Math 202 Complex Analysis
Fall 2021
Faculty of Science, Department of
Mathematics, Room: SA-121
Phone: 290 1490
Office Hours: by appointment
Schedule:
Tue: 13:30-15:20 SA-Z20
Fri: 09:30-10:20 SA-Z20
Textbook and Other Required Material:
Phone: 290 1490
Office Hours: by appointment
Schedule:
Tue: 13:30-15:20 SA-Z20
Fri: 09:30-10:20 SA-Z20
Textbook and Other Required Material:
- Required - Textbook: Complex Analysis, J. Bak & D. J. Newman, 2010, 3rd Edition, Springer [download]
- Recommended - Textbook: Complex Analysis, T. W. Gamelin, 2001, Springer [download]
- Recommended - Textbook: Complex Analysis, J. M. Howie, 2003, Springer [download]
- Recommended - Textbook: Complex Variables and Applications, J. W. Brown & R. V. Churchill, 2014, 9th edition, McGraw Hill Education
Assessment Methods:
| Type | Count | Total Contribution |
|---|---|---|
| Homework | 3 | 15% |
| Midterm | 1 | 40% |
| Final | 1 | 45% |
Minimum Requirements to
Qualify for the Final Exam:
Minimum 50% attendance and minimum 40% average from the Midterm Exams.
Minimum 50% attendance and minimum 40% average from the Midterm Exams.
Syllabus:
| Week |
Date |
Hours | Subjects to be covered |
| 1 | 24 Sep | 1 | Complex numbers, polar representations,
roots of unity |
| 2 | 28 Sep, 1 Oct |
3 | Topology of the complex line,
stereographic projection, limits and continuity of
complex functions |
| 3 | 5, 8 Oct |
3 | Differentiation of complex functions,
Cauchy-Riemann equations, necessity and sufficiency. Basic examples of holomorphic functions |
| 4 | 12,15 Oct |
3 | Mapping properties of $z^2$, $\sin z$,
$e^z$, $\log z$, |
| 5 | 19, 22 Oct | 3 | Complex integration, antiderivatives,
Cauchy-Goursat theorem, Cauchy integral formulaand its
general form |
| 6 | 26 Oct | 2 | Cauchy bound, Liouville's theorem,
Morera's theorem, fundamental theorem of algebra,
maximum modulus principle |
| 7 | 2, 5 Nov |
3 | Series, absolute and uniform convergence
of power series, term by term differentiation and
integration of power series, holomorphic functions are
analytic, zeros of analytic functions, Laurent series |
| 8 | 9, 12 Nov |
3 | Residue theory |
| 9 | 16, 19 Nov | 3 | Problems |
| 10 | 23, 26 Nov | 3 | Applications to real improper integrals |
| 11 | 30 Nov, 3 Dec |
3 | Jordan's inequality and application to improper trigonometric integrals, Integration through a branch cut |
| 12 | 7, 10 Dec |
3 | Mobius transformations, rigid motions of the Riemann sphere, cross-ratio |
| 13 | 14,17 Dec | 3 | Symmetry using cross-ratio, mapping the
upper half plane onto the unit disk, conformal maps |
| 14 | 21, 24Dec | 3 | Infinite products using basic tools |
| 15 | 28, 29 Dec | 3 | Weierstrass infinite product theorem and
application to sine function, Rouché's theorem |
| Exams
and Homework |
||
| Midterm Exam |
20 November 2021 Saturday,
10:00-12:30 at V-02 |
Solution |
| Final Exam | 8 January 2022 Saturday 12:00 |
Solution |
| Homework-1 |
Due date 15 October 2021
Friday Class Time |
Solution |
| Homework-2 | Due date 14 December 2021 Tuesday Class Time | Solution |
| Homework-3 | Due date 28 December
2021 Tuesday Class Time |
Solution |
The course will be graded according to the following catalogue:
| [0,34) | F |
| [34,40) | D |
| [40,44) | D+ |
| [44,50) | C- |
| [50,55) | C |
| [55,59) | C+ |
| [59,63) | B- |
| [63,65) | B |
| [65,70) | B+ |
| [70,75) | A- |
| [75,100] | A |
Old Exams are on Old Courses Web Page
Contact address is:
