Complex Analysis
MTH 431, Section 17909, Spring 2014
Mondays & Wednesdays 12:20 - 2:15 3S-108
Goal: The goal of this course is to learn functions of
a complex variable, differentiation and integration of complex
functions, Cauchy integral theorem, power series, residues and poles,
and elementary conformal mapping.
Book:
Complex Analysis by John Howie, Springer Undergraduate
Mathematics Series, ISBN: 1-85233-733-8
Prerequisites: Applied Mathematical Analysis I MTH 330.
Homework and Quizzes: Homework problems will be announced in
class and posted on the class homepage. A subset of the homework
problems will be collected and graded every week. It is very
important to do the homework to understand the topics covered in the
class. I highly recommend working jointly on homework problems with
fellow students. We will have some in-class quizzes.
Exams: We will have two exams druing the semester and a final exam at the
end of the semester. Dates will be announced later.
Grading: Your total score will be computed as follows: 20%
Homework & Quizzes + 25 % Exam 1 + 25% Exam 2 + 30% Final Exam. Your
total score will be assigned a letter grade. Missing the Final exam
will result in an F grade.
Help: You are encouraged to use my office hours on Mondays and
Wednesdays from 2:30 - 4 pm in my office 1S-230. Email is the best way to
contact me.
Optimal Method of Study: (1.) Come to class (attendance is
mandatory). (2.) Read the relevant sections from the book after
class. (3.) Do the homework. Leave time to think--do not put homework
off until it is due! (4.) Discuss topics and homework with other
students. (5.) Come to office hours or email with any questions.
Course Outline and Homework
Homework problems in bold will be collected very week on the due
date. Unless otherwise noted, the section numbers and problem numbers
refer to the textbook.
| Date |
Topic |
Homework |
Hand in |
Due Date |
| 01 Mon Jan 27 |
2.2 Complex Numbers |
2.1 abcd |
|
Feb 5 |
| 02 Wed Jan 29 |
2.2 Complex Numbers |
2.4ab,2.7,2.8,2.15, 2.17 |
2.1ac, 2.4a, 2.8, 2.17a |
Feb 5 |
| 03 Mon Feb 3 |
3.3 Functions and Continuity & 3.4 |
3.4, 3.6 |
|
|
| 04 Wed Feb 5 |
4.1 Differentiation |
4.1ab, 4.3 |
|
|
| 05 Mon Feb 10 |
4.1 Differentiation |
HW2 |
HW2 |
Feb 19 |
| Wed Feb 12 |
College closed |
|
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| Mon Feb 17 |
College closed |
|
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| 07 Wed Feb 19 |
4.2 Power Series |
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| 08 Thu Feb 20 |
4.2 Power Series (Monday schedule) |
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| 09 Mon Feb 24 |
4.5 Singularities |
HW3 |
HW3 |
March 3rd |
| 10 Wed Feb 26 |
4.3 Logarithms |
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| 11 Mon Mar 3 |
4.4 Branch Cuts |
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| 12 Wed Mar 5 |
Exam 1 Review |
Quiz Solutions |
|
|
| 13 Mon Mar 10 |
5.2 Parametric curves |
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| 14 Wed Mar 12 |
5.3 Integration |
HW4 |
HW4 |
|
| 15 Mon Mar 17 |
5.3 Integration, 5.4 Estimation |
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| 16 Wed Mar 19 |
4.2 Power Series (Revisitied) |
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| 17 Mon Mar 24 |
Greens Theorem and Cauchy's Theorem |
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| 18 Wed Mar 26 |
6.3 Deformation Theorem |
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| 19 Mon Mar 31 |
6.1 Proof of Cauchy's Theorem |
HW5 |
HW5 |
|
| 20 Wed Apr 2 |
7.1 Cauchy's Integral Formula |
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| 21 Mon Apr 7 |
7.2 The Fundamental Theorem of Algebra |
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| 22 Wed Apr 9 |
7.3 Logarithms & 7.4 Taylor Series |
HW6 |
HW6 |
April 30th |
| Mon Apr 14 |
Spring break |
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| Wed Apr 16 |
Spring break |
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| Mon Apr 21 |
Spring break |
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| 23 Wed Apr 23 |
8.1 Laurent Series |
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| 24 Mon Apr 28 |
Exam 2 Review |
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| 25 Wed Apr 30 |
8.3 Residue Theorem |
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| 26 Mon May 5 |
8.3 Residue Theorem |
HW7 |
HW7 |
May 12th |
| 27 Wed May 7 |
9.1 Real Integrals |
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| 28 Mon May 12 |
11.2 Harmonic Functions |
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| Wed May 14 |
Review for Final |
Review |
Review |
|
| Wed May 21 |
Final 12:20 - 2:15, 3S - 108 |
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Useful Links and Resources:
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