Final & Grades

Final grades are posted. The registrar should have "rolled" them last night. To pick up your final either (1) email me over break and we can meet at my office; or (2) stop by next semester.

Good job on the final and overall. You guys were a fun class!

-Jesse

More review

Here's a link to Tom Hayes's review sheet -> here.

Stop by my office or post a comment on the blog if you have questions.

Have fun studying!

-Jesse

Chapter 5, section 5

Integration by substitution (i.e. undoing the chain rule).

Sadly, this is the last section we cover in 181.

-Jesse

Chapter 5, section 4

Post any questions pertaining to sections 4.9-5.3 here as well.

* Extra Credit *

I have uploaded six extra credit problems to the "Quiz and Exam Keys" link to the right. Each question is worth up to 5 pts. You should attempt all six, but hand in only your best four.

They are due no later than Thursday, December 11.

You are welcome to work with other students, ask me questions, or go to the MLC. But you must hand in your own copy.

Have fun!

-Jesse

Chapter 4, Section 8

Newton's method. Some websites with good resources:

Newton's Method @ Wiki
Newtons Method @ utah (includes a nifty applet)
Newton's Method - Flash ex. (follow the "Discussion [Using Flash]" link)

-Jesse

Chapter 4, Section 7

Optimization problems... do the worksheet as well as the homework problems. In all of them, write down the domain. Don't forget to test the endpoints (if applicable) or the use a derivative test to prove that the critical value you found is truly a max/min.

-Jesse

Chapter 4, section 5

Asymptotes:

Wikipedia has a nice page (here) with some more examples.

-Jesse

Tuesday office hours

On Tuesday I will be in my office from 10-12 (which lines up with normal class and office hours). If you'd like to arrange another time, send me an email to make sure I'll be there.

Also, there will be a review session during normal class time on Thursday.

-Jesse

Some exam review problems

I. Below are some problems from the Chapter 3 review that will hopefully cover all the basics plus more:

• 89, 93 (eqn of motion and exponential growth)
• 21, 24-26, 29-34, 37-42, 46, 49, 50 (these cover everything from plain ol' chain rule through implicit differentiation, logarithmic differentiation, as well as derivatives of inverse trig functions.)
• 99, 100, 103, 105 (related rates and linear approximation)

Now, some problems from the Chapter 4 review:

• 7-14 (limits from 4.4)
• 45, 48.

And a few from 4.2 & 4.3 that should sum up the beginning of Chapter 4:

• 4.2: 19, 13, 14, 15
• 4.3: 45-52, 67

Exam III

Information on the exam is here. As always, the best way to get startedstudying is the HW. In each section tested over do the "middle" HW problems. I'll put up some supplementary problems (of a more difficult nature) later this weekend. The take home quiz should provide a good source of "fun" as well.

Hint for the quiz problem with "tan(2x)": Double angle. (edit: This doesn't make it as simple as I'd hoped... it's one of many ways to tackle this one. Enjoy!)

-Jesse

Chapter 4, section 4

Someone left a textbook in class. You can pick it up in my office, or I'll bring it to class on Friday.
-Jesse

Chapter 4, section 3

Chapter 4, section 2

Continuous functions that are not differentiable

As mentioned on Friday, the hypothesis in the Mean Value Theorem (and Rolle's Theorem) that f(x) is continuous on [a,b] and differentiable on (a,b) covers most nice functions that we deal with in class. There is one family of examples that we've dealt with a lot that have at least one point of discontinuity:

f(x) = |x-c|, where c shifts the function so that the cusp/point lands in [a,b].

What are some variants of this function? (Think of a piecewise function that looks looks like a sawtooth--lots of little absolute value functions put together. How would you define this function?)

Now, some pathological examples. The Weierstrass function (here at wikipedia) is one very interesting example of a function that is *continuous everywhere* (why?) but differentiable nowhere (a bit harder to prove). The discussion on Wikipedia is a little beyond what we've covered in class, but from the graph you get the idea that it essentially builds on the "jagged" idea of the absolute function. Weierstrass found a way to make a function that changes direction infinitely often.

