Subject Datasheet

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Budapest University of Technology and Economics
Faculty of Transportation Engineering and Vehicle Engineering
1. Subject name Analitical Methots in System Technique I.
2. Subject name in Hungarian Analitikus módszerek a rendszertechnikában I.
3. Code BMEKOVJD001 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 15
Reading written materials 15 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  
14. Description of lectures
Sets. Basic number sets. Numerical sequences and numerical series. Convergency. Defining functions. Description of functions. Multivariate functions. Limit value, continuity and differentiability. Concept of Riemann-integral. Convergency concepts. Important function series: Taylor-series and Fourier-series. Basic numerical methods. Polynomial interpolations. Lagrange-interpolation, Hermite-interpolation and spline-interpolation. The method of least square. Numerical solution to algebraic equations. Method of intervallum-dividing. String-method. Section method. Tangent method. Successive approximation. Numerical integration. The Newton-Cotes procedure. The trapeze-rule. The Simpson-trule. Linear algebra and matrix calculus. Linear space. Linear sub-space. Linear independence. Generator-system. Basis. Scalar product. Ortogonality. Norma.Metric space. Matrices and vectors. Standard basis. Description of the elements of the linear space by using different bases. Homogeneous linear mappings and their matrices. Rang of matrices. Basis-dependence of the matrix of a linear mapping. Matrix product. Determinants. Inverse matrix. Linear set of equations. Condition of solvability based on the rang of the coefficient matrix. The Gaussean algorithm. Improvement of the accuracy. Iterative methods. The accelerating algorithm of Seidel. Treatment of contradictory (principally not solvable) set of equations.
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: examination procedures of single variate and multivariate functions; procedures for interpolation and numerical integration; methods of linear mapping; operations of matrix algebra; methods of solution to linear system of equations.
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)
Accepted homework sent before the deadline and written exam.
19. Opportunity for repeat/retake and delayed completion
According to the TVSZ.
20. Learning materials
1. Zobory, I.: Analitikus módszerek a rendszertechnikban I. Egyetemi jegyzet. BME Vasúti Járművek és Járműrendszeranalízis Tanszék. Budapest, 2011.
2. Rudin, W.: A matematikai analízis alapjai. Tipotex Kft., Budapest, 2010.
Effective date 27 November 2019 This Subject Datasheet is valid for Inactive courses