Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Partial differential equations (17.D0M02L)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Summer)
Doctoral Academic Studies	Mathematics in Engineering (Godina: 1, Summer)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
Interdisciplinary	Yes
ECTS	10

Educational goal:

To enable students to think abstractly and acquire knowledge in partial differential equations.

Educational outcome:

Acquired knowledge utilized in professional subjects and practical work and designing and solving mathematical models in professional subjects using acquired knowledge in partial differential equations.

Course content:

Theoretical classes (lectures): Introduction. First and second order PDE. Mathematical physics equations (Schrodinger equation. Euler equation and Navier-Stokes equation.). Numerical solution of PDE (Finite differences. Finite element method). Sobolev spaces (The notion of weak derivative. Weak solution for more dimensional wave equation.). Nonlinear PDE (Steady-state problems. Evolution problems). Research and study work includes active following of primary scientific sources, organization and conducting experiments and statistical data processing, numeric simulation, possible writing of scientific paper in the field of mathematics.

Teaching methods:

Lectures. Consultations. Lectures are realized by combining theory and practice. Theoretical part is followed by appropriate examples which lead to clarification of the theoretical part. Apart from lectures and practical classes, consultations are held regularly. Part of subject content, which represents a logical unity, can be taken as a part of the exam during the teaching process. During lectures (through project work) it is necessary to prove elementary knowledge of at least one program packages (Maple, Matlab. Mathematica) needed for sloving PDE. Part of subject content as agreed upon and which makes unity is can be taken orally as a presentation and submitted in written form as a seminar paper. Oral part of the final exam is eliminatory. Through research and study work, student studies scientific journals and other relevant literature and individually expands subject content covered in classes. In cooperation with professor, student is enabled for independent writing of scientific paper.

Literature:

Authors	Title	Year	Publisher	Language
Roubiček, T.	Nonlinear Partial Differential Equations with Applications	2005	Birkhauser Verlag, Basel	English
Sobolev, S.L.	Partial Differential Equations of Mathematical Physics	1989	Dover Publications, Inc. New York	English
E. Sapiro	Geometric Partial Differential Equations and Image Analysis	2001	Cambridge University Press, Cambridge, New York	English
T. Dauxois, M. Peyrard,	Physics of Solitons	2006	Cambridge University Press,Cambridge, New York,	English
V.S. Vladimirov	Equations of Mathematical Physics	1980	Nauka	English
G. Evans, J. Blackledge, P. Yardley,	Numerical Methods for Partial Differential Equations	2000	Springer, Berlin, Heidelberg, New York,	English
Dodd, R.K. et al.	Solitons and Nonlinear Wave Equations	1984	Academic Press, London	English