Partial Differential Equations (AN6)

School	School of Science
Academic Unit	Department of Mathematics
Level of Studies	Graduate
Course Code	AN6
Semester	2
Course Title	Partial Differential Equations
Independent Teaching Activities	Lectures (Weekly Teaching Hours: 3, Credits: 7.5)
Course Type	General Background
Prerequisite Courses	Vector Analysis (undergraduate), Real Analysis, Functional Analysis
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	The course, apart from the instruction in the classical quartet of Partial Differential Equations (PDEs) (transport, Laplace, heat and wave) in several space variables, aims, first, to highlight the modern, analytic approach to the theory of PDEs and the reasons that suggest it, and, second, to provide an introduction to nonlinear PDEs, especially concerning first-order and hyperbolic equations. The skills and competences the students will acquire concern, on the one hand, the paradigmatic transition from the resolution of a problem to the theoretical analysis of its properties and the investigation of its structural foundation, and, on the other hand, the recognition of the essential difference between linear and nonlinear problems and the limitations of the method of approximation of a nonlinear problem by linear problems.
General Competences	Search for, analysis and synthesis of data and information Adapting to new situations Decision-making Working independently Working in an interdisciplinary environment Criticism and self-criticism Production of free, creative and inductive thinking

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