Partial Differential Equations and Applications (EM3)

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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.