Math 413 - Complex Analysis Homework
Final: Tuesday, Dec. 16, 8:00-10:00 in CW 212
Textbook: Fundamentals
of Complex Analysis with Applications to Engineering and Science (3rd
edition) by Saff & Snider.
Your graded Homework 17 is the tray outside my office CW 312.
Also, in the tray are solutions to some of the most recent practice
problems. Please pick up a copy and
study it.
Class 43 Fri Dec 12
1. Laurent series examples.
2. Comprehensive Final: Tuesday,
Dec. 16, 8:00-10:00 in CW 212
Class 42 Wed Dec 10
Exam 3 on Sections 4.1, 4.2, 4.3, 4.4(b), 4.5, 5.1, & 6.2.
Class 41 Mon Dec 8
1. Exam 3 on Wed will cover Sections
4.1, 4.2, 4.3, 4.4(b), 4.5, 5.1, & 6.2.
2. Hwk 17 is due Fri: 1(e), 5(f), 8(a), 11(a), & 14 starting on p.250.
Also for
Friday:
3. Skip 5.4. In Section
5.5, read the theorems (but skip the proofs) and study the examples.
4. Practice
problems: 5 & 6 on p.259 and 3 & 4 on p.276.
Exam 3 is postponed until
Wednesday!
Class 40 Fri Dec 5
Exam 3 on
Monday will cover Sections 4.1, 4.2, 4.3, 4.4(b), 4.5, 5.1, & 6.2.
For next Wednesday:
1. Read Section 5.3
2. Hwk 17 is due next Wed: 1(e), 5(f), 8(a), 11(a), & 14 starting on p.250.
3. Practice problems in Section 5.3: 2, 3(d), 13(b) starting on p. 258.
Class 39 Wed Dec 3
1. Section
5.2.
2. Hwk 17 is due next Wed: 1(e), 5(f), 8(a), 11(a), & 14 starting on p.250.
Reminders.
Exam 3 will be on Monday, Dec 8 and
cover 4.1, 4.2, 4.3, 4.4(b), 4.5, 5.1, & 6.2.
Class 38 Mon Dec 1
1. Read
Section 5.1.
2. Some practice
problems starting on p.239: 1(a), 1(c), 1(f), 3, 5, 6.
Reminders.
Hwk 16 is due Wed:
2, 3(a), & 7 starting on p.213 and 1 & 5 on p. 317.
Exam 3 will be on Monday, Dec 8
and cover 4.1, 4.2, 4.3, 4.4(b), 4.5, 6.2, and ?
Happy
Thanksgiving!
Class 37 Wed Nov 26
1. Read the
examples in Sec 6.2; however we will use
Cauchy’s integral formula to work these.
2. Hwk 16 is due Wed (after
Thanksgiving): 2, 3(a), & 7 starting on
p.213 and 1 & 5 on p. 317.
Reminder.
Exam 3 will be on Monday, Dec 8
and cover 4.1, 4.2, 4.3, 4.4(b), 4.5, 6.2, and ?
Class 36 Mon Nov 24
1. Read the
examples in Sec 6.2; however we will use
Cauchy’s integral formula to work these.
2. Hwk 16 is due a week from today: 2,
3(a), & 7 starting on p.213 and 1 & 5 on p.
317.
Reminder.
Hwk 15 is due Wed: 10(d) & 18
starting on p. 201.
Announcement.
Exam 3 will be on Monday, Dec 8
and cover 4.1, 4.2, 4.3, 4.4(b), 4.5, 6.2, and ?
Class 35 Fri Nov 21
1. Practice 10(c), 13, & 15 starting on p. 201.
2. Hwk 15 is due next Wed: 10(d) & 18 starting on p. 201.
Class 34 Wed Nov 19
1. Read Section
4.4b [pp. 191-199]. (We will use the
vector analysis approach.)
Reminder:
2. Hwk 14 is due Friday: 3(d), 6(c),
8, 13, & 14(b) on p. 171.
Class 33 Mon Nov 17
1. Read
Section 4.3.
2. Hwk 14: Friday, turn in 3(d), 6(c),
8, 13, & 14(b) on p. 171.
Class 32 Fri Nov 14
1. Practice 5, 7,
9, 11 on p. 171.
2. Maple
worksheet Residue calculation.
Class 31 Wed Nov 12
1. Practice 1, 3(a), 3(c), & 4 on p. 170.
2. Hwk 13: Friday, turn in 4, 8 (make the parametric interval
[1,2]) & 10 on p. 160 & 2 (property 2) on p.
170.
Class 30 Mon Nov 10
1. Read
Section 4.2.
2. Hwk 13: Friday, turn in 4, 8 (make the parametric interval [1,2]) & 10 on p. 160 & 2 (property 2) on p. 170.
Class 29 Fri
Nov 7 Exam 2
emphasizing
Sections 2.4 & 2.5 and Sections 3.1, 3.2, 3.3, 3.4, & 3.5.
