## Subject Datasheet Budapest University of Technology and Economics Faculty of Transportation Engineering and Vehicle Engineering
 1. Subject name Mathematical methods I. 2. Subject name in Hungarian Matematikai módszerek I. 3. Code BMEKOKAD003 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 56 Preparation for seminars 20 Homework 10 Reading written materials 10 Midterm preparation 0 Exam preparation 24 10. Department Department of Control for Transportation and Vehicle Systems 11. Responsible lecturer Dr. Péter Tamás 12. Lecturers Dr. Péter Tamás 13. Prerequisites 14. Description of lectures Extreme value theorem.Regression analysis. The basic equation of regression. Ritz method. Regression surface. Multidimensional regression. Scalar vector function. Regression of vector-vector function. Complex function regression. Implicit function regression. Regression of a Parameter Assigned Function. Regression of the space curve Special Regression Procedures. Statistical linearization method. SISO and MIMO models. Harmonic linearization. Inverse linearization.Calculus of variations. Functional concept. Subject of the variation calculation. The "Brachisztochron problem". The Ritz method. The Lemma of variation calculation. The Euler-Lagrange equation. The variational method in mechanics.The equation of motion, in mathematical physics. The variation principle in mechanics. The Hamilton's principle. Applications for dynamic systems. Lagrange equations. Fermat's principle in geometrical optics.Theory of Linear Systems. Zadeh's definition of the system. Abstract objects. Equivalence of two or more objects. Convolution, convolution batch. Weight function batch, SISO and MIMO systems. Transmission matrix and weight function matrix..The Stochastic processes. Definition. Classification. Categories. The multivariate distribution. The Stationarity. Determining the expected value of the process and its autocorrelation function. The ergodic processes. Auto and cross correlation function Definition of auto and cross spectrum Properties. SISO and MIMO systems. The definition of spectral density. Definition and relationship of spectra. Calculation of spectral density. 15. Description of practices 16. Description of labortory practices 17. Learning outcomes A. Knowledge   B. Skills   C. Attitudes   D. Autonomy and Responsibility 18. Requirements, way to determine a grade (obtain a signature) The credits are obtained by completing the assignment and by passing the oral exam. 19. Opportunity for repeat/retake and delayed completion 20. Learning materials Effective date 27 November 2019 This Subject Datasheet is valid for 2023/2024 semester I