Fall, 2016
(Grading rubrics from that exam)

Here is the Common Final from Spring, 2017
(Answers and some hints)


This gives my best guess(es) as to what your grade would be if you get a solid A or a solid B on the final exam.

(NOTE: They do NOT include the last quiz, the WebWork work, or any extra credit, and do not exclude quizzes excused for illness etc. Also, while the predictor reports +/- grades, the actual class grades will not be +/-)