Subject Datasheet
Download PDFI. Subject Specification
1. Basic Data
1.1 Title
Functional Analysis
1.2 Code
BMEEOTMDT71
1.3 Type
Module with associated contact hours
1.4 Contact hours
| Type | Hours/week / (days) |
| Lecture | 2 |
1.5 Evaluation
Exam
1.6 Credits
3
1.7 Coordinator
| name | Kovács Flórián |
| academic rank | Associate professor |
| kovacs.florian@emk.bme.hu |
1.8 Department
Department of Structural Mechanics
1.9 Website
1.10 Language of instruction
english
1.11 Curriculum requirements
Ph.D.
1.12 Prerequisites
1.13 Effective date
1 September 2017
2. Objectives and learning outcomes
2.1 Objectives
The aim of the subject is to give mathematical formulation for concepts widely used in engineering, more specifically, in structural analysis: proving the existence and uniqueness of solutions to problems that are intuitively accepted in the procedure of the design.
2.2 Learning outcomes
Upon successful completion of this subject, the student:
A. Knowledge
- knows the definitions of some basic mathematical concepts (linear space, operator, norm, convergence, distribution, boundary value problem).
B. Skills
- is able to identify mathematical structures beyond engineering problems,
- is able to use the concepts of strong and weak solutions to a BVP in structural analysis,
- is able to consider mechanical problems in an abstract approach.
C. Attitudes
- aims at strict logical problem-solving.
D. Autonomy and Responsibility
- is able to individually think over boundary value problems.
2.3 Methods
1. Lectures with theoretical knowledge and computational examples
2.4 Course outline
| Hét | Előadások és gyakorlatok témaköre |
| 1. | Vector spaces, subspaces, linear manifolds |
| 2. | Dimension, spanning sets, and (algebraic) basis |
| 3. | Linear operator |
| 4. | Normed spaces |
| 5. | Convergence, complete spaces |
| 6. | Continuous and bounded linear operator |
| 7. | Dense sets, separable spaces |
| 8. | Inner product, Hilbert space |
| 9. | Sets of measure zero, measurable functions |
| 10. | The space L2 |
| 11. | Generalized derivatives, distributions, Sobolev spaces |
| 12. | Weak (or generalized) solutions |
| 13. | Orthogonal systems, Fourier series |
| 14. | The projection theorem, the best approximation |
The above programme is tentative and subject to changes due to calendar variations and other reasons specific to the actual semester. Consult the effective detailed course schedule of the course on the subject website.
2.5 Study materials
- Popper, Gy.: Some concepts of functional analysis using Mathematica.
- Lecture notes, BME (2006).
2.6 Other information
2.7 Consultation
The instructor is available for consultation during office hours. Special appointments can be requested via e-mail: kovacs.florian@emk.bme.hu
This Subject Datasheet is valid for:
Inactive courses
II. Subject requirements
Assessment and evaluation of the learning outcomes
3.1 General rules
3.2 Assessment methods
| Evaluation form | Abbreviation | Assessed learning outcomes |
| A.1; B.1-B.3; C.1; D.1 |
The dates of deadlines of assignments/homework can be found in the detailed course schedule on the subject’s website.
3.3 Evaluation system
| Jele | Részarány |
| Összesen | 100% |
3.4 Requirements and validity of signature
3.5 Grading system
| Érdemjegy | Pontszám (P) |
| jeles (5) | |
| jó (4) | |
| közepes (3) | |
| elégséges (2) | |
| elégtelen (1) |
3.6 Retake and repeat
3.7 Estimated workload
| Tevékenység | Óra/félév |
| Összesen |
3.8 Effective date
1 September 2017
This Subject Datasheet is valid for:
Inactive courses