| Course Department: |
Department of Mathematics and Statistics |
| Course Code: |
MAS 003 |
| Course Title: |
Elements of Complex Analysis |
| Number of ECTS: |
7.5 |
| Level of Course: |
1st Cycle (Bachelor's Degree) |
| Year of Study (if applicable): |
3 |
| Semester/Trimester when the Course Unit is Delivered: |
Fall Semester
|
| Name of Lecturer(s): |
Evangelides Pavlos |
| Lectures/Week: |
2 (1.5 hours per lecture) |
| Laboratories/week: |
-- |
| Tutorials/Week: |
1 (1 hours per lecture) |
| Course Purpose and Objectives: |
To introduce students to basic facts and methods of Complex Analysis and illustrate the applications of its fundamental principles to sciences.
|
| Learning Outcomes: |
The student should understand the concept of analyticity of a function. The students should be able to compute contour integrals (residue theory) and be able to find conformal maps from one particular region to another given one.
|
| Prerequisites: |
MAS 018, MAS 019 |
| Co-requisites: |
Not Applicable |
| Course Content: |
Complex Numbers, analytic (holomorphic) functions and Cauchy-Riemann equations. Harmonic functions. Exponential, logarithmic and trigonometric functions Integrals, Cauchy Theorem. Cauchy integral formula. Morera and Liouville’s Theorems. Maximum principle. Fundamental Theorem of Algebra. Taylor and Laurent series. Residue calculus Conformal mappings and Mobius transformations. Applications to problems from physics and engineering.
|
| Teaching Methodology: |
Classroom instruction, problem solving session
|
| Bibliography: |
Complex Analysis and applications (J. Brown-R. Churchill) / Complex variables (Schaum’s outliner)
|
| Assessment: |
Midterm exams, final exam |
| Language of Instruction: |
Greek
|
| Delivery Mode: |
Face-To-Face |
| Work Placement(s): |
Not Applicable |
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