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Partial Differential Equations and Applications (EM3): Διαφορά μεταξύ των αναθεωρήσεων

Partial Differential Equations and Applications (EM3): Διαφορά μεταξύ των αναθεωρήσεων

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Αναθεώρηση της 15:54, 10 Νοεμβρίου 2022

Graduate Courses Outlines - Department of Mathematics

General

School School of Science
Academic Unit Department of Mathematics
Level of Studies Graduate
Course Code EM3
Semester 1
Course Title

Partial Differential Equations and Applications

Independent Teaching Activities Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type Special Background
Prerequisite Courses -
Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students Yes (in English)
Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The student in this course will apply the mathematical tools obtained from previous courses to better understand concepts arising from natural (and not only) phenomena and the way these are transformed into mathematical problems. More specifically, by completing this course, students should be able to

  • use the method of characteristics to solve partial differential equations
  • classify partial differential equations of second order in elliptic, parabolic and hyperbolic type
  • use Green’s functions to solve elliptic type equations
  • have a basic understanding of diffusion equations
  • use separation of variables to solve linear partial differential equations
General Competences
  • Adapting to new situations
  • Decision-making
  • Working independently
  • Team work

Syllabus

Basic concepts. Linear, quasi-linear and semi-linear equations of the first order. The Cauchy problem and its solution by the method of characteristic. Linear equations of 2nd order: classification (hyperbolic, parabolic, elliptic), examples (wave equation, heat equation, Laplace equation). Problems of initial and boundary values for the wave and heat equations. Boundary value problems and the Laplace equation. The Cauchy problem for the wave and heat equations.

Teaching and Learning Methods - Evaluation

Delivery

In class

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Self study 78
Homework - Projects 70.5
Course total 187.5
Student Performance Evaluation
  • Weekly assignments
  • Final project

Attached Bibliography

  • Fluid Mechanics with Applications, M. Xenos and E. Tzirtzilakis, 2018 (in Greek)
  • Fluid Mechanics, Volume 1, A. Papaioanou, 2nd Edition, 2001 (in Greek).
  • Computational Fluid Mechanics, I. Soulis, 1st Edition, 2008 (in Greek).
  • Numerical heat transfer and fluid flow, S.V. Patankar, McGraw-Hill, New York, 1980.
  • The Finite Element Method, Vol. 1, The Basis, O.C. Zienkiewicz, R.L. Taylor, 5th Ed., Butterworth-Heinemann, Oxford, 2000.
  • Computational Techniques for fluid Dynamics, C.A.J. Fletcher Volumes I and II, 2nd Ed. Springer-Verlag, Berlin, 1991.
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