Another example is due to Bolzano. Here is a link at Math World (here and a definition of the function here). The idea is similar, but Bolzano did not use continuous cosine functions in the construction. He simply extended the sawtooth idea (ad infinitum).

-Jesse

Chapter 4, section 1

(We're skipping 3.11 -- check it out to see math in unexpected places (such as the Arch in St. Louis).)

Cahpter 3, section 3.10

Cahpter 3, section 3.9 - Related Rates

Applications of implicit differentiation.

Chapter 3, section 8

Chapter 3, section 7

Chapter 3, section 6

Derivatives of Logs and Log differentiation.

Chapter 3, section 5

Implicit Differentiation and Inverse Trig functions

Review Session

Kelly Vogel will hold an exam review on Wednesday, 6-7pm in Wilson 1-141. As of now this is also a regular PASS session time/location (see sidebar).

Also, I will hold a review session Thursday during the normal class time.

Supplemental review problems are located on the Quiz and Exam Keys page (sidebar).

-Jesse

Exam II

The second midterm is schedule for Thursday, October 16. It's at the same and in the same room as the first midterm (Wilson 1-130, 6-7pm). The exam will cover all of chapter 2 through 3.4 (chain rule).

The Exam information page is located here. Extra special note: Over 60% of Exam II will be over chapter 2.

-Jesse

Chapter 3, section 4

Chapter 3, section 3

Chapter 3, section 2

Chapter 3, section 1

Pre-Quiz review

I will be at my office by around 8.15 tomorrow. If you have questions before the quiz feel free to stop by.
-Jesse

Quiz 2 key is posted at Quiz and Exam Keys site (link on the right).

Mandatory Quiz -- Thursday, Oct 2

Will focus on Chapter 2 (limits, continuity, derivatives (calculation via the definition)).

Chapter 2, section 8

Someone asked a question after class about the derivative of the absolute value. Here's a little more verbage for clarification:

The derivative of f(x)=|x| at any point to the right of 0 is 1 (eg., the slope of the line is 1). The derivative of |x| to the left of 0 is -1. So the derivative f'(x) is a piecewise function. (This is what I forgot to write down.) It is

{ 1, x >= 0
{ -1, x < 0

So as we found, the limit of f'(x) does not exit at 0 (left and right hand limits are not equal). But this is made more clear by the jump from -1 to 1 in the graph of f'(x).
-Jesse

Chapter 2, section 7

Exam I key is posted on bulletin board outside my office. (If you make a copy, please return it within 20 minutes or so.)
-Jesse

Chapter 2, section 6

Chapter 2, section 5

Chapter 2, section 4

Definitely read this section before class.

Chapter 2, section 3

Chapter 2, section 2

Exam I covers Sections 1.1 to 2.2 (excluding 1.4). The exam will focus primarily on homework problems. See the homework section on the general course website for any updates on problems.

Exam info here.
Exam location is Wilson 1-130.
Exam time: Thursday, Sept 18, 6-7pm; Wilson 1-130

Chapter 2, section 1

Chapter 1, section 6

Chapter 1, section 5

Chapter 1, section 3

Key for Quiz 1 posted here.

Chapter 1, section 2

Chapter 1, section 1

Welcome

Welcome to Math 181, Calculus I, at Montana State University. This is a blog for section 3. One purpose is to post necessary bureaucratic items (syllabus, office hours, etc.).

In addition, I hope that students will use it to post questions on homework. To do this, one would post a comment under the chapter and section that the homework problem occurs in. I will check the blog as often as possible, but the best characteristic of a blog is that others can comment as well. So if Student A is perusing the blog and can provide assistance to a question posted by Student B, by all means, post another comment.

If you have any questions feel free to contact me, or post a comment.

-Jesse