MA 224, Spring 2012

This is the webpage for my sections (002 and 012) of MA 224 for the spring 2012 semester. Mainly I will host the in-class quizzes, exams, and their solutions, as well as any other pertinent material for the course.

Please note: My common office hours in Math 205 have changed since the beginning of the semester. They are now on Thursdays at 1:30 PM. For the course ground rules, you should visit the main MA 224 course webpage here

Lecture Overview

Lecture is held three times weekly on Mondays, Wednesdays, and Fridays. Usually, we will spend about 5 minutes covering the previous quiz (if any), 10 minutes covering homework problems, 30 minutes covering new material, and the last 5 minutes will be a new quiz (if any).

Expositions

These are a few extra pdf links that I have prepared that you may find helpful in learning the material for the course. They are not intended to be a replacement for lecture, so do not treat them as such.

Tips for u-substitition

Examples using these steps: Example 1 (doesn't need step 4), Example 2 (requires step 4)

Finding the area enclosed by two curves
The multivariate chain rule (or, plugging the right things into the right places)
Solving systems of equations when optimizing functions of two variables
Formulas for the nth term of a series

Homework

(Most of) your homework this semester is online at MathZone. For problems that are available online, you will have roughly 60 hours to complete each assignment after the corresponding lecture. If you require an extension (due to illness, family emergency, etc.) you should contact the MathZone coordinator, not me.

There are a few problems listed on the assignment sheet in bold which are not available online. These should be completed on your own with pencil and paper. They are fair game for quizzes and exams, so make sure you're doing them!

I am more than happy to help you with your homework over e-mail. In your e-mails, you should indicate what you have tried so far - don't just e-mail me asking "How do I do number 3?" but show me that you've at least attempted the problem. I will not give full solutions over e-mail but will offer hints and point out where you may have made mistakes. You should also be sure to e-mail me well in advance of the deadline. I cannot always respond to e-mails that are sent close to the deadline.

Answers to Even Homework Problems

Final answers to the odd numbered homework problems are in the back of your textbook, but unfortunately I am not permitted to post answers to the even numbered homework problems on the web. They will be disseminated in class, so if you miss a class you will have to get them from a neighbor.

Quizzes/Solutions

Roughly once each week there will be an in-class quiz about five minutes in length and consisting of 2-3 questions that are based on the lectures since the last quiz. There will be no make-up quizzes - if you miss a quiz, you will receive a zero for it unless you have a valid excuse (e.g. illness, family emergency, or other university-approved absences).
All quizzes are out of 5 points maximum unless otherwise noted.

Exams/Solutions

Exam 1 / Solution
Please note that I have been asked by Owen Davis to not post solutions to this year's exam 2. If you would like to see solutions to any of them you should attend office hours.
Exam 3 / Solution

Review materials

Full solutions to the spring 2010 exam 2
Notes that I used during the in-class review for the final (Day 1 / Day 2). We didn't get to cover much of the notes that I had for day 2 since I answered your questions first (which is totally okay, that's what I wanted to do), so just consider those as even more new examples.
Final exam study guides (Chapters 5-7 / Chapters 8-10). The chapter 8-10 study guide is in the order in which we covered the material (chapter 9, chapter 8, chapter 10). These include examples, reminders, and tricks to simplify some things. They're pretty long and detailed, but I'm not going to say that they are totally comprehensive.
In addition to reviewing old homework problems and examples from class (these should be your first priority), here are a few (optional) extra practice problems for the final. Obviously since there are so many of them, you should pick and choose which ones you think look the most difficult and attempt those. If there are questions on any of them, we will discuss them in class on during the review on Wednesday and Friday before the exam.
p.442, #19
p.465, #6, 13, 16, 28, 29, 37, 69, 70, 76
p.513, #1, 8, 23, 26, 28, 34 (trapezoid rule only)
p.614, #9, 10, 14, 19, 26, 31, 34, 35, 40, 43, 44, 55, 59
p.749, #6, 19, 20, 22, 23, 29, 32, 42
p.694, #5, 23, 48 (see comment below), 51 (hint: the rate of change of glucose is equal to the rate at which it is infused minus the rate at which it is excreted)
p.821, #9, 24, 27 (part a only)
For #48 on page 694, do the problem under the assumption that the liquid that's flowing in is just pure water. If you try to do it without modifying the problem, you end up needing a technique that we didn't cover in class (integrating factors).

Word Problems

Below are the word problems presented as examples in class, as well as a few extras that may be useful on homework.

Set Lecture Number Date

Set 1 / Solution Lecture 3 1/13/12

Set 2 / Solution Lecture 4 1/18/12

Set 3 / Solution Lecture 7 1/25/12

Set 4 / Solution Lecture 9 1/30/12

Set 5 / Solution Lecture 16 2/15/12

Set 6 / Solution Lecture 19 2/22/12

Set 7 / Solution Lecture 20 2/24/12

Set 8 / Solution Lecture 22 2/29/12

Set 9 / Solution Lecture 27 3/19/12

Set 10 / Solution Lecture 32 3/30/12

Set 11 / Solution Lecture 38 4/13/12

Set 12 / Solution Lecture 40 4/18/12

Set 13 / Solution Lecture 42 4/23/12

Links to helpful examples

Polynomial Long Division (via S.O.S. Math) - Useful for some of the homework problems since your online homework is looking for answers obtained this way.