Fall 2012: Math 5320-1 Complex Variable I


Instructor: Dr. Alexander Solynin

Place:  MA 108

Office Hours: MWF 10:00-11:00am

or by appointment

Text: Class Notes and

Functions of One Complex

Variable, 2nd Edition
by John Conway

Office: MA 231

Time: 12:00-12:50 MWF

Phone: 742-2580x256

Email: alex.solynin@ttu.edu



Course Prerequisite: Department: MATH 4350 or 4356. Sets, functions, vector fields, partial derivatives, power series, theory of integration, line, surface, and multiple integrals.

Instructor: Some familiarity with real analysis of one variable and multivariable calculus as well as basic knowledge of high school algebra and trigonometry is required. The fundamental necessary ideas will be reviewed.

Learning Outcomes: Upon completion Complex Variable I and Complex Variable II students will master concepts and theories of calculus of one complex variable, geometry and topology of the complex plane. In particular, for the Fall Semester I plan to cover Chapters I-V. Students will learn the following subjects:

analytic functions,

conformal mapping,

complex integration,

harmonic functions,

power series in the complex plane,

isolated singularities,

the residue calculus.


Assessment of the learning outcomes will be achieved through one or more activities such as class discussion, board work, selected non-graded homework, and other optional activities deemed appropriate by the instructor. It is important to note that these assessments are for learning benefit.



The final exam is a comprehensive, course wide exam.


Wednesday, December 12 FINAL EXAMINATION 1:30 4:00 pm 200 pts

This exam is scheduled before the semester begins.

Students should eliminate any conflicts NOW.


MIDTERM EXAM: (October 15) 160 pts

Midterm exam consists of In-Class Hourly Segment @ 80 pts

and Take Home Segment @ 80 pts


HOMEWORK: There will be 8 homework assignments 830 = 240 pts


5 min QUIZZES:

There will be several 5 minute quizzes (usually first 5 minutes of a class) total = 60 pts

where students will be asked to write a particular formula/definition/theorem/etc.


Perfect attendance ( ≤ 3 missed classes,

all excused absences must be supported by official notes) 30 pts




Problem Solving Session: All students are invited to attend an optional problem solving session which will be held every second Friday from 4:00 to 5:00 pm, Room: MA 011. During these sessions I will answer some of your questions and give hints to solutions of some homework exercises.


Optional Research Projects: Research projects are optional and may be used to substitute midterm exam or 95% of the actual maximal score on the Final Exam. You may continue this project in the Spring Semester. Currently I suggest six topics listed below so my policy will be: First come-first served.

  1. Analytical Geometry from the complex analysis point of view.
  2. Doubly-periodic functions of one complex variable.
  3. Catalog of conformal mappings.
  4. Special functions of one complex variable and their properties.
  5. Basic notions of complex dynamics.
  6. Applications in electrostatics, heat flow, and fluid mechanics.



A - 90 - 100%

B - 80 - 89%

C - 70 -79%

D - 60 - 69%

F - ≤ 59%


Students with Disabilities: Any student who because of a disability may require special arrangements in order to meet course requirements should contact the instructor as soon as possible to make any necessary accommodations. Students should present appropriate verification from AccessTECH. No requirement exists that accommodations be made prior to completion of this approved university procedure.


Absence due to religious observance: The Texas Tech University Catalog states that a student who is absent from classes for the observance of a religious holy day will be allowed to take an examination or complete an assignment scheduled for that day within a reasonable time after the absence. Notification must be made in writing and delivered in person no later than 15th class day of the semester.


Absence due to officially approved trips: The Texas Tech University Catalog states that the person responsible for a student missing class due to a trip should notify the instructor of the departure and return schedule in advance of the trip. The student may not be penalized and is responsible for the material missed.


Academic Integrity: It is the aim of the faculty of Texas Tech University to foster a spirit of complete honesty and a high standard of integrity. There will no tolerance for cheating or plagiarism. Texas Tech University policies will be enforced in such cases.


Important Dates:

August 27 - Classes begin

September 3 - Labor Day Holiday.

September 12 - Last day to drop a course without penalty.

October 29 - Last day to drop a course with penalty.

November 21-25 - Thanksgiving Vacation.

December 5 - Last Day of classes.

December 12 1:30 4:00pm MA 108 FINAL EXAM



Course Calendar


Date Tentative Lecture Topics


Aug. 27,29,31 Sept. 5,7 Complex Numbers

Sept. 10,12,14,17 Geometry and Topology of the Complex Plane

Sept. 19,21,24,26,28 Functions: Basic Properties and Examples

Oct. 1,3,5,8,10,12 Theory of Differentiation: Analytic Functions

Oct. 15 Midterm Exam

Oct. 17,19,22,24,26,29,31 Complex Integration

Nov. 2,5,7,9,12,14,16 Complex Integration - Continuation

Nov. 19,26,28,30,Dec. 3 Laurent Series and Singularities

Dec. 5 Review of the Course. Last day of classes.


December 12 MA108 FINAL EXAMINATION 1:30 4:00 pm