MATH 147
Course Content: The theory of complex variables and its applications.
Textbooks: "Complex Variables and Applications", 9th Edition, by Brown & Churchill.
Location: Lectures will be online, MWF 10:00 a.m. - 10:50 p.m.
My office hours: TBA.
Discussions: Joe Li, TTh 8:00 a.m. - 8:50 a.m.
Office RH 540M, office hours: TBA
Exams: There will be one midterm exams and a comprehensive final exam as stated below in the Course Schedule. No books are allowed on exams. The dates and times of all exams are fixed so make make sure that you have no conflicting plans. No make up exams will be given under any circumstances. Please remember to bring your student ID to all exams.
Grading: Your course grade will be based on the homework, midterm and the final exams in the following way: homework grade = 20%, midterm exam = 30% and final exam = 50%. For the homework one of the lowest scores will be dropped.
Curve: The course grade may be curved if the median appears to be far below the B-/C+ region.
Related Links:
Text: "Complex Variables and Applications", 9th Edition, by Brown & Churchill.
DAY |
SECTION |
TOPIC |
| 1. 04/03 |
1-3, (4-5) |
Complex Numbers, Basic Algebraic Properties |
2. 04/05 |
6-7 |
Conjugation, Principal Value, Euler's Formula |
3. 04/07 |
8-9 |
Product, Quotient and Roots |
4. 04/10 |
10, (11), 12 |
Roots Cont'd and Regions in Complex Plane |
5. 04/12 |
13, (14) |
Complex Functions & Mappings |
6. 04/14 |
15-16, 18 |
Limits & Continuity |
7. 04/17 |
19-22 |
Differentiation & Cauchy-Riemann Equations |
8. 04/19
|
23, (24), 25 -27 |
Analytic and Harmonic Functions |
9. 04/21 |
(28), 30 |
Exponential Function |
10. 04/24 |
31-33 |
Logarithmic Function & Branches |
11. 04/26 |
34-36 |
Logarithmic Identities and Complex Exponents |
12. 04/28 |
37-38 |
Trigonometric Functions |
13. 05/01 |
(40), 41-42 |
Inverse Trigonometric Functions & Integral of Complex-Valued Functions |
14. 05/03 |
43-45 |
Contour Integrals |
15. 05/05 |
46-47 |
Contour Integrals Cont'd and Integral Boundss |
16. 05/08 |
48-49 |
Antiderivatives |
17. 05/10, regular class time |
Midterm |
|
18. 05/12 |
50, 52-54 |
Cauchy-Goursat, Cauchy Integral Formula |
19. 05/15 |
55-58 |
Morera, Liouville, Fundamental Theorem of Algebra |
20. 05/17 |
58-59 |
Fund Theorem Cont'd, Mean Value Theorem, Maximum Principle |
21. 05/19 |
60-62 |
Complex Sequences, Series, Taylor Series |
22. 05/22 |
63-66, (67) |
Proof of Taylor Series, Laurent Series |
23. 05/24 |
68-70, (71), 72, (73) | Other Properties of Series |
24. 05/26 |
74-76, 78-79 |
Cauchy Residue Theorem & Characterization of Singularities |
25. 05/31 |
80-81, (82), 83 |
Zeroes and Poles and Other Residue Theorems |
26. 06/02 |
85-86 |
Evaluation of Improper Integrals |
27. 06/05 |
86-87 |
Examples, Integrals with Trigonometric Functions |
28. 06/07 |
Review |
|
29. 06/09 |
Review |
|
| 06/14 Wed. 1:30 p.m. -3:30 p.m. | Final Exam |
|
Notes:
Homework assignemts.
1. HW #1 (Due 04/11)
Sec. 2: 2, 4
Sec. 3: 1, 2, 6
Sec. 5: 2, 3, 5
Sec. 6: 1, 4, 10, 15
Sec: 9: 1, 2, 3, 4, 7, 8
2. HW #2 (Due 04/18)
Sec. 11: 1, 4, 8
Sec. 12: 2, 3, 4
Sec. 14: 3, 4, 7
Sec. 18: 1, 3, 5, 8, 9
3. HW #3 (Due 04/25)
Sec. 20: 1, 2, 3, 4
Sec. 26: 2, 4, 6, 7
Sec. 30: 1, 2, 3, 4, 5, 6, 11
4. HW #4 (Due 05/02)
Sec. 33: 1, 3, 4, 5, 8, 9
Sec. 34: 1, 2
Sec. 36: 1, 2, 3, 4, 5, 6
Sec. 38: 1, 2, 3, 4, 5, 7, 12
5. HW #5 (Due 05/09)
Sec. 41: 2(a,b), 3, 4
Sec. 43: 1, 2, 3, 4
6. HW #6 (Due 05/16)
Sec 46: 1, 2, 3, 5, 6, 7
Sec. 47: 1, 2
7. HW #7 (Due 05/23)
Sec. 49: 1, 2, 3, 4,
Sec. 53: 1, 2, 3, 4, 6
Sec. 57: 1, 2, 3, 4, 5
8. HW #8 (Due 05/30)
Sec. 61: 1, 2, 3, 5, 6, 7, 8
Sec. 65: 1, 2, 3, 4, 7
9. HW #9 (Due 06/06)
Sec. 68: 1, 2, 3, 4, 5, 6, 7
Sec. 72: 1, 2, 3.
Sec. 77: 1, 2, 4
Sec. 79: 1, 2 b, c