Partial Differential Equations I

Syllabus:

Regular class: Thursdays 13:30 to 15:15.

Recitation: Wednesdays 15:30 to 17:15.

Lecture rooms: Wednesdays F647, Thursdays Q105 (on Wed. Nov. 30 in F253).

Teaching assistents:

Hala Elrofai, email: elrofai@few.vu.nl
Vincent Guyonne, email: vincent@few.vu.nl

Office hours:

Tuesdays: 11:00-12:00 (Hala), room R319
Fridays: 11:00-12:00 (Vincent), room S240

Books:

Partial Differential Equations, an introduction, by P. DuChateau and D. Zachmann, Schaum's Outlines, ISBN 0-07-017897-6.
Fourier Series, by G.P. Tolstov, Dover, ISBN 0-486-63317-9.

Summaries:

Overview Fourier Theory (pdf), Fourier Theory (quicktime).

Assignments:

Assignment I: due Thursday October 13, pdf-file.
Assignment II: due Thursday November 17, pdf-file.
Assignment III: due Friday December 16, pdf-file.
Grades of all the assignments: xls-file.

Exams:

Midterm 1: Tuesday, October 25, 2005, 13:30 - 15:30, room t.b.a
Midterm 2/Final exam: Thursday December 22, 2005, 9:30 - 11:30/12:30, room t.b.a

Material for the final exam is listed below! Of the sections listed below only consider those subjects covered in class. The exam material also includes some subjects not contained in the book. The solved problems that are part of the material and are given in the weekly list!

Midterm 1:
- Chapter II: 2.1 and 2.3
- Chapter VI: 6.1 and 6.2
- Chapter VII: 7.2 (Solved problems 7.1, 7.9, 7.18)
- Tolstov Chapters III, Sec. 1, 3, 4, 5, 6, 7, 10, Chapters V, Sec. 7, 8
- Old exams: I, II.
Midterm 2:
- Chapter VI: 6.3 and 6.4 (Solved problems: 6.1 - 6.4)
- Chapter VII: 7.1, 7.2, 7.3 (Solved problems 7.10, 7.11, 7.13, 7.14, 7.15, 7.16)
- Chapter VIII: 8.1, 8.2, 8.3 (Sloved problems 8.1, 8.3, 8.4, 8.7, 8.8, 8.9, 8.10)
- Old exams: I, II, III
Final:
- Chapters II, VI, VII, VIII
- Material of both midterms 1 and 2
Homework assignments:
- Details to be announced.
Options:
- I: Assignments + midterm 1 + midterm 2 = final grade
- II: Assignments + final exam = final grade. In this case the material is everything covered under midterm 1 and midterm 2.

Material covered in the course:

Chapter I:

[7/9]: Read chapter I

Chapter II:

[7/9]-[8/9]: Sections 2.1, 2.3
Solved problems: 2.2, 2.3, 2.11, 2.12, 2.13, 2.15

Chapter VI:

[14/9]: Sections 6.1, 6.2
Solved problems: 6.1 - 6.4

[22/9]: Section 1, 3, 4, 5, 6, 7 in Tolstov Ch. 3

[29/9]: Section 10 in Tolstov Ch. 3

[6/10]: Section 7, 8 in Tolstov Ch. 5

Chapter VII:

[13/10]: Section 7.2
Solved problems: 7.1 and 7.4

[20/10 and 3/11]: Section 7.2
Solved problems: 7.9

[10/11]: Section 7.3
Solved problems: 7.10, 7.11, 7.13, 7.14, 7.15, 7.16

Chapter VIII:

[17/11]: Section 8.1

[24/11]: Section 8.2
Solved problems: 8.1

[1/12]: Section 8.3
Solved problems: 8.3, 8.4

8/12-15/12]: Section 8.1-8.3
Solved problems: 8.7, 8.8, 8.9, 8.10

Homework problems (supplementary problems):

Chapter II:

[15/9]: 2.19a,b,c, 2.23, 2.24, 2.26, 2.28b,c,d, 2.31, 2.33
(given in class): Solve u_x + u_y + u =0

Chapter VI:

[21/9]: 6.8, 6.10, 6.11, 6.12, 6.15

[28/9]: 6.9, and
Tolstov: Ch. 3; 1, 2, 5, 6, 7, 8

[5/10]: 6.16, 6.17
Tolstov: Ch. 3; 6, 7, 8
Schwarz inequality.

[12/10]: Tolstov: Ch. 5; 1, 2, 4, 7, 10

Chapter VII:

[19/10]: 7.27, 7.28, 7.30, 7.38

[2/11 and 9/11]: 7.35, 7.37, 7.39, 7.40, 7.41

[16/11]: 7.36, 7.24, 7.25, 7.26

Chapter VIII:

[23/11]: 9.3.5, 9.3.7, 9.3.8, 9.3.12 from the file Green's functions.

[30/11]: 9.3.6, 9.3.9, 9.3.11
8.19, 8.20, 8.21, 8.22

[7/12]: 8.23
Solved Problems: 8.4

[14/12]: 8.30, 8.37
Rieview, or 'Vragenuurtje'

Return to Robert VanderVorst's Home Page.