Professor Hwang (rhymes with song).
Last modified: May 1, 2017
Please bookmark this page and check it every week for new assignments and other current course information. As the term progresses, periodically re-read the academic honesty information below to be sure your habits aren't slipping.
| This Week's Assignment |
| Expectations for Written Work |
Important note: The problem sets are your chance to work through ideas and course concepts in a low-risk setting. It's far more important to learn from your mistakes on the problem sets than it is to get a high score on each assignment. Please treat written work accordingly. Don't mindlessly mimic your classmates' work just for the sake of getting a few more homework points. This bad habit will come back to bite you on the midterms.
You are welcome to engage in honest collaboration with your classmates on the problem sets. Specifically, write up the first draft of each problem set entirely on your own. Let the ideas sit for a day or two. Then meet with one or two classmates and compare your ideas.
Do not exchange written work with classmates; doing so constitutes dishonest collaboration. As noted above, this bad habit will also harm your course grade in the long run.
Problem Set 12: Due Friday, May 5
| For practice | Assigned | |
| Chapter 8 (pp. 170-176): | 20, 21, 22, 23 | |
| Chapter 9 (pp. 188-196): | 1, 2, 3, 6, 9 | 4, 8, 20 |
Note: In Practice Question 9.9, you may assume $f$ is continuous. In Question 9.20(b), please read \[ \sum_{k=1}^{\infty} k^{2} x^{k} = x + 4x^{2} + \mathbf{9} x^{3} + \cdots. \]
Problem Set 11: Due Friday, April 28
| For practice | Assigned | |
| Chapter 8 (pp. 170-176): | 1-3, 5, 11, 13 | 6, 9, 12 |
Problem Set 10: Due Friday, April 21
| For practice | Assigned | |
| Chapter 7 (pp. 151-154): | 10, 11, 13 | 12, 14 |
Problem Set 9: Due Friday, April 7
| For practice | Assigned | |
| Chapter 7 (pp. 151-154): | 2, 4, 5, 9 | 1, 6, 7, 8 |
Problem Set 8: Due Friday, March 31
| For practice | Assigned | |
| Chapter 6 (pp. 124-128): | 6 (see Example 6.71, page 123), 11, 14 | 2, 5, 13 |
Notes: In Practice Question 6.14(a), please
read:
If $0 < \delta < \frac{1}{2}$, then
$\delta < \frac{1 - \delta}{\delta}$, and $f$ maps the interval
$[\delta, \frac{1 - \delta}{\delta}]$ to itself contractively.
Problem Set 7: Due Friday, March 24; “Quiz 3”.
| For practice | Assigned | |
| Chapter 5 (pp. 92-102): | 17, 18, 19, 22, 23, 24, 25 | 20 |
| Chapter 6 (pp. 124-128): | 1(a), 4, 8 | 1(b), 3, 7 |
Midterm 1 Review Sheet; “Quiz 2”.
Problem Set 6: Due Friday, March 17
| For practice | Assigned | |
| Chapter 5 (pp. 95-102): | 1-5, 7-10, 13 | 6, 11, 14, 26 |
Problem Set 5: Due Friday, February 24
| For practice | Assigned | |
| Chapter 4 (pp. 76-78): | 1, 3, 13 | 4, 9, 12 |
Problem Set 4: Due Friday, February 17; “Quiz 1”, and solutions.
| For practice | Assigned | |
| Chapter 4 (pp. 76-78): | 2, 7, 11 | 5, 6, 10 |
| Chapter 3 (pp. 50-52): | 14 | 11 |
Problem Set 3: Due Friday, February 10
| For practice | Assigned | |
| Chapter 3 (pp. 50-52): | 1, 2, 5, 7, 10 | 3, 4, 8, 11 8 (i) |
Notes: In Question 3.3, please
read:$\newcommand{\Abs}{\mathsf{A}}$ “Let $x$, $h$,
and $r$ be real numbers, with $h \neq 0$ and $r > 1$.
(a) Show that $(x + h)^{2} - x^{2} \approx 2xh + \Abs(rh^{2})$.
(b) Show $(x + h)^{3} - x^{3} \approx 3x^{2}h + (3|x| + |h|)\Abs(rh^{2})$.
(c) Find an analogous formula for $(x + h)^{4} - x^{4}$.
(d) Use part (a) to show
\[
\frac{(x + h)^{2} - x^{2}}{h} \approx 2x + \Abs(r|h|).
\]
Find corresponding formulas for parts (b) and (c).”
In Question 3.10, please read $A_{n} = [\frac{1}{n+1}, \frac{n}{n+1}]$.
Problem Set 2: Due Friday, February 3
| For practice | Assigned | |
| Chapter 2 (pp. 31-32): | 1-3, 6-9, 12 | 4, 5, 10, 11 |
Problem Set 1: Due Friday, January 27
| For practice | Assigned | |
| Chapter 1 (pp. 10-12): | 1-7, 9, 10 | 8 |
General Guidelines: Briefly, treat each written assignment like a job application.