Courses – Fakultet tehničkih nauka u Novom Sadu

Subject: Equations in Mathematical Physics (17.0M502)

Native organizations units: Department of Fundamentals Sciences

Type of studies	Title
Master Academic Studies	Mathematics in Engineering (Year: 1, Semester: Winter)

General information:

Category	Scientific-professional
Scientific or art field	Teorijska i primenjena matematika
ECTS	4

Enabling students to develop abstract thinking and acquire knowledge in the field of partial differential equations

To use the acquired knowledge in engineering subjects and in practice, to postulate and solve mathematical models in engineering subjects using the material covered in the course.

Theoretical part (lectures): Introduction (Cauchy–Kowalevska theorem) First order equations (linear and quasi linear equations-method of characteristics, Pfaffian equation, nonlinear equations-Lagrange-Sharpit method). Second order equations (classification, canonical forms, characteristic manifold for higher order equations) Cauchy problem for one dimensional wave equation – energy interval. Mixed problem for one dimensional wave equation. – Fourier method for separation of variables. Cauchy problem for heat conduction equation – maximum principle. Dirichlet and Neiman problem for Laplace’s equation – maximum principle. Numerical solution of PDE. Use of computer for solving PDE. Sobolev spaces. The notion of weak derivative. Weak solution for more dimensional wave equation. Mathematical physics equations. Schrodinger equation. Euler equation and Navier-Stokes equation.. Practice classes (placticals) During these classes the subject matter rom theory classes is supported by examples to provide futher practice and better understanding.

Lectures. Numerical and calculation practice. Consultations. Lectures are organized in combined form. The presentation of the theoretical part is followed by the corresponding examples which contribute to better understanding of the theoretical part. During the practice classes which follow the lectures, the subject matter is supported by charactristic examples to provide futher practice and better understanding In addition to lectures and practice classes there are regular consultations. There is a possibility of taking partial examinations which cover certain logical units during the course.

Authors	Title	Year	Publisher	Language
E. Sapiro,	Geometric Partial Differential Equations and Image Analysis,	2001	Cambridge University Press, Cambridge, New York,	English
Sobolev, S.L.	Partial Differential Equations of Mathematical Physics	1989	Dover Publications, Inc. New York	English
V.S. Vladimirov	Equations of Mathematical Physics	1980	Nauka	English
Rubinstein, Z.	A Course in Ordinary and Partial Differential Equations	1969	Academic Press, New York	English

Course activity	Pre-examination	Obligations	Number of points
Practical part of the exam - tasks	No	Yes	40.00
Theoretical part of the exam	No	Yes	30.00
Project defence	Yes	Yes	10.00
Lecture attendance	Yes	Yes	5.00
Exercise attendance	Yes	Yes	5.00
Term paper	Yes	Yes	10.00