Introduction to Complex Variables

Time: MWF 8:00-9:00

Building: Geography

Room:
200

- Homework 1 , Solutions
- Homework 2 , Solutions
- Homework 3 , Solutions
- Homework 4 , Solutions
- Homework 5 , Solutions
- Homework 6 , Solutions
- Homework 7 , Solutions
- Homework 8 , Solutions
- Homework 9 , Solutions
- Homework 10 , Solutions

There will be a script made available before the lectures. I give no guarantee on the script, it may be errorneous.

- chapter I and II (pages 1 to 22)
- chapter III (pages 23 to 34)
- chapter IV.1 to IV.3 (pages 35 to 41)
- chapter IV.4 to IV.6 (pages 42 to 52) errors on page 44 corrected
- chapter V (pages 53 to 66)
- chapter VI (pages 67 to 72)

- Complex numbers and exponentials
- The Cauchy-Riemann equations
- The Partial Fraction Decomposition
- The complex function sin(z)

There will be two midterms.

- Midterm 1 is on Friday, October 4th, 8:00 am to 8:50 am in the classroom.
- Solutions
- Midterm 2 is on Friday, November 8th, 8:00 am to 8:50 am in the classroom.
- Solutions

One of MATH 200, MATH 217, MATH 226, MATH 253, MATH 263.

Christian Sadel

office: LSK building room 126C

csadel[at]math.ubc.ca

http://www.math.ubc.ca/∼csadel/

** office hours: ** Wednesday and Friday, 9:00 - 11:00 am in **
LSK 303D **

My own script, and the textbook:
E.B. Saff and A.D. Snider, Fundamentals of Complex Analysis with Applications to
Engineering and Science, Pearson, Third Edition, 2003. ISBN-13: 9780139078743.

The material from the script will be the material tested,
the textbook offers additional explanations and sketches.

The script will be very dense and I do not give a guarantee on correctness of every
formula in the script. ** It is the students responsibility to clarify
possible discrepancies between text and lecture with the instructor and to make sure
that the contents and aspects of the lectures are understood. Students are always
welcome to ask questions, go to office hours and make appointments. **

If you only want to use the script then it is highly recommended to visit all lectures and make notes on additional explanations and sketches which are missing in the script.

- Complex Numbers (§1.1-1.6)
- Analytic Functions (§2.1-2.5)
- Elementary Functions (§3.1-3.3, 3.5)
- Complex Integration (§4.1-4.6)
- Series Representations for Analytic Functions (§5.1-5.3,5.5,5.6)
- Residue Theory (§6.1-6.3)
- Additional stuff from §6 and §7 if time permits.

- There will be two midterms, weekly homework problems and a final exam.
- Midterm 1 is on Friday, October 4th, 8:00 am to 8:50 am in classroom.
- Midterm 2 is on Friday, November 8th, 8:00 am to 8:50 am in the classroom.
- midterms are non-cumulative, but the final exam will be about the whole term
- There are two grading schemes:
- scheme 1: Homework 10%, worst homework will be dropped; midterms 2 x 20% = 40%, Final: 50%
- scheme 2: Homework 10%, worst homework will be dropped; best midterm 25%, Final: 65%
- The grade will be based on the maximum of scheme 1 and scheme 2. In other words, with a good final you get the chance to annihilate your worst midterm and replace it by part of the other midterm and the final. This way, it is recognized when a student catches up for the final. BUT BE WARNED: The final is typically harder than the midterms. Past statistics reveal that performances on final exams are typically worse than on midterms.
- Extra credit will not be given!
- Grades might be scaled if the statistics reveal that the exams were too hard. Any curving will be only applied to the final marks, individual tests will not be curved.

Missing a homework or midterm normally results in a mark of 0. Exceptions may be granted in two
cases: prior consent of the instructor or a medical emergency. In the latter case, the instructor must be
notified within 48 hours of the missed test, and presented with a doctor's note immediately upon the
student's return to UBC. Failure to comply also results in a 0 mark.

If a homework was missed for legitimed reason, the homework grade will be based on all other homeworks, if a midterm
was missed, there will be a make up midterm for the particular student(s), except in exceptional cases with long illness.

**
In any circumstance, the grade will not be based on the homework and the final alone! There has to be at least one midterm grade.**