**To read:**Finish the section, then re-read the whole thing-- really work to make sense of it all.- sum(sin(k), k=0..infinity)
- sum(1/k , k=1..infinity)
- Monday is the deadline to receive 90% on the antidifferentiation exam. If you haven't passed it yet, don't let this opportunity go by without the attempt -- several, if necessary!
**To read:**Through Example 3.4.**Be sure to understand:**How you can use the integral test to determine the convergence or divergence of a sum*or*an itnegral; (for Thursday) how it's used to approximate the value of a series.- Explain in a couple of sentences (in your own words, of course) why the integral test makes sense. That is, explain the idea behind the integral test.
- Bring questions on PS 9.
- Take advantage of tutoring hours
**To read:**Through Example 3.7

**Be sure to understand:**How to use the comparison test to determine convergence- Explain in a couple of sentences why the Comparison Test makes sense. That is, explain the idea behind it.
- Begin PS 10. This is a group assignment - remember the usual guidelines: variety in group make-up; 2-3 people; don't divvy; switch and label primary authors.
**To read:**While I will not be covering the Limit Comparison Test in class, do read the rest of the section -- while it is not obvious how it can be used in approximating a series, it does resolve some of the difficulties we can run into with the Comparison Test. Also, re-read the entire section, making sure you understand each example and looking for more nuance than you saw on the first read-through.

**To read:**In class, I covered using the Integral and Comparison Tests to help approximate convergent series in more detail than the text did. Read through your notes and in-class work related to this.

- Show that the series converges.
- Estimate the limit of the series within 0.01.
- Is your estimate an over- or under- estimate?
- Bring questions on PS 10
- Begin PS 11
**To read:**Again, re-read through your notes and in-class work related to the choosing which series to use and also to finding upper and lower bounds for the limit of a convergent series, and to estimating a convergent series within a certain margin of error (i.e. within a certain error bound).

- Show that the series converges.
- Estimate the limit of the series within 0.01.
- Is your estimate an over- or under- estimate?
- Just a reminder of the obvious: each of you should be doing your best to contribute equally on the project.
**To read:**All**Be sure to understand:**The statement of the Alternating Series test- Does sum(
^{(-1)k}⁄_{sqrt(k)}, k=1..∞) converge or diverge? - How closely does S
_{100}approximate the series sum((-1)^{k}(1/k), k=1 .. infinity) ? Why? - You should have the mathematics behind project 2 solved by Wednesday morning, so you can begin writing your response. I once again encourage you to bring me a draft.
**To read:**Through Example 5.3.- Give an example of a series that is conditionally convergent. Explain.
- Give an example of a series that is absolutely convergent. Explain.
- Begin PS 12
- If you still have the antidifferentiation exam hanging over you, Friday is the last day you can receive 75% on it. After that, it goes down to 50% until the end of classes.
**To read:**The section*The Ratio Test*and the section*Summary of Convergence Tests*. Optional: the section*The Root Test*.**Be sure to understand:**How to use the ratio test to determine convergence and divergence, and when the ratio test is inconclusive.- Explain in a couple of sentences why the Ratio Test makes sense.
- Remember to attach a copy of the checklist to the front of your project with a paperclip.
- Just a reminder that Exam 3 is the Thursday after Thanksgiving break. While I know you just now finishing Project 2, you may want to look at your post-break schedule and decide whether you want to get a good start on preparing yourself.
**To read:**Through Theorem 6.1- How do power series differ from the series we have looked at up to this point?
- What is the
**interval of convergence**of a power series? Why have we not discussed the interval of convergence before? Explain in your own words. - Begin studying for the Exam, if you haven't already.
- PS 12 will not be collected, but it will be covered on the exam.
- As always, you may have handwritten notes on one side of a standard sheet of paper, and may begin the exam at 12:30.
- Get as many questions resolved before class on Wednesday as possible, through office hours and tutoring hours.
**To read:**Through Example 6.4- Suppose the power series sum(b
_{k}(x-c)^{k}, k=0..∞) has a non-trivial and non-infinite interval of convergence. Where will the midpoint of that interval be? - Begin PS 13
**To read:**Finish the section- As you have read, we can differentiate and integrate a convergent power series term-by-term. Why is this
**not**obvious? - Why might you want or need to use a power series?
**To read:**All**Be sure to understand:**The definition of a Taylor series- How does a Taylor series differ from a Taylor polynomial?
- Give two good reasons for writing a known function ( such as cos(x) ) as a power series.
- Bring questions on PS 13 to class
**To read:**All- If you wanted to find exp(sqrt(3)) using a Taylor series, what would you as a base point?
- If you still have the antidifferentiatione exam hanging over your head, Friday is the deadline to receive any credit.

