MATHEMATICS 120A ELEMENTS OF COMPLEX ANALYSIS
July 2, 2012
INSTRUCTOR: Carl FitzGerald (858)-534-2654 (no voice mail) cfitzgerald@ucsd.edu
OFFICE HOURS: 5816 AP&M Monday 2:10 PM - 3:10 PM and Wednesday 2:10 PM – 2:50 PM
TEACHING ASSISTANT: Miles Jones
OFFICE HOURS:
TEXT: Churchill and Brown: COMPLEX VARIABLES AND APPLICATIONS 8th edition, McGraw
Hill, 2009.
TOPICS: (The formal statement of topics is given in the catalogue. This is an informal description.) The
geometry of complex numbers. Formal calculations with complex numbers. Trigonometric identities
derived with complex numbers. Real variable calculus extended to complex numbers. Extensions of realvariable functions to complex-valued functions of a complex variable. Computation of complex
derivatives. Power series expansions. Integration of a complex functions on a contour. The use of complex
integrals to evaluate real integrals. The inverse of the Laplace transform.
GRADING: Homework 12%. Midterm examinations 24% each. Final 40%.
SPECIFICATIONS: In doing homework, you are encouraged to seek help from books, fellow students,
the teaching assistant and the instructor. Homework must not be a copy of another person's work; you
should understand what you submit. The homework is due at the beginning of the section meeting. No late
homework will be accepted, except for medical or other emergency. Grades will be based on a small
sample of assigned problems plus a small amount for the overall work. The lowest homework grade will
be dropped.
In taking examinations, you may not use any notes or texts or receive help from another person,
except the teaching assistant or instructor. You may not use a calculator, a cell phone or other electronic
device. You may be asked to show a photographic identification at examinations. Some of the test
questions will be based on homework problems. Each midterm examination will be given during the
lecture period; and will last one hour and twenty minutes.
Cheating is unacceptable. Possible penalties include the assignment of an F for the course and a
report to the administrator in charge of academic integrity.
MIDTERMS: The midterms are scheduled for Thursday, July 12 and Thursday, July 26 during the lecture.
FINAL EXAMINATION: Friday, August 3, from 7:00 – 9:59 PM in a room to be announced.
HOMEWORK: Homework is due at the beginning of the section on the dates indicated.
I. July 3: page 5 #1ab, 2, 3, 6b, 7, 11. Look at the other problems. Consider the formula for the square roots
of a complex number that is not real:

2
2
2
2 
a a b
a  a  b 

a  ib  
 i sign b
,


2
2


1 if b  0
where sign b  
. Find the square roots of 5  12i .
1 if b  0

page 8 #1a, 3, 4, 5, 6.


f1 and f 2 are complex numbers and
L  f 2  f1 , then the set of points z such that the distance from z to f1 plus the distance
from z to f 2 equals L is an ellipse with foci f1 and f 2 .)
II. July 5: page 12 #1(a), 2, 3, 4, 5, 6 (You may use that if
page 14 #1abcd, 2ab, 7, 9, 12, 15.






III.July 10: page 22#1ab, 2ab, 5abcd, 9 Note the following remark.
Remark: A series is geomtric if and
 onlyif there is a common factor such that, after the first
term, each term equals the previous term times the common factor. The sum of a geometric series
is worth knowing:
n1
2
3
n w  wz
, provided z  1 . The sum can be
w  wz  wz  wz   wz 
1 z
remembered as being the quantity that consist of the first term minus the first omitted term all
divided by one minus the common factor, provided that the common factor is not equal to one.

page
 29 #1ab, 2ab, 6, 7 (A geometric series again.), 8 Add a part (c): Explain why one should
know the formula without doing the work of part (a).
page 33 #1abcdef, 2, 3, 4abcd, 5, 7abcd, 10.
page 37 #1abcd, 3, 4.
page 44 #3, 7, 8.
IV. July 12: page 55 #1, 2ab, 5, 7, 9, 13.
page 62 #1abcd, 2ab (This type of expansion will be developed for many other functions.), 3, 4,
8ab, 9.
page 71 #1abcd, 2abc. (There will be more problems assigned from this section in the next
homework
Thursday, July 12, MIDTERM I will be in lecture. It will cover through the material of Homework IV.