# Applied Mathematics

Semester:
5ο
Course Type:
Elective Specialization courses (ΠΜ-E)
Track:
CΕT (Computer Engineering and Telecoms)
Code:
Κ20β
ECTS:
6
TEACHING HOURS per week
Theory:
3
Seminar:
1
Laboratory:
-
Specializations
Foundations of Computer Science (Ε1):
-
Data and Knowledge Management (Ε2):
-
Software (Ε3):
-
Hardware and Architecture (Ε4):
-
Communications and Networking (Ε5):
-
Signal and Information Processing (Ε6):
B Βασικό
Related Courses
Detailed Description
Course Content
• Ordinary differential equations: definitions, examples. First order equations: separable, linear, reducible to linear (Bernoulli, Riccati), exact, reducible to exact - integrating factors, homogeneous. An introduction to issues on existence and uniqueness of solutions of initial value problems for first order equations. An introduction to qualitative theory: population models (exponential and logistic growth), phase diagrams, linearization, elements of bifurcation theory. Second order linear equations: homogeneous, non-homogeneous, constant coefficients, the methods of variation of constants and of undetermined coefficients, Euler’s equation, mechanical and electrical oscillations. Systems of first order linear equations: emphasis in the case of constant coefficients and in dimensions 2 and 3.
• Complex analysis: complex numbers, sequences and series of complex numbers, complex functions (continuous, analytic, the elementary functions), integration (definite and indefinite integral, Cauchy’s formula), isolated singularities, Laurent expansion, residues and applications in integrating complex and real functions, applications in electrical circuits.
LITERATURE AND STUDY MATERIALS - READING LIST
• N. D. Alikakos, G. E. Kalogeropoulos, Ordinary Differential Equations (in Greek), Sygkhroni Ekdotiki, Athens, 2007.
• J. Bak, D. Newman, Complex Analysis (translation into Greek), Leader Books, Athens, 2004.
• W. E. Boyce, R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (translation in Greek of the 10th edition), Panepistimiakes Ekdoseis Ε.Μ.Π., Athens, 2015.
• I. G. Stratis, An Introduction to Complex Analysis, Lecture Notes (in Greek), Athens, 2006  (via e-class).