COURSE INFO

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SYLLABUS

HOMEWORK

WRITING ASSIGNMENTS

OFFICE HOURS

Give brief but clear answers to the questions below. Click on this link to send me an email with your answers. Make sure to type 'Calculus Assignment' and the date in the subject line.

For Tuesday, April 4

1. Find a presentation or poster for which you understand at least half of the words in the title.
2. Attend that presentation or see that poster.

For Thursday, April 6

1. Compare (booooo) this section with the comparison test in Section 7.8.
2. Give a prose explanation of the Limit Comparison Test and intuitively why it's true.
3. Look at exercise 39. Can you think of a series for which the squares of the terms converge but the series itself does not? (That is, find a counterexample to the converse)

For Friday, April 7

1. What will happen to a series that is alternating, whose terms are getting smaller and smaller, but the terms are not approaching zero?
2. Give a prose explanation as to why the Estimation theorem is as easy to use as it is.

For Tuesday, April 11

1. What is the intuitive difference between absolute convergence and conditional convergence?
2. How does the Comparison Test lead to the Ratio Test?
3. Summarize the discussion on page 745. Does it seem somewhat counterintuitive to you?

For Thursday, April 13

1. Give an explanation of your own personal strategy for attacking a series question. Explain as though you were talking to one of next year's Calc 2 students when they are studying for their exam.
2. Look over exercises 1-38 on page 748. Pick out three that look interesting. (the most popular ones will be discussed in class)

For Friday, April 14

1. How is a power series like a polynomial?
2. What nice properties does a polynomial have with regard to calculus?
3. What is a radius of convergence? Why do we call it a 'radius'?

For Thursday, April 20

1. How do we differentiate/integrate a power series? Why might this be easier than dealing with the basic function?
2. Look at the 'beautiful' result in the margin of page 758 for the evaluation of pi. How many terms do we need to take in order to get 1 decimal place? 2 decimal places? (Use your calculator to make an educated guess on this one.) Would we use this to approximate pi today? Note: The result is still beautiful, despite in anachrity.

For Friday, April 21

1. Review tangent lines (and for those of you that have studied them, quadratic and cubic approximations). How do these sections generalize those concepts?
2. How do we choose the coefficients for the power series used to represent a function?
3. There is an exam in a week!!!! What would be most helpful for you in preparation for the test?

For Tuesday, April 25

1. We can now integrate some of those unintegrable functions (well, sort of). How?
2. Why might it be inefficient to use a Taylor series to compute the digits of pi?
3. How does your calculator determine something like sin(2.5) or e^(pi)?

For Thursday, April 27

Also, please send me an email addressing the following: I am open to suggestions as to which types of applications you'd like to see for the rest of the semester. Please look over sections 8.3, 8.4, 8.5, and chapter 9, and let me know where your interests lie and which topics you'd like to see covered.

For Friday, April 28

1. Study well and arrive for the exam prepared to work hard.
2. Take a swig of water and breathe...we're nearing the final push.