Class 28 Wed Nov 5
For Monday,
1. Read Section 4.1.
2. Practice problems: 1, 2, 3, 5, 7, 11, & 13 starting on p.159.
Class 27 Mon Nov 3
1. Be sure to work the practice problems assigned last
Friday before Friday’s exam.
2. Read Section 3.5.
3. As
for pages 134-136, I will only hold you responsible for knowing how to derive
formulas (5) and (9) [See exercise 9 on p.137.]
4. Start reading
Section 4.1.
Reminder:
Exam 2 on Friday will essentially cover
everything but with an emphasis on Sections 2.4 & 2.5 and Sections 3.1,
3.2, 3.3, 3.4, & 3.5.
Class 26 Fri Oct 31
1. Exam 2
will be a week from today. It will
essentially cover everything but with an emphasis on
Sections 2.4 & 2.5 and Sections
3.1, 3.2, 3.3, 3.4, & 3.5.
2. Read 3.4.
3. Practice
(a) 6, 8, 9,
11, 13(a), & 13(c) on p.123;
(b) 1 &
5 on p.129;
(c) 1(a), 1(c), 1(e), & 3(c) on p.136.
Class 25 Wed Oct 29
Reminder. Hwk 12: Friday, turn in 1b, 1c, 4,
5a, 5c on p. 123.
See this link: Branches
of the natural logarithm.
Class 24 Mon Oct 27
1. Read Section 3.3.
Fall Break
Oct. 20 - 24
Class 23 Fri Oct 17
Wishing you a safe & happy Fall
Break!
1. Continue studying Section 3.2 & work the practice problems: 1, 5, 7, 9 on p.115.
2. Hwk 11 is due Monday, Oct. 27.
Class 22 Wed Oct 15
1. Read Section 3.2.
2. Practice problems: 1, 5, 9 on p.115.
3. Hwk 11 is due Monday, Oct. 27: 5(a), 7,
11(d), 15(b), 15(d) on p.108.
Class 21 Mon Oct 13
1. Practice 5, 7, 11 on p.108.
2. Hwk 10 is due Wednesday: 1(a), 3(d), 6
on p.84 and 1 & 3(a) on p.108.
Class 20 Fri Oct 10
1. Read Section 3.1.
2. Hwk 10 is due Wednesday: 1(a), 3(d), 6
on p.84 and 1 & 3(a) on p.108.
A possible senior project: is a study of harmonic
functions---see me if you are interested.
I did not get very far on grading
Exam 1, but I will return it on Monday.
Class 19 Wed Oct 8 Exam 1
Class 18 Mon Oct 6 Discussion
of some problems for exam..
Class 17 Fri Oct 3
Read Section 2.5 about harmonic
functions.
Exam 1 will be next Wed
instead of Mon
so that you will have time to work all of the problems on pp. 77-78 & so
that I can grade the last 2 homework assignments & return them on
Monday.
But you need to attempt them
first. We will reserve Monday for
working some of the problems 1, 2, 3, 4, 5, 7, 8, 10, 13, & 15 on pp77-78
in class. (Extra 10 minutes: 30 more
minutes to make up).
Class 16 Wed Oct 1
Read Section 2.4.
As far as Section 2.4 is concerned for Exam 1 you are
responsible for knowing the statements of the theorems, Examples 1 & 2,
examples done in class,
and the following problems on
pp.77-78: 1, 2, 3, 4, 5, 7, 8, 10, 13, & 15.
Exam 1 will cover Chapter 1
(Sections 1-6) and Chapter 2 (Sections 1-4).
Class 15 Mon Sept 29
Start reading Section 2.4.
Practice p. 77: 1 & 4.
Hwk 9 is due
Wednesday.
Reminder: Exam 1 will be next Monday.
It will cover Chapter 1 (Sections 1-6) and Chapter 2
(Sections 1-4).
Class 14 Fri Sept 26
Read Section 2.3.
Practice p. 70: 1, 2, 3, 4, 5, 9.
Hwk 9 – On
Wednesday, turn in on p. 70: 4(a), 5(rule 5), 6, &
7(c) & 10.
Exam 1 will be Monday, October 6.
(We went an extra 10 minutes today to make up part
of Class 13: 40 more minutes to make up).
Class 13 Wed Sept 24
Class cancelled.
Class 12 Mon Sept 22
There will be no class this
Wednesday. We will make it up by
extending classes on Fridays until we have made up the 50 minutes.
Exam 1 will be on Friday,
Oct. 3. It will cover Chapter 1
(Sections 1-6) and Chapter 2 (Sections 1, 2, ?)
For Friday, read 2.3.
Hwk 8 – On Friday, turn in p. 63: 9 (find delta in
terms of epsilon), 13, 17, 21(d), 25(b).
Class 11 Fri Sept 19
Hwk 7 – On Monday, turn in p. 56: 4b, 6, 8a.
Read Section 2.2.
Practice p. 63: 1, 3, &
7. Add 5, 6, 8, and 11.
Class 10 Wed Sept 17
Hwk 7 – On Monday, turn in p. 56: 4b, 6, 8a.
Read Section 2.2.
Practice p. 63: 1, 3, &
7.
