Overview
Mathematics 366: Complex Variables I is an introductory complex-variable course covering complex numbers, complex-variable functions, continuity, limits, derivatives, transcendental functions, integration on the complex plane, infinite series with complex variables, and the residue theorem with some of its applications.
Outline
MATH 366 consists of the six units listed below:
- Unit 1: Complex Numbers
- Unit 2: The Complex Function and Its Derivative
- Unit 3: The Basic Transcendental Functions
- Unit 4: Integration in the Complex Plane
- Unit 5: Infinite Series Involving a Complex Variable
- Unit 6: Residues and Their Use in Integration
Learning outcomes
Upon successful completion of this course, you should be able to
- demonstrate understanding of the concept of complex numbers and the complex or Argand plane, and carry out basic mathematical operations with complex numbers expressed in either plane notation or polar notation.
- determine if a complex function is continuous, differentiable, analytic, and harmonic, and find its derivative.
- work with basic complex transcendental functions such as the exponential, logarithmic, trigonometric, and hyperbolic function.
- evaluate contour integrals of complex functions to solve practical problems by applying the fundamental theorem of calculus for analytic functions, Cauchy’s integral formula, and the theory of complex integration.
- determine the power series of elementary analytic functions and their convergence.
- demonstrate understanding of the concept of residue and apply this concept to evaluate certain real integrals.
Evaluation
To receive credit for MATH 366, you must achieve a course composite grade of at least D (50 percent), including a grade of at least 50 percent on both the midterm and final assessments. You must also complete and submit all the course assignments to the satisfaction of your instructor. The weighting of the course composite grade is as follows:
| Activity | Weight |
| Assignment 1 | 10% |
| Assignment 2 | 10% |
| Midterm Assessment | 30% |
| Assignment 3 | 10% |
| Assignment 4 | 10% |
| Final Assessment | 30% |
| Total | 100% |
To learn more about assignments and examinations, please refer to Athabasca University’s online Calendar.
Materials
Physical course materials
The following course materials are included in a course package that will be shipped to your home prior to your course’s start date:
Wunsch, A. D. (2005). Complex variables with applications (3rd ed.). Pearson.