MATH313-001 44939 Complex Variables for Engineering

Time TTh 1230-1345, Location DSH-233


Instructor: Dimiter Vassilev     Office :  SMLC, Office 326  Email:  Phone Number: 505 277 2136


Office Hours: Monday 3:30-4:30pm, Wednesday 4pm-5pm, Thursday 4:30-5:30pm. Feel free to stop-by anytime when you have a quick question.


Textbook: Joaquim Bruna & Julia Cufi, Complex Analysis. We will cover most of Chapters 1-5 and parts of Chapters 7 & 8. Quick link to the Homework.

Other texts:

Catalog Description: Theory of functions of a complex variable with application to physical and engineering problems. Although not required, skill in vector analysis will be helpful in taking this course. Prerequisite: C (not C-) in 264 and one MATH course 300-level or above.

Please note the following guidelines for the course:

GRADING: Your total course grade is based on your ranking and percentile in the class computed using the in-class exams, homework, and the final exam scaled as follows:

Not all homework problems will be graded. You will get credit if you turn in the statements of all the homework problems written in the correct order. The Final Exam score will replace all midterm scores that are lower than the Final Exam score. All grades will be posted on UNMLearn. Although a small curve might be used, 90% , 80% or 70% of the possible maximum points guarantees at least an A, B or C, respectively.

To get full credit on exams and quizzes you need to show your work, neatly, in clear and correct mathematical notation, annotated by English sentences where appropriate. You will be graded based on the work shown, not on the answer. All grades will be posted on UNMLearn. If you withdraw after the 3rd week of class, you will receive a W. If you do not withdraw, you will receive a letter grade of A,B,C,D or F (and not a W).

CALCULATORS: We will not use any (graphing or non-graphing) calculators on the exams or quizzes.

EXAMS: The exam dates are given in the syllabus. No makeup exams will be given unless you contact your instructor ahead of time with a documented “university authorized absence” (illness, family emergency, active participation in scholarly or athletic events).

ATTENDANCE: Attendance at UNM and homework is mandatory. If you have missed more than 4 attendance+homework+quizzes in the first 3 weeks you will be dropped from the course. Similarly, students with absences and lack of work during the rest of the semester may be dropped. Tardiness or early departure may be regarded as absence. Please note that it is the students responsibility to drop the course if he/she stops attending. A failing grade of F may be assigned if the student stops attending and does not drop. You can find the precise statemenet of the University policy here.

Be courteous and respectful and refrain from any activity that could be disruptive to the class. Cheating will not be tolerated.

ACCESSIBILITY STATEMENT: In accordance with University Policy 2310 and the Americans with Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor’s attention, as he/she are not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Resource Center at 277-3506 for additional information

FINAL EXAM: Thursday, December 13, 10:00 a.m.‐12:00 p.m. Students having conflicts with this examination schedule must notify the appropriate instructor before Friday, November 3, 2018. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before Friday, November 2, 2018, the instructor shall make arrangements to give a special examination. Conflicts arising as a result of scheduling out of normal hours-pattern or day sequences must be resolved by the instructor of the off-pattern courses. Changes in this examination schedule are not permitted except by formal approval of the instructor’s College Dean.

HOMEWORK: Homework related material including solutions of some problems will be posted on UNMLearn. The general rule is that homework assigned in one week is due at the beginning of the Tuesday or the first class of the following week. No late homework will be accepted.

Class Week Topics and Section Homework (due Tuesday the following week)
1. Aug 20 1.1 Arithmetic and geometry in the complex plane. HW1: Problems

2. Aug 27


1.1 Arithemtic and geometry in the complex plane 1.3 Topological notions.

- open/ closed, connected, simply connected sets. Extended complex plane.

HW2: Problems

3. Sep 3


More on topological notions -boundary points; limits and continuity of functions.

2.2-2.3 Functions of a complex variable: exponential function; logarithm

HW3: Problems


4. Sep 10


2.4-2.6 Differentiation of functions of a complex variable, conformal maps,

analytic functions. Power series (see reading material).

HW4: Problems


5. Sep 17


Power series and analytic functions. 3.1-3.5 Complex line integrals, Cauchy's theorem


HW5: Problems


6. Sep 24



3.5 Applications of Cauchy's theorem to computation of some integrals. Goursat's theorem.

3.6 -3.7 Holomorphic functions as vector fields - irrotational/ conservative and

solenoidal/ incompressible vector fields, conjugate harmonic function.

HW6: Problems



7. Oct 1


4.1 Cauchy's integral formula

4.2 Analytic functions and holomorphic functions.

HW7: Problems


8. Oct 8


Exam 1

October 11-12, Fall Break


9. Oct 15


4.2 Morera's theorem. 4.6 Cauchy's inequality. Liouville's theorem.

4.4 Zeros of analytic functions; analytic continuation (unique continuation principle); the Schwarz reflection.

HW8: Problems


10. Oct 22


2.2 Continuous (holomorphic) branches of the logarithm and power functions, their derivatves and Taylor series.

4.1 Mean value property and Mean Value inequality 4.5 The open maping theorem. The maximum modulus principle.

HW9: Problems


11. Oct 29 5.1- 5.2 Isolated singularities - characterizations, the Casorati-Weierstrass and Picard's big theorems. Laurant series. HW10: Problems

12. Nov 5

5.3-4 Residues. Calculus of real integrals

HW11: Problems
13. Nov 12 5.6 The argument principle and Rouche's theorem. HW12: Problems

14. Nov 19


Exam 2

November 22-25 Thanksgiving Break


15. Nov 26


The Gamma function 7. Harmonic functions-relation to holomorphic, harmonic conjugate, max/min principle, mean value property

8.1 Conformal maps

HW13: Problems


16. Dec 3




Conformal maps and biholomorphisms; 8.7 & 8.2 Elementary conformal transformations, linear fractional transformations,

the Riemann mapping theorem. 8.4 the automorphisms of the plane, the Schwarz lemma and the automorhisms of the unit disc.

8.2 Boundary correspondence.


No homework,.

Review: quizzes, concepts from the list of covered

Topics, homework, and past exams- solutions

posted on UNMLearn)

Dec 13


Final Exam 10:00 a.m.‐12:00 p.m. in the usual room.

The office Hours during the Final Exams week are MW 4-5pm & T 2:30pm-3:20pm.