Functional- and Fourieranalysis (5530)
  
Coordinating lecturer :Prof. dr. Jochen SCHÜTZ 
  
Member of the teaching team :De heer Arjun THENERY MANIKANTAN 
 De heer George SCRIVEN 

Language of instruction : English
Credits: 5,0
  
Period: semester 2 (5sp)
  
2nd Chance Exam1: Yes
  
Final grade2: Numerical
 
Sequentiality
 
   Advising sequentiality bound on the level of programme components
 
 
  Following programme components are advised to also be included in your study programme up till now.
    Analysis 2 (3190) 5.0 stptn
    Linear algebra (3983) .0 stptn
 

Prerequisites

The student knows the following topics from Calculus 1.2, Analysis and Linear Algebra. Items marked with * are repeated briefly

-- Complex numbers

-- Normed vector spaces*, linear maps between vector spaces*

-- Lebesgue Integration, Beppo-Levi Theorem*

-- Cauchy Sequence*, Continuity*

-- Orthogonality and projections*


Content
  • Infinite-dimensional normed spaces, completeness, Banach and Hilbert spaces, projections
  • Fourier series for periodic functions, Parseval, L^2-convergence, Bessel
  • Discrete Fourier transformation, convergence, aliasing, FFT
  • Linear operators on Banach spaces, boundedness, Banach-Steinhauss, Dual spaces, Riesz
  • Fourier transform, Plancherel, inverse Fourier transform, Shannon's sampling theorem


Organisational and teaching methods
Organisational methods  
Lecture ✔  
Response lecture ✔  


Evaluation

Semester 2 (5,00sp)

Evaluation method
Written evaluation during teaching period10 %
Homework✔
Written exam90 %

Second examination period

Evaluation second examination opportunity different from first examination opprt
No
Explanation (English)100% oral exam.
 

Recommended reading
 

Wavelets: A primer,Christian Blatter,Springer,9781568811956

A first course in Fourier Analysis,David W. Kammler,Cambridge,9780521709798,Available as e-book: https://ebookcentral.proquest .com/lib/ubhasselt/detail.action?docID=328964 


Learning outcomes
Bachelor of Mathematics
  •  EC 

    • EC 1: A graduate of the Bachelor of Mathematics programme has a thorough basic knowledge and insight in various disciplines of Mathematics including algebra, geometry, analysis, numerical mathematics, probability theory, statistics, aspects of discrete mathematics and logic.

     
  •  DC 

    • 1.3: A graduate of the Bachelor of Mathematics programme has a thorough basic knowledge and understanding of analysis

     
  •  DC 

    • 1.4: A graduate of the Bachelor of Mathematics programme has a thorough basic knowledge and understanding of numerical mathematics

  •  EC 

    • EC 5: A graduate of the Bachelor of Mathematics programme can apply the theories and methods to relatively simple mathematical problems (theoretical as well as computational). He/she can make and write down a mathematical line of reasoning by him/herself.

     
  •  DC 

    • 5.1: A graduate of the Bachelor of Mathematics programme can apply computational methods (e.g., integration, derivation of functions, variation of parameters, hypothesis testing, etc.) to solve simple mathematical problems

     
  •  DC 

    • 5.2: A graduate of the Bachelor of Mathematics programme can apply mathematical theories to analyze simple mathematical problems

  •  EC 

    • EC 6: A graduate of the Bachelor of Mathematics programme is able to integrate the acquired knowledge in new mathematical topics.  He/she understands the connection between subjects. 

     
  •  DC 

    • 6.1: A graduate of the Bachelor of Mathematics programme can recognize common mathematical and logical principles in various mathematical subfields

     
  •  DC 

    • 6.2: A graduate of the Bachelor of Mathematics programme can take a bird''s eye view of various mathematical topics and subfields

     
  •  DC 

    • 6.3: A graduate of the Bachelor of Mathematics programme understands the relationship between various topics

  •  EC 

    • EC 10: A graduate of the Bachelor of Mathematics programme has knowledge of a number of applications of mathematics.

     
  •  DC 

    • 10.1: A graduate of the Bachelor of Mathematics programme has knowledge of applications from the natural sciences

 
Bachelor of Physics
  •  EC 

    • EC 7: A graduate of the Bachelor of Physics programme is able to apply the mathematical methods which are used in physics and possesses good numerical skills, including computational techniques and programming skills.

 
  EC = learning outcomes      DC = partial outcomes      BC = evaluation criteria  
Offered inTolerance3
2de bachelorjaar in de fysica twin selectie keuze J
2nd year Bachelor of Mathematics J
Exchange Programme Mathematics J
Exchange Programme Physics J



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