Fall 2009, Math 104

**November and December, 2009**

**Be sure to check back often, because assignments may change!**

(Last modified:
Wednesday, January 18, 2012,
12:36 PM )

I'll often use Maple syntax for mathematical notation on this page.

All section and page numbers refer to sections from **Calculus: Early Transcendental Functions**, Smith and Minton, 3rd Edition.

__ Due Monday 11/2 at 9am__

**Section 8.2: Infinite Series**

**E-mail Subject Line:** Math 104 Your Name 11/2

**Reading Questions:**

What does the kth Term Test tell you about each of the following series? Explain.

__ Due Wednesday 11/4 at 9am__

**Section 8.3: The Integral Test and Comparison Tests**

**E-mail Subject Line:** Math 104 Your Name 11/4

**Reading Questions:**

__ Due Friday 11/6 at 9am__

**Section 8.3: The Integral Test and Comparison Tests **

**E-mail Subject Line:** Math 104 Your Name 11/6

**Reading questions:**

**Reminders:**

__ Due Monday 11/9 at 9am__

**Section 8.3: The Integral Test and Comparison Tests **

**No Reading Question Today**

__ Due Wednesday 11/11 at 9am__

**Section 8.3: The Integral Test and Comparison Tests **

**E-mail Subject Line:**Math 104 Your Name 11/11

**Reading questions:**

Consider the series sum( ^{1}⁄_{2+3j}, j=0..infinity). (This is Maple notation for a sum or series).

**Reminders:**

__ Due Friday 11/13 at 9am__

**Continue Working on Project 1**

**No Reading Questions Today **

**Reminders: **

__ Due Monday 11/16 at 9am__

**Section 8.3: The Integral Test and Comparison Tests **

**E-mail Subject Line:** Math 104 Your Name 11/16

Consider the series sum( ^{1}⁄_{(k4+5)}, k=1..infinity). (This is Maple notation for a sum or series).

**Reminder:**

__ Due Wednesday 11/18 at 9am__

**Section 8.4: Alternating Series**

**E-mail Subject Line:** Math 104 Your Name 11/18

**Reading Questions: **

**Reminder:**

__ Due Friday 11/20 at 9am__

**Section 8.5: Absolute Convergence and the Ratio Test **

**E-mail Subject Line:** Math 104 Your Name 11/20

**Reading Questions:**

__ Due Monday 11/23 at 9am__

**Section 8.5: Absolute Convergence and the Ratio Test**

**E-mail Subject Line:** Math 104 Your Name 11/23

**Reading Questions:**

__ Due Wednesday 11/25 at 9am__

**Thanksgiving Break! **

__ Due Friday 11/27 at 9am__

**Thanksgiving Break! **

__ Due Monday 11/30 at 9am__

**Section 8.6: Power Series **

**E-mail Subject Line:** Math 104 Your Name 11/30

**Reading Questions:**

__ Due Wednesday 12/2 at 9am__

**Bring Questions for Exam 3 **

**No Reading Questions Today! **

**Reminders:**

__ Due Friday 12/4 at 9am__

**Section 8.6: Power Series **

**E-mail Subject Line:** Math 104 Your Name 12/4

**Reading Questions:**

__ Due Monday 12/7 at 9am__

**Section 8.6: Power Series **

**E-mail Subject Line:** Math 104 Your Name 12/7

**Reading Questions:**

__ Due Wednesday 12/9 at 9am__

**Section 8.7: Taylor Series**

**E-mail Subject Line:** Math 104 Your Name 12/9

**Reading Questions: **

**Reminder:**

__ Due Friday 12/11 at 9am__

**Section 8.8: Applications of Taylor Series**

**E-mail Subject Line:** Math 104 Your Name 12/11

**Reading Questions:**

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