## Subject Datasheet Budapest University of Technology and Economics Faculty of Transportation Engineering and Vehicle Engineering
 1. Subject name Analitical Methots in System Technique III. 2. Subject name in Hungarian Analitikus módszerek a rendszertechnikában III. 3. Code BMEKOVJD003 4. Evaluation type exam grade 5. Credits 4 6. Weekly contact hours 2 (0) Lecture 0 (0) Practice 0 (0) Lab 7. Curriculum PhD Programme 8. Role Basic course 9. Working hours for fulfilling the requirements of the subject 120 Contact hours 28 Preparation for seminars 30 Homework 0 Reading written materials 30 Midterm preparation 0 Exam preparation 32 10. Department Department of Aeronautics and Naval Architectures 11. Responsible lecturer Dr. Zoller Vilmos 12. Lecturers Dr. Zoller Vilmos 13. Prerequisites recommended: BMEKOVJD001 - Analitical Methots in System Technique I.recommended: BMEKOVJD002 - Analitical Methots in System Technique II. 14. Description of lectures In the main part linear partial differential equations. First order equations. The solution as an integral-manifold. Homogeneous and non-homogeneous equations. Characteristic curve, characteristic equation. First order partial differential equations. Constant coefficient linear partial differential operator with complex coefficients. The Cauchy-Riemann operator. In the main part linear second order partial differential equations. Classification. Constant coefficient second order partial differential equations. Hyperbolic type equations. The wave operator. Parabolic type equations. Thermal operator. Schrödinger operator. Fourth order operators: Euler-Bernoulli, Rayleigh and Timoshenko beam operators. Elliptic type equations. Initial value and Boundary value problems. The Fourier method. Basic concepts of topology. Generalisation of the metric space, the topologic space. Local convexity. The space of basic functions. Distributions. Direct product. Convolution. Fourier transform of distributions. Basic solutions. Linear differential operator of constant coefficient. First order case. The wave operator. Klein-Gordon equation. Basic solution to the wave-equation. Basic solution for the thermal operator. Basic solution for the Cauchy-Riemann operator. Basic solution for the Laplace operator, connection with the Poisson equation. Basic solution for the Helmholtz operator 15. Description of practices 16. Description of labortory practices 17. Learning outcomes A. Knowledge   B. Skills Students must know comprehensively, interpret in a constructive ay and apply in his research activities in an innovative way the following elements of analysis methods: solution methods of partial differential equations; procedures of topology and distribution theory; application methods of Laplace transformation and Fourier operator. C. Attitudes   D. Autonomy and Responsibility Students must pursue to get knowledge of the new scientific results, the latter is applied with responsibility and initiates new resource activities in new fields of knowledge in an innovative way. 18. Requirements, way to determine a grade (obtain a signature) Regular participation at the lectures and written exam. 19. Opportunity for repeat/retake and delayed completion According to the TVSZ. 20. Learning materials 1. Zoller, V.: Analitikus módszerek a rendszertechnikban III. Kézirat. BME Vasúti Járművek és Járműrendszeranalízis Tanszék. Budapest, 2013.2. Brown, F.T.: Engineering System Dynamics. Taylor & Francis, Boca Raton, London, New-York, 2007 Effective date 27 November 2019 This Subject Datasheet is valid for Inactive courses