MATH 158 ASSIGNMENTS

MATH 158 Homework Assignments

Homework 1, due 2/9

Read chapter 13 of the text, pages 253-270 [250-267 in 3rd ed]. You may skip Theorem 8 for now, as we will discuss it later. Also, you don't have to go through all the details of the proofs of Theorems 3,4,5 (of course if you do you will learn a lot).

Do the following problems:

chapter 13: 1, 5, 7(i,iii), 8(i,ii,iii,vi), 9, 13.

Homework 2, due 2/16

Read Theorem 8 and its proof in chapter 13, pages 270-271 [267-268 in 3rd ed]. Also read chapter 14, pages 285-294 [282-291 in 3rd ed].

Do the following problems:

chapter 13: 21, 31(a,b), 37.

chapter 14: 1(i,iii,iv,v), 3 [4 in 3rd ed] (hint: differentiate with respect to x), 4 [5 in 3rd ed].

Don't miss: The best solutions to this week's problems will be published in the prestigious Antarctica Mathematics Journal.

Homework 3, due 2/23

Light assignment this week, as we met only once. Take a look at the solutions to some of the HW2 problems that I've posted on the main page. Also, familiarize yourself with the general content of chapter 15, even if you don't plan to read it carefully now.

Do the following problems:

chapter 14: 8, 9, 11, 25(a) [11, 12, 14, 25(a) in 3rd ed].

"Oompa Loompa doompadee doo, I've got a perfect puzzle for you."

Homework 4, due 3/2

Read chapter 15 of the text.

Do the following problems:

chapter 15: 1(ii,iv), 2(i,iii,v), 4(b), 9(a), 14(a), 15(a), 16 (Hint: working with a little "test triangle" will help), 17 (to avoid possible confusion, note that x is tan(u/2) not (tan u)/2), 19.

Homework 5, due 3/16

Read chapter 18 of the text.

Do the following problems:

chapter 18: 1(iv,ix), 4(c,d), 13(e) (Hint: It suffices to find the limit of log(x^x) = x log(x) as x tends to 0), 14, 25 [1(iv,ix), 4(c,d), 12(e), 13, 24 in 3rd ed].

What do you find unusual about the sentence "We present a mnemonic to memorize a constant so exciting that Euler exclaimed"?

Homework 6, due 3/23

Read chapter 19 of the text.

Do the following problems:

chapter 19: 1(i,ii,iii) (Hint for (ii): Multiply and divide by the conjugate term), 2(i,ii,vi,viii), 3(i,ii,ix)

Don't miss the first issue of the Antarctica Mathematics Journal.

Homework 7, due 4/6

Read the appendix to chapter 19 ("The Cosmopolitan Integral").

Do the following problems:

chapter 19: 4(ii,vii), 5(i,ii,iv), 6(i,v), 9(iv,v) [8(iv,v) in 3rd ed], 24 [23 in 3rd ed], 30(v) [29(v) in 3rd ed].

appendix: 1, 3 (Answer: (4π/3)ab²), 4 (Answer: 2π²ab²).

Do a random act of kindness today: Find a total stranger and explain the Cavalieri's Principle to him/her (keep a safe distance).

Homework 8, due 4/27

Read pages 411-416 and 424-426 of chapter 20 of the text as well as pages 286-290 of Apostol's book that I handed out in class.

Do the following problems:

chapter 20: 1(i,ii,iv,v), 2(iii), 3(i)

Apostol page 290-291: 1, 8, 9, 13, 23 [Hint: Write x = 1-t and compute the limit as t tends to zero. For that take the logarithm first].

Caution: The above limit problems must be solved using Taylor polynomials; in particular, you are not supposed to use L'Hopital's rule.

The best solutions to this week's problems will be awarded as follows:

First prize: One-year subscription to the Antarctica Mathematics Journal (AMJ)

Second prize: Two-year subscription to AMJ

Third prize: Three-year subscription to AMJ

Homework 9, due 5/13 (Note the new due date!)

Read chapter 22 pages 452-458 [445-451 in 3rd ed] and chapter 23 pages 471-482 [464-475 in 3rd ed].

Do the following problems:

chapter 22: 1(iv,vii,viii), 2(i,iii), 5

chapter 23: 1(vi,vii,x,xiii,xiv,xviii)

chapter 25: 1(i,iii), 3(i,iii), 4, 5

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