Partial Differential Equations (Master, Spring 2012)
Syllabus:
Regular class: Tuesday 14:00 - 16:45 (VU)
Lecture rooms:
- week 6-12: Mathematics building, room P647
- week 13: Mathematics building, room C121
- week 14-21: Mathematics building, room P647
Teaching assistent:
Simone Munao, email: smunao@few.vu.nl
May 22 class cancelled!!! Exam is online!!!
Book:
Partial Differential Equations, L.C. Evans, AMS, ISBN 0-8218-0772-2.
Notes on distributions (Renardy and Rogers).
Notes on finite ranks operators and compactness (Gohberg and Goldberg).
Notes on higher-order equations (Renardy and Rogers).
Notes on regularity estimate.
Notes on Hille-Yosida (Brezis).
Exams: Two midterms exams (take home)
- Take home exam 1: March 27, due April 10
- Take home exam 2: May 22
Material covered in the course (tentative):
February 7:
- Chapter I, Sect's 1.1 - 1.4, pages 1 - 13.
- Chapter II, Sect. 2.1, 2.2 (2.2.1), pages 14 - 25.
February 14:
- Notes on Green's identities and Green's functions.
- Notes on symbols and fundamental solutions.
February 21:
- Chapter V, Sect. 5.1- 5.2 (5.2.2).
February 28:
- Chapter V, Sect. 5.2 - 5.7.
March 6:
- Chapter VI, Sect. 6.1 - 6.2.
March 13:
- The Fredholm alternative.
- Recitation.
March 20:
- Symbols.
- Higher order elliptic equations, see Renardy & Rogers.
March 27:
- Boundary conditions.
- Chapter VI, Sect. 6.3.
April 3:
- Chapter VI, Sect. 6.3 (6.3.1) pages 313 - 3.16, read Sect. 6.3 (6.3.2) pages 316 - 326.
April 10:
- Chapter VII, Sect. 7.4 (7.4.1), pages 413 - 415.
April 17:
- Chapter VII, Sect. 7.4 (7.4.1), pages 416 - 418.
April 24:
- Chapter VII, Sect. 7.4 (7.4.2), pages 418 - 420.
May 1:
- Chapter VII, Sect. 7.4 (7.4.3), pages 420 - 422.
April 8:
- Chapter VII, Sect. 7.4 (7.4.3), pages 423 - 424, Hille-Yosida on Hilbert spaces (notes).
Return
to Robert VanderVorst's Home Page.