Math 413 - Complex Analysis Homework
Final exam: Monday, December 11, 8:00–10:00 in S
112
Textbook: Fundamentals of Complex Analysis with
Applications to Engineering and Science (3rd edition) by Saff & Snider.
Correction: The answer to Problem 3 on Exam 3 is (1/2)*Pi*i*(2cos1 – sin 1), not (1/4)*Pi*i*(2cos1
– sin 1).
Don’t forget to bring your textbook and class notes (only
yours), which you may use on Part 2 of the Final Exam.
This does
not extend to homework solutions.
Class 43 Wed
Dec 6
Final exam:
Monday, December 11, 8:00–10:00 in S 112.
It is
comprehensive covering today’s lecture and the topics listed below.
Bring your
textbook & classnotes.
Make sure you go over today’s keys, particularly
of Exam 3. There will be similar
problems.
Know statements (all hypotheses and assumptions) of
all theorems & definitions that have names, such as
analytic, entire,
Fundamental Theorem of Algebra, Liouville’s
theorem, Cauchy-Riemann equations,
Cauchy’s theorem, Cauchy’s
formula, Cauchy’s residue theorem, etc.
Class 42 Wed
Dec 6
Exam 3 (final version) is due Friday (no
late papers will be accepted).
Read Theorem 14 p. 269 and study the
Laurent series examples on pp. 273-275.
Read Section 6.1 (Cauchy’s residue
theorem).
Class 41 Mon Dec 4
Exam 3 (final
version) is due Friday (no late papers will be accepted).
Read Definition 5 p.
252 & Theorem 11 on p. 256.
Read Theorem 14 p. 269
and study the Laurent series examples on pp. 273-275.
Class 40 Fri Dec 1
Exam 3 (updated Thursday, Nov 30, 2:25
P.M.)
Study
the examples of
Practice
p. 249: 1(a), 1(d), 2(a), 2(d).
Read
Definition 5 on p. 252 and Theorem 11 on p. 256.
Skip
Section 5.4.
Class 39 Wed Nov 29
Read
Sections 5.1 & 5.2.
Practice
p. 239: 1(b), 2(b), 2(d), 7(d), 7(e), 11(b).
Exam 3 (as of Thursday, Nov 30, 10:50 A.M.)
Class 38 Mon Nov 27
Study Cauchy’s generalized integral formula (Theorem
19) and Examples 4 & 5 on pp. 211-212.
Practice p. 212: 3(b), 3(c), & 7.
Study the Cauchy estimates for the derivatives of an
analytic function (Theorem 20) and Liouville’s
Theorem (Theorem 21) on pp. 214–215.
Exam 3 Wed Dec 6
Happy Thanksgiving!
Class 37 Wed Nov 22
Look at the examples in Section 6.2.
Fundamental Theorem of Algebra (Theorem 22) in Section
4.6.
Practice p. 317: 1 & 2 (but we are using
Cauchy’s integral formula instead of Cauchy’s residue theorem).
Exam 3 Wed Dec 6
Class 36 Mon Nov 20
Read 4.5.
Practice p. 212: 1, 3(a), 3(f).
Exam 3 Wed Dec 6
Class 35 Fri Nov 17
Read 4.5.
Hwk 24–turn in p. 202: 13(c) and 18.
I have a committee meeting today from 2:00 to 5:00.
Class 34 Wed Nov 15
Continue studying Section 4.4b on pp. 191–199.
Hwk 23–Friday, turn in Problems 12, 16, 21, 22 on pp.
906-907 Calculus (4th ed.) by Hughes-Hallett.
Practice p. 201: 9, 10a, 10c, 15.
Class 33 Mon Nov 13
Read Section 4.4b on pp. 191–199. [Omit Section 4.4a].
Hwk 22–Wednesday, complete the proof of Green’s Theorem.
Hwk 23–Friday, turn in Problems 12, 16, 21, 22 on pp.
906-907 Calculus (4th ed.) by Hughes-Hallett.
Class 32 Fri Nov 10 Exam 2
Class 31 Wed Nov 8
For Monday, read Section 4.3.
Practice p. 178: 1a, 1c, 1e, 1 h.
Monday: Hwk 21–turn in p. 178: 1f, 2, 5.
Also, review the definition of a line integral
(Hughes-Hallett 4th edition Section 18.1; see notation top of p.
888.).
Green’s Theorem ((Hughes-Hallett 4th
edition pp. 901-902; see Theorem 18.3).
Class 30 Mon Nov 6
Practice p. 171: 5, 7, 11, 9, 11, 13, 14.
Hwk 20–turn in p. 171: 3d, 6c, 8, 13, 14b.
Exam Friday!
Class 29 Fri Nov 3
Practice p. 170: 1–5 (all).
Study for the exam next Friday (instead of Wed)!
It will cover all
practice & turn-in problems, reading assignments, definitions, theorems,
and lectures related to 3.1, 3.2, 3.3, 4.1, and 4.2.
Of course, you may
have to use the stuff we learned in Chapters 1 & 2.
I will get all
recent past homework to you Monday.
Class 28 Wed Nov 1
Practice p. 160: 7, 9.
Hwk 19–turn in p. 160: 8.
Read Section 4.2.
Practice p. 170: 1, 2.
