Subject Datasheet

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Budapest University of Technology and Economics
Faculty of Transportation Engineering and Vehicle Engineering
1. Subject name Functionalanalysis for Engineers
2. Subject name in Hungarian Funkcionálanalízis mérnököknek
3. Code BMEKOVJD018 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  
14. Description of lectures
Linear normed spaces, operators and functionals on linear spaces. Operations among operators. Metric spaces. The Baire-theorem. Semi-norm. Compactness. Continuity of linear operators. Contraction operators. Complementary concepts. The geometry of Hilbert-spaces. Complete ortonormal systems. The Gram-Schmidt ortogonalization. The projection theorem. The ortogonal complementer. Direct-sum of Hilbert spaces. The representation theorem of Frigyes Riesz. The dual space of a linear space. Unitary and izometric operators. Fourier transform, Fourier operator. The Hahn-Banach theorem. Application of functional analysis in the numerical methods. The Ritz-process.
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: theory of linear functionals and operators; application of the functional analysis in numerical methods.
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
1. Zobory I.: Funkcionálanalízis mérnököknek. Egyetemi jegyzet. Vasúti Járművek Tanszék, Budapest, 2007.
2. Máté László: Funkcionálanalízis műszakiaknak. Műszaki Könyvkiadó. Budapest, 1976.
3. Reddy, J.N.: Applied Functional Analysis and Variational Methods in Engineering. Krieger Publishing Company, Malabar, Florida, 1991.
4. Mikolás M.: Valós függvénytan és ortogonális sorok. Tankönykiadó, Budapest, 1978
Effective date 27 November 2019 This Subject Datasheet is valid for Inactive courses