Applied Mathematics I
| Title | ΕΦΑΡΜΟΣΜΕΝΑ ΜΑΘΗΜΑΤΙΚΑ Ι / Applied Mathematics I |
| Code | ΜΑ0501 |
| Faculty | Engineering |
| School | Electrical and Computer Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter |
| Coordinator | Nikolaos Atreas |
| Common | No |
| Status | Active |
| Course ID | 20000617 |
| Academic Year | 2018 – 2019 |
| Class Period | Winter |
| Faculty Instructors | |
| Weekly Hours | 4 |
| Class ID | 600130534
|
Course Type 2016-2020
- Background
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600130534
- Other: http://users.auth.gr/natreas
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus and multivariable Calculus, Linear Algebra and Analytic Geometry.
Learning Outcomes
1. Perform calculations with complex numbers and use elementary complex functions as a tool of geometric
transformations.
2. Use complex integration as a tool for qualitative study of two dimensional vector fields (circulation-
flux, complex potential).
3. Use complex analysis techniques as a tool in signal processing (calculating Fourier, Laplace and zeta
transforms).
4. Use conformal mappings for solving problems of electromagnetism (calculating the electric field in a region, given boundary conditions) and for solving PDE’s.
General Competences
- Apply knowledge in practice
- Retrieve, analyse and synthesise data and information, with the use of necessary technologies
- Advance free, creative and causative thinking
Course Content (Syllabus)
Algebra of complex numbers, polar form, roots of unity. Functions of a complex variable (exponential, logarithmic, trigonometric, hyperbolic, linear functions and inverse functions). Limit, continuity and complex derivative. Holomorhic (analytic) functions and Cauchy-Riemann equations. Complex integration. Cauchy theorem and Cauchy integral formulas. Applications (Liouville theorem, Cauchy inequality, max/min modulus principle). Series of complex numbers. Taylor and Laurent series. Removable singularities, poles and essential singularities. Residuals and applications. Conformal mappings. Ηarmonic and conjugate harmonic functions. Dirichlet's problem for the disk and half plane.
Keywords
Analytic functions, Cauchy theorem, residuals, harmonic functions
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 52 | 1.7 | ✓ | ✓ | |
| Reading Assigment | 30 | 1 | |||
| Exams | 38 | 1.3 | |||
| Total | 120 | 4 |
Student Assessment
Description
Written examination at the end of the semester.
Student Assessment methods
- Written examination
Bibliography
Course Bibliography (Eudoxus)
1. Μιγαδικές συναρτήσεις και εφαρμογές, Churchill R., Brown J.
2. Βασική Μιγαδική Ανάλυση, Marsden Jerrold E.,Hoffman Michael J. μτφσ. Παπαλουκάς Λ.
Additional bibliography for study
Mιγαδικές συναρτήσεις και εφαρμογές. Ε. Γ. Γαλανής. Εκδόσεις Συμεών. (1994).
Τheory and problems of complex Variables. M. Spiegel, McGraw-Hill.
Last Update
15-10-2017