Class 27 Mon Oct 30
Read Section 4.2.
Hwk 18–turn in p. 159: 1(b), 1(d), 10.
Class 26 Fri Oct 27
Section 4.1.
Practice p. 159: 1, 10, 11.
Class 25 Wed
Oct 25
Hwk 17–turn in
p. 109: 15(e); p. 116: 18(a); p. 123: 1(b), 3, 5(a).
Read
Section 4.1.
Class 24 Mon Oct 23
Hwk 16–turn in p. 115: 5(d), 6, 10, 13(a), 14(b).
Read Section 3.3.
Fall Break
Class 23 Fri Oct 13
More practice problems on p. 115: 7, 8, 9(c) & (d),
10, 12(b), 15, 18(a).
Class 22 Wed Oct 11
Read Section 3.2.
Practice p. 115: 1, 2, 4, 5.
Hwk 15–On Friday, turn in p. 109: 13(b) [show work of
course]; 15(b) and on p. 115: 3 [explain how the answer is obtained].
Exam
2–Wed, Nov 8.
Class 21 Mon Oct 9
Practice p. 108: 7, 11, 13(d), 15(c).
Read Section 3.2.
Class 20 Fri Oct 6
Continue reading Section 3.1.
Turn in Hwk 13 on Monday.
Also on Monday, in a separate stack, turn in Hwk 14–p. 108: 3 (c) (hint #20
p.32) & 6.
Class 19 Wed Oct 4 Exam 1
Class 18 Mon Oct 2
Study Section 3.1.
The exam Wed will
cover all practice & turn-in problems, reading assignments, and lectures
related to Chapters 1 & 2.
Hwk 13–for Friday, p. 108 turn in: 1, 3(a), 5(a).
Class 17 Fri Sept 29
Study for the exam
next Wed (will cover all practice & turn-in problems, reading assignments,
and lectures).
Also, for Monday,
read 3.1 (pp. 99–108).
Practice p. 108: 1, 3(b), 3(c) [hint see #20 p. 108], 5
(all).
Class 16 Wed Sept 27
Read 3.1 (pp.
99–108).
Hwk 12–Turn in p. 77: 4, 8, 15.
Class 15 Mon Sept 25
Read 2.4.
Practice p. 70: 9,
10, 11, 13, 14, 15; p. 77: 1, 3, 5.
(Possible questions for next week’s exam)
Class 14 Fri Sept 22
Practice p. 70: 1,
2, 3, 5, 7(d), 7(e).
Hwk 11–Turn in p. 70: 4 & 6.
Read 2.4.
Class 13 Wed Sept 20
Read 2.3.
Practice p. 63: 11,
13, 15, 20 and p. 70: 1, 2, 3.
Class 12 Mon Sept 18
Exam 1–Wed
Oct 4
Hwk 10–Turn in p. 64: 17, 18, 19.
Read 2.3.
Class 11 Fri Sept 15
For Monday:
Practice p. 63: 1,
3, 7.
Hwk 9–Turn in p. 57: 7a, 8a, 10a & p. 63: 2, 4.
Read Section
2.3.
Exam 1–Wed
Oct 4
Class 10 Wed Sept 13
Hwk 8–Turn in p. 56: 4b and 6.
Read Section
2.2.
Class 9 Mon Sept 11
Read Section
2.1.
Practice p. 56: 1a, 1c, 1d, 2a, 2c, 2d, 3a, 4a, 5.
Hwk 7–turn in p. 42: 1–7 (all) [just for function
(d)] and p. 56: 1(c), 2(c).
Class 8 Fri Sept 8
Read and study
Section 1.6.
(I will not present Section
1.6 in class; but I will refer to it in the future and assume that you have
studied it. Of course, you can come to
my office to discuss any part that is not clear to you).
Practice p. 42:
1–13 (odd); 19.
Memorize the proof
of the quadratic formula (Example 3 on pp. 36-37).
Class 7 Mon Sept 6
Read pp.
33–37.
Practice p.37: 1, 2,
4b, 5f, 9.
Hwk 6–turn in p. 23: 10b, 12d, 28.
Class 6 Fri Sept 1
Hwk
5–Turn in p. 31: 6a, 10, 12b, 23a.
Class 5 Wed Aug 30
Practice p.
31: 1, 3.
Read the Wikipedia article Mathematical
Induction.
Hwk
4–Turn in p. 6: 27 (using mathematical induction); p 31: 2b & 4a.
Class 4 Mon Aug 28
Read
Section 1.4. Practice p. 22: 1, 3, 5(b), 5(c), 6(b), 7(d), 7(g), 9; p. 31:
12.
Hwk
3–Turn in p.12:
9, 13; p.22: 6d, 7h, 15.
Class 3 Fri Aug 25
Read Section 1.3.
Practice p. 12: 1, 3, 7, 9, 10, 12, 13, 14,
17.
Class 2 Wed Aug 23
Hwk
2–Turn in p. 5: 4, 10, 19, 20b, 24.
Read Section 1.2.
Class 1 Mon Aug 21
Course handout & grading policy.
Read pp. 1–4.
Practice p. 4: 1–13 (odd).
Hwk 1–Divide
3+2*sqrt(2) by 1-sqrt(2); that is, write the result
in the form a+b*sqrt(2). Also, p.6: 29.