Class 9 Mon Sept 15
Read Section 2.1.
Practice p.56: 1a,
1c, 1d, 2a, 2c, 2d, 3a, 4a, 5.
Class 8 Fri Sept 12
Read Section 2.1.
Practice 19, 21, 24 on p.43.
Hwk 6: On Monday, turn in 11 & 19 on p.37 and 2d,
3d, 4d, 5d, 6d, 7d on p. 42.
Class 7 Wed Sept 10
Memorize the proof of the
quadratic formula (Example 3 on pp. 36-37).
Read Section 1.6.
Hwk 6: On Monday, turn in 11 & 19 on p.37 and 2d,
3d, 4d, 5d, 6d, 7d on p. 42.
I will focus on catching up
with grading tomorrow.
Class 6 Mon Sept 8
Read the Wikipedia article: Mathematical Induction.
Hwk 5: On Wed., turn in 1,
2, 4b, 5f, & 9 on p.37.
Other uncollected work for practice in Chapter 1:Read 1.1 p. 5: 1 4 3 5 7 9 10 11 13 19 20b 24Read 1.2 p. 12: 1 3 7 9 10 12 13 14 17Read 1.3 p. 22: 1 3 5 b c 6b 7 d g 9 10 12b 23aRead 1.4 p. 31: 2b 4a 6a 10 12b 13 23Read 1.5 p. 37: 1 2 4b 5f 9Read 1.6 p. 41: 1 3 5 7 9 11 13 19 Skip 1.7
Class 5 Fri Sept 5
Additional practice problem: 17 on p. 32.
Hwk 4: On Monday, turn in 16, 18(b) & 20 on p. 32.
Read Section 1.5.
Other uncollected work for practice:Read 1.1 p. 5: 1 4 3 5 7 9 10 11 13 19 20b 24Read 1.2 p. 12: 1 3 7 9 10 12 13 14 17Read 1.3 p. 22: 1 3 5 b c 6b 7 d g 9 10 12b 23aRead 1.4 p. 31: 2b 4a 6a 10 12b 13 23Read 1.5 p. 37: 1 2 4b 5f 9Read 1.6 p. 41: 1 3 5 7 9 11 13 19 Skip 1.7
Class 4 Wed Sept 3
Read Sections 1.5.
Other uncollected work for practice:Read 1.1 p. 5: 1 4 3 5 7 9 10 11 13 19 20b 24Read 1.2 p. 12: 1 3 7 9 10 12 13 14 17Read 1.3 p. 22: 1 3 5 b c 6b 7 d g 9 10 12b 23aRead 1.4 p. 31: 2b 4a 6a 10 12b 13 23Read 1.5 p. 37: 1 2 4b 5f 9Read 1.6 p. 41: 1 3 5 7 9 11 13 19 Skip 1.7
Class 3 Fri Aug 29
Homework 3.
1. Do p. 6 # 27. Explain your work. 2. Do p. 31 # 2b and 4a. Explain your work. 3. Do p. 31 # 6b and 10. Explain your work. 4. Do p. 31 # 12b and 23a. Explain your work.
Other uncollected work for practice:Read 1.1 p. 5: 1 4 3 5 7 9 10 11 13 19 20b 24Read 1.2 p. 12: 1 3 7 9 10 12 13 14 17Read 1.3 p. 22: 1 3 5 b c 6b 7 d g 9 10 12b 23aRead 1.4 p. 31: 2b 4a 6a 10 12b 13 23Read 1.5 p. 37: 1 2 4b 5f 9Read 1.6 p. 41: 1 3 5 7 9 11 13 19 Skip 1.7
Class 2 Wed Aug 27
Homework 2.
1. Do p. 5 # 4 10 19 20c. Explain your work.
2. Do p. 12 # 9 13. Explain your work.
3. Do p. 22 # 6d 7h 15. Explain your work.
Other uncollected work for practice:Read 1.1 p. 5: 1 4 3 5 7 9 10 11 13 19 20b 24Read 1.2 p. 12: 1 3 7 9 10 12 13 14 17Read 1.3 p. 22: 1 3 5 b c 6b 7 d g 9 10 12b 23aRead 1.4 p. 31: 2b 4a 6a 10 12b 13 23Read 1.5 p. 37: 1 2 4b 5f 9Read 1.6 p. 41: 1 3 5 7 9 11 13 19 Skip 1.7
Class 1 Mon Aug 25
Read pp. 1 - 4.
Homework 1.
1. Divide 3 + 2 * sqrt( 2 )
by 1 - sqrt( 2 ); that is, write the result in
the form a + b * sqrt(
2 ).
2. Do p. 6 # 29.
Explain your work.
Other uncollected work for practiceRead 1.1 p. 5: 1 4 3 5 7 9 10 11 13 19 20b 24Read 1.2 p. 12: 1 3 7 9 10 12 13 14 17Read 1.3 p. 22: 1 3 5 b c 6b 7 d g 9 10 12b 23aRead 1.4 p. 31: 2b 4a 6a 10 12b 13 23Read 1.5 p. 37: 1 2 4b 5f 9