Applied Mathematics II

Course Information
TitleΕφαρμοσμένα Μαθηματικά ΙΙ / Applied Mathematics II
Code055
FacultyEngineering
SchoolElectrical and Computer Engineering
Cycle / Level1st / Undergraduate
Teaching PeriodWinter
CoordinatorAthanasios Kechagias
CommonNo
StatusActive
Course ID600001004

Programme of Study: Electrical and Computer Engineering

Registered students: 209
OrientationAttendance TypeSemesterYearECTS
ELECTRICAL ENERGYElective Courses744
ELECTRONICS AND COMPUTER ENGINEERINGElective Courses744
TELECOMMUNICATIONSElective Courses744

Class Information
Academic Year2022 – 2023
Class PeriodWinter
Faculty Instructors
Weekly Hours4
Class ID
600218050
Course Type 2021
Specialization / Direction
Course Type 2016-2020
  • Scientific Area
Course Type 2011-2015
Specific Foundation / Core
Mode of Delivery
  • Face to face
Digital Course Content
Language of Instruction
  • Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Calculus I, Linear Algebra, Calculus II, Αpplied Mathematics
Learning Outcomes
At the conclusion of this class the students will be able to do the following. 1. Solve analytically the basic linear partial differential equations: Laplace equation, wave equation, heat equation. 2. Solve the same equations as well as their nonlinear extensions using numerical software (e.g., Matlab) and/or symbolic algebra software (e.g., Maple). 3. Use the PDE formalism in modeling and solving applied problems (e.g. applications to electromagnetic field, image processing, transportation problems etc.). 4. To be able to solve 2nd order linear differential equations by series methods. 5. To know the basic special functions (Bessel, Legendre, Chebyshev). In addition, the students will have a clear intuitive understanding of the physical significance of partial differential equations as well as their connection to systems of algebraic equations.
General Competences
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Work autonomously
  • Work in teams
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Partial differential equations (PDE's): Laplace equation, heat equation, wave equation. In the first part of this course solution methods will be taught. 1. Separation of variables. 2. Integral transforms (Fourier, Laplace). 3. Solution using symbolic algebra software (computer algebra systems, CAS) e.g. Maple, Mathematica. 4. Solution using numerical methods and introduction to the corrsponding software (e.g. Maple, Mathematica, Matlab PDE Toolbox, MathPDE). In the second part of the course, the students will study and present papers from the current literature, related to the applications of PDE's (e.g., applications to electromagnetic field, image processing, transportation problems, stochastic processes etc.).
Keywords
Partial differential equations (PDE's): Separation of variables, Laplace equation, heat equation, wave equation.
Educational Material Types
  • Notes
  • Interactive excersises
  • Book
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures521.7
Reading Assigment250.8
Exams30.1
Other / Others401.3
Total1204
Student Assessment
Student Assessment methods
  • Written Assignment (Formative, Summative)
  • Written examination
Bibliography
Course Bibliography (Eudoxus)
1. Σ. Τραχανάς, Μερικές Διαφορικές Εξισώσεις. 2. Γ. Παντελίδης, Δ. Κραβαριτης, Εισαγωγή στις διαφορικές εξισώσεις μερικών παραγώγων
Additional bibliography for study
1. Σπανδάγος, Διαφορικές εξισώσεις με μερικές παραγώγους. 2. D. Betounes, Partial differential equations for computational science. 3. W. Stauss, Partial Differential equations.
Last Update
19-10-2022