Numerical Analysis with applications in Ordinary and Partial Differential Equations

Course Information
TitleΑΡΙΘΜΗΤΙΚΕΣ ΜΕΘΟΔΟΙ ΜΕ ΕΦΑΡΜΟΓΕΣ ΣΤΗΝ ΕΠΙΛΥΣΗ ΚΑΝΟΝΙΚΩΝ (ΣΥΝΗΘΩΝ) ΚΑΙ ΜΕΡΙΚΩΝ ΔΙΑΦΟΡΙΚΩΝ ΕΞΙΣΩΣΕΩΝ / Numerical Analysis with applications in Ordinary and Partial Differential Equations
Code0853
FacultySciences
SchoolMathematics
Cycle / Level2nd / Postgraduate
Teaching PeriodWinter
CommonYes
StatusActive
Course ID40002464

Programme of Study: PMS Tmīmatos Mathīmatikṓn (2018-sīmera)

Registered students: 12
OrientationAttendance TypeSemesterYearECTS
THEŌRĪTIKĪ PLĪROFORIKĪ KAI THEŌRIA SYSTĪMATŌN KAI ELEGCΗOUCore Courses A11110
Class Information
Academic Year2022 – 2023
Class PeriodWinter
Faculty Instructors
Weekly Hours3
Class ID
600223541
Course Type 2021
General Foundation
Course Type 2016-2020
  • Background
Course Type 2011-2015
General Foundation
Mode of Delivery
  • Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
  • English (Instruction, Examination)
Prerequisites
General Prerequisites
Fundamental numerical and mathematical analysis and a programming language knowledge.
Learning Outcomes
Upon successful completion of the course, students should understand initial value problems and be able to analyze and solve differential equations as well as systems of linear differential equations. Understand the role of continuous problem stability, order of accuracy and various stability properties of numerical methods for initial value problems. Know the basic numerical methods for initial value problems, as well as their advantages and disadvantages. To be able to implement the aforementioned methods on the computer.
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Adapt to new situations
  • Work autonomously
  • Work in teams
  • Work in an interdisciplinary team
Course Content (Syllabus)
Initial-value and boundary-value problems. Numerical methods for solving ordinary differential equations with initial conditions and/or boundary conditions. Linear and non-linear Shooting methods. Linear and non-linear finite difference methods. Calculus of variations techniques. Introduction to finite element method. Finite element methods for elliptic, parabolic, and hyperbolic problems.
Keywords
Numerical Analysis, Numerical Analysis for Partial Defferential Equations.
Educational Material Types
  • Slide presentations
  • Book
Use of Information and Communication Technologies
Use of ICT
  • Use of ICT in Course Teaching
  • Use of ICT in Laboratory Teaching
  • Use of ICT in Communication with Students
Description
Slides projector, computer.
Course Organization
ActivitiesWorkloadECTSIndividualTeamworkErasmus
Lectures752.5
Seminars250.8
Laboratory Work501.7
Reading Assigment1505
Total30010
Student Assessment
Description
Αssignment, presentation of assignment, written exams.
Student Assessment methods
  • Written Exam with Short Answer Questions (Formative)
  • Written Exam with Extended Answer Questions (Formative)
  • Written Assignment (Formative)
  • Oral Exams (Summative)
  • Performance / Staging (Summative)
  • Written Exam with Problem Solving (Formative)
  • Report (Summative)
Bibliography
Course Bibliography (Eudoxus)
-Αριθμητικές Μέθοδοι για Συνήθεις Διαφορικές Εξισώσεις, Γ. Δ. Ακρίβη και Β. Α. Δουγαλή, Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, δεύτερη έκδοση, 2013. -Αριθμητική Ανάλυση: Συνήθεις Διαφορικές Εξισώσεις, Μ. Ν. Βραχάτη, Εκδόσεις Κλειδάριθμος, Αθήνα, 2012.
Additional bibliography for study
-Numerical Python book by Johansson: https://link.springer.com/book/10.1007%2F978-1-4842-0553-2 -The Finite Element Method: Theory, Implementation, and Applications: book by Larson-Bengzon: https://link.springer.com/book/10.1007%2F978-3-642-33287-6 -Pro Git book by Chacon/Straub:https://git-scm.com/book/en/v2
Last Update
24-05-2023