MAT 333–Complex Variables

Semester: Spring 2017 Lecture time: MWF 10:00-11:00 A.M Section: A Room: S103
Credits/ Contact hours: 3 credits / Three 50-minutes lecture sessions a week
Instructor:Roger Nakad, Ph. D.
Office hours / contact : MWF 11:00-1:00 P.M. / Room S 343,
Textbook:R. Churchill and J. Ward Brown, Complex Variables and Applications: Seventh Edition, McGraw Hill
Catalog description: Analytic functions; derivatives; Cauchy-Reimann equations; complex integration; Cauchy integral theorem; power series; Laurent series; residue theorem; conformal mapping; Cauchy-Christofell transformation.
Type of course : Major course for Math students
Pre-requisite: MAT 224
Course Learning outcomes and their Correlation to ProgramLearning Outcomes:
Course Learning outcomes / Program Learning Outcomes*
a)Represent complex numbers algebraically and geometrically / (2) (3) (6)
b)Define and analyze limits and continuity for complex functions as well as consequences of continuity / (3) (6)
c)Apply the concept and consequences of analyticity and the Cauchy-Riemann equations and of results on harmonic and entire functions including the fundamental theorem of algebra / (2) (3) (5)
d)Analyze sequences and series of analytic functions and types of
convergence / (2) (3) (1)
e)Evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy integral formula / (2) (3)
f)Represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem / (1) (2) (3)

*Program Learning Outcomes

  1. To demonstrate proficiency in basic knowledge in a broad range of mathematical areas.
  2. To apply acquired mathematical concepts and techniques to analyze and solve problems.
  3. To read, understand and write mathematical proofs.
  4. To function as team players.
  5. Identify the interdependency of different areas of mathematics, as well as connections between mathematics and other disciplines.
  6. Explain and communicate mathematical principles and ideas with clarity and logic, both writtenand verbally, demonstrating communication skills to be used in any future career.
  7. Use mathematical tools to solve larger real world problems.

Course topics

Date / Material / RequiredExercises
(To be done in class) / Homework Exercises
(To be done by students)
Week 1 / Chapter 1. Complex Numbers
  1. Sums and Products
  2. Basic Algebraic Properties
  3. Further Properties
  4. Vectors and Moduli
  5. Complex Conjugates
  6. Exponential Form
  7. Products and Quotients in Exponential Form
  8. Arguments for products and quotients
  9. Roots of Complex Numbers
  10. Examples
  11. Regions in the Complex Plane
/ Page 15 (9)
Page 22 (4, 6, 9--10)
Page 29 (2, 6--7)
Page 33 (1--3, 5--10) / Homework Sheet 1:
Page 12(3--4)
Page 14 (2, 7, 10)
Page 22 (1, 5)
(+ 2 Additional Problems)
Week 2 / Chapter 2. Analytic Functions
  1. Functions of a Complex Variable
  2. Mappings
  3. Mappings by the Exponential Function
  4. Limits
  5. Theorems on Limits
  6. Limits Involving the Point at Infinity
  7. Continuity
/ Page 37 (1b, 1c, 3)
Page 44 (2)
Page 55 (5, 7, 9, 10a, 11, 13)
Week 3 /
  1. Derivatives
  2. Differentiation Formulas
  3. Cauchy-Riemann Equations
  4. Sufficient Conditions for Differentiability
  5. Polar Coordiantes
  6. Analytic Functions
  7. Examples
  8. Harmonic Fucnitons
/ Page 62 (1a, 2, 4, 8a)
Page 71 (1d, 3c, 4a, 5)
Page 77 (2a, 3, 4a, 7)
Page 81 (1a, 2--4) / Homework Sheet 2:
Page 37(1a, 1d, 2, 4)
Page 55(2, 3, 4, 10b, 10c)
Page 62 (1b, 1c, 1d, 8b)
Page 71 (1a, 1b, 1c, 2, 3a, 3b, 4b, 4c)
Page 77 (1, 2b, 4b, 4c)
Page 81 (1b, 1c, 1d)
(+ 3 Additional Problems)
Week 4
Week 5
Week 6
Week 7
Week 8
Week 9
Week 10
Week 11
Week 12
Week 13
Week 14
Week 15

Assessment measures:

Exam #1 25%

Exam # 2 25%

Final Exam (Comprehensive) 40%

Attendance 10%

100%

Additional course policies and requirements:

  • Homework assignments will be announced in class.
  • Make-up exams are given only in the case of an emergency with a valid excuse

accepted by the SAO.

  • Each student should acquaint her/himself with NDU’s codes, policies and procedures involving academic misconduct, including, but not limited to plagiarism and cheating. A source of guidance can be found at

Prepared on: September 2015

Revised on: January 2017