## Subject Datasheet Budapest University of Technology and Economics Faculty of Transportation Engineering and Vehicle Engineering
 1. Subject name Analitical Methots in System Technique II. 2. Subject name in Hungarian Analitikus módszerek a rendszertechnikában II. 3. Code BMEKOVJD002 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. Zobory István 12. Lecturers Dr. Zobory István 13. Prerequisites recommended: BMEKOVJD001 - Analitical Methots in System Technique I. 14. Description of lectures Algebraic and trigonometric form of complex numbers. Euler-relation. Defining complex functions. The complex function as mapping. Differentiability of complex functions. The Caucy-Riemann differential equations. Integration of complex functions. Integral theorems. Integration along a given curve with respect to arclength. Harmonic functions. Elements of Laplace- and Fourier transform. The concept and classification of differential equations. The general initial value problem. The equivalent integral equation. The Picard-Lindelöf iteration. The Lipschitz condition. Tracing back higher order differential equations to a first order set of differential equations. Solution methods for treating linear differential equations. Application of Laplace transform for the solution of differential equations. Numerical solution to differential equations: The Euler-method, the Heun-method, the Runge-method and the Runge-Kutta method. Differential-equation systems. Solution to the homogeneous part of the linear differential equation via treating an eigenvalue-problem. Test function method for the solving inhomogeneous set of differential equations. The general solution and the particular solutions. Tracing back higher order differential equation systems to a first order linear differential equation system. Numerical solution to differential equation systems. Stability of the solution to differential equations and differential equation systems in the case of perturbing the initial values or the coefficients. Stability analysis for linear differential equations, the Hurwitz-criterion. Stability analysis for non-linear differential equations. The method of Ljapunov.. Construction of Lajapunov functions. The basic lemma of the variation calculus. The Euler-Lagrangean equation. Direct methods of the variation calculus. Euler-method based on broken lines. The Ritz-method. 15. Description of practices 16. Description of labortory practices 17. Learning outcomes A. Knowledge   B. Skills Students must know comprehensively, interpret in a constructive way and apply in his research activities in an innovative way the following elements of analysis methods: relationships in complex function theory; analytical and numerical solution methods to linear or non-linear differential equations and equation systems; methods of function variation theory. C. Attitudes   D. Autonomy and Responsibility Students must pursue to get knowledge of the new scientific results, the latter are 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 Zobory, I.: Analitikus módszerek a rendszertechnikban II. Egyetemi jegyzet. BME Vasúti Járművek és Járműrendszeranalízis Tanszék. Budapest, 2011.2. 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