Numerical Functional Analysis (7.5hp)
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|Lecture||Date||Time||Place||Hand in/Prepare||Key concepts|
|L1||19XXYY||XX--YY||NNNN||Read Chap. 1 (Metric spaces)||Continuity, Separability, Convergence|
|L2||19XXYY||XX--YY||NNNN||Inlupp #1, Read Chap. 2 (Banach spaces)||Completion, Compactness, Bounded linear operators|
|L3||19XXYY||XX--YY||NNNN||Inlupp #2, Read Chap. 3 (Hilbert spaces)||Orthogonal and Riesz's representations, Adjoints|
|L4||19XXYY||XX--YY||NNNN||Inlupp #3, Read Chap. 4+5+6 (Theorems and Applications), group presentations||"Big" Theorems and Applications|
|L5||119XXYY||XX--YY||NNNN||Group presentations||"Big" Theorems and Applications|
|-||19XXYY||Draft mini-essay (2--6 pages) ready/sent to 2 referees (With CC to Stefan Engblom|
|-||19XXYY||2 reviews (1/2--1 A4-page), sent to 2 authors (With CC to Stefan Engblom)|
|-||19XXYY||Final version of mini-essay ready|
Tips: room 2345 means "house 2, floor 3, room (23)45".
About the written mandatory assignments: Work together if you like, but hand in your own solutions. Practise a formal style, clarity, and non-ambiguous constructs. Hand in your solutions (on paper) no later than at the communicated deadline. If you cannot make it I prefer that you hand in whatever material you have at that occasion, let me correct it, and then hand in a final version at a later occasion. Note: hand-written solutions are NOT accepted.
Prepare the lectures thoroughly by reading what has been indicated, and by attempting the exercises. Bring sketches of your own solutions and be prepared to discuss and explain them to others. Your active participation is of vital importance for the quality of each meeting. Please read these instructions once more. Thanks!
Before the meeting: Read Chap. 1 and try to solve the exercises (finishing about half of them before class should be reasonable). It is recommended to try as many exercises as you can. The following is a selection which connects in various ways to Numerical Analysis (all from Chap. 1):
- 1.1.6, 1.1.7, 1.1.8, 1.1.9
- 1.2.4, 1.2.5, 1.2.11, 1.2.13, 1.2.14, 1.2.15
- 1.3.3, 1.3.8, 1.3.12
- 1.4.2, 1.4.8
- 1.5.6, 1.5.8, 1.5.9, 1.5.15
- 1.6.6, 1.6.13, 1.6.14
Written assignment: hand in solutions to at least one of the exercises in boldface in each group of the list (= each section of Chap. 1). The minimum total is thus 6 exercises. Hand in your solutions at the second meeting.
This course is an introduction to Functional Analysis with a particular emphasis on constructs and results that connect in various ways to Numerical Analysis. Hence the name Numerical Functional Analysis!
- Reading course with 5 lectures in the form of theory expositions and discussions
- 3 written assignments and 1 group presentation
- 1 a bit more "in-depth" written assignment, (come up with your own suggestion if you like), written and corrected/criticized by others (you write one, and you give feedback to 2 other)
This is the second time this course is given. Your continuous feedback will be very much appreciated. Thank you!
Book: Kreyzig, Introductory functional analysis with applications.
Contents: metric, normed, and inner product spaces, completeness,
Banach/Hilbert spaces, bases, strong/weak convergence, open mapping
theorem, Banach fixed point theorem, formal error analysis, stability, (...)
Responsible: Stefan Engblom