Difference between revisions of "NMMO302 Functional analysis for physicists"

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Link to SIS [https://is.cuni.cz/studium/eng/predmety/index.php?id=061695605b45da5bb3803e7550e4e8b2&tid=&do=predmet&kod=NMMO302&skr=2021&fak=11320]
 
Link to SIS [https://is.cuni.cz/studium/eng/predmety/index.php?id=061695605b45da5bb3803e7550e4e8b2&tid=&do=predmet&kod=NMMO302&skr=2021&fak=11320]
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== Syllabus and exams ==
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[[Media:NMMO302.pdf|Syllabus, general comments to the exam, literature]] SS 2021/2022 <!-- [[Media:NMMO302.pdf]] -->
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[[Media:NMMO302Zk-1.pdf|Sample exam]] <!-- [[Media:NMMO302Zk.pdf]] -->
  
 
== Lectures ==
 
== Lectures ==
  
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[[Media:LFA_1v1.pdf|Introduction]]  
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[[Media:LFA_1v1.pdf|1. Introduction.]]
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[[Media:LFA_2v1.pdf|2. Linear operators between Banach spaces; boundedness, examples and finite-dimensional vector spaces.]]
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[[Media:LFA_3v2.pdf|3. Seminorms and Frechet spaces. Hahn-Banach theorem.]]
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[[Media:LFA_4v2.pdf|4. Dual spaces. Reflexivity. Weak and weak-star convergences.]]
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[[Media:LFA_5v1.pdf|B. Baire's theorem.]]
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[[Media:LFA_6v2.pdf|5. Great theorems of LFA.]]
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[[Media:LFA_7v1.pdf|6. Adjoint operators. Compact operators.]]
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[[Media:LFA_8v2.pdf|7. Linear operators in Hilbert spaces. Riesz representation theorem.]]
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[[Media:LFA_9v2.pdf|8. Fredholm theory/Fredholm alternative.]]
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[[Media:LFA_10v1.pdf|9. Spectrum. An introduction to spectrum theory.]] [[Media:LFA_10bv1.pdf|9. Spectrum focusing on Hilbert spaces over complex scalars.]]
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[[Media:LFA_AAv2.pdf|A. Arzela-Ascoli theorem. (in czech)]]
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[[Media:LFA_Cv1.pdf|C. Bases in vector spaces.]]
  
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[[Media:LFA_2v1.pdf|Linear operators between Banach spaces; boundedness, examples and finite-dimensional vector spaces]]
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[[Media:LFA_Fv1.pdf|F. Abstract Fourier series. (in czech)]]
  
 
== Recordings ==
 
== Recordings ==
  
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[[Week 1 - ]] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_1.mp4 L1] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_2.mp4 L2] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_2.mp4 L3]
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Week 1 - [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_1.mp4 L1] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_2.mp4 L2] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_3.mp4 L3]
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Week 2 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_4.mp4 L4] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_5.mp4 L5]
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Week 3 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_6.mp4 L6] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_7.mp4 L7] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_8.mp4 L8]
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Week 4 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_9.mp4 L9] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_10.mp4 L10] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_11.mp4 L11]
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Week 6 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_12.mp4 L12] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_13.mp4 L13] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_14.mp4 L14]
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Week 7 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_15.mp4 L15]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_16.mp4 L16]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_17.mp4 L17]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_18.mp4 L18]
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Week 8 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_19.mp4 L19] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_20.mp4 L20] [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_21.mp4 L21]
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Week 9 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_22.mp4 L22] 
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Week 10 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_23.mp4 L23]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_24.mp4 L24]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_25.mp4 L25]
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Week 11 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_26.mp4 L28]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_27.mp4 L28]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_28.mp4 L28]
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Week 12 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_29.mp4 L30]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_31.mp4 L30]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_32.mp4 L31]
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Week 13 -  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_33.mp4 L33]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_34.mp4 L34]  [http://www.karlin.mff.cuni.cz/~malek/video/FAP/faph_35.mp4 L35]
  
 
== Problems ==
 
== Problems ==
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[[Media:P_1v1.pdf|Feb 25: Finite-dimensional vector spaces]]
 
  
 
== Homeworks ==
 
== Homeworks ==

Latest revision as of 16:41, 20 May 2022

Link to SIS[edit]

Link to SIS [1]

Syllabus and exams[edit]

Syllabus, general comments to the exam, literature SS 2021/2022

Sample exam

Lectures[edit]

1. Introduction.

2. Linear operators between Banach spaces; boundedness, examples and finite-dimensional vector spaces.

3. Seminorms and Frechet spaces. Hahn-Banach theorem.

4. Dual spaces. Reflexivity. Weak and weak-star convergences.

B. Baire's theorem.

5. Great theorems of LFA.

6. Adjoint operators. Compact operators.

7. Linear operators in Hilbert spaces. Riesz representation theorem.

8. Fredholm theory/Fredholm alternative.

9. Spectrum. An introduction to spectrum theory. 9. Spectrum focusing on Hilbert spaces over complex scalars.

A. Arzela-Ascoli theorem. (in czech)

C. Bases in vector spaces.

F. Abstract Fourier series. (in czech)

Recordings[edit]

Week 1 - L1 L2 L3

Week 2 - L4 L5

Week 3 - L6 L7 L8

Week 4 - L9 L10 L11

Week 6 - L12 L13 L14

Week 7 - L15 L16 L17 L18

Week 8 - L19 L20 L21

Week 9 - L22

Week 10 - L23 L24 L25

Week 11 - L28 L28 L28

Week 12 - L30 L30 L31

Week 13 - L33 L34 L35

Problems[edit]

Homeworks[edit]

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