Vector Calculus

Syllabus:

Regular class: Mondays 10:45 to 12:30, Thursdays 11:45 to 12:30

Recitation: Mondays 9:45 to 10:30 and Thursdays 9:45 to 11:30.

Teaching assistent: K. van Winden, email: winden@cs.vu.nl.

Book: J.E. Marsden and A.J. Tromba, Freeman & Co, 4th Ed.

Exam: to be announced.

Material covered in the course:

Functions of several variables.

Continuity and differentiability.

Integration: the theorems of Gauss, Green and Stokes.

Change of variables.

Hypersurfaces in R^n

Introduction to differential forms

Homework problems:

Chapter II:

Section 2.1 (3/2):
- 1a,c, 2a,c, 5, 10, 12, 16, 17
- 22, 25, 27, 32
Section 2.2 (3/2):
- 1b,d, 4, 5d, 6b,d
- 9, 12, 14, 15a, 16
Section 2.3 (10/2):
- 1b, 2b, 3b, 4b, 5, 6b, 8
- 11, 13, 14, 15, 16, 17, 20
Section 2.4 (13/2):
- 1, 3, 5, 7, 10, 12
- 13, 14, 15, 17
Section 2.5 (13/2):
- 1, 2, 4, 6, 9
- 13, 15
Section 2.5 (17/2):
- 18, 20, 24, 27

Chapter IV:

Section 4.1 (20/2):
- 1, 2, 5, 7, 10, 12, 13, 17, 20
Section 4.2 (20/2):
- 3, 6, 9, 12
Section 4.3 (26/2):
- 4, 5, 8, 10, 13, 15, 17, 20
Section 4.4 (26/2):
- 2, 7, 11, 14, 17, 22, 25, 26, 28, 30-32

Chapter VII:

Section 7.1 (3/3):
- 2b, 3b, 4a, 7, 10, 13
Section 7.2 (3/3):
- 1a, 2c, 4, 7, 11, 14
Section 7.3 (10/3):
- 3, 4, 7, 9a, 10b, 11a,b,c, 15a,b
Section 7.4 (10/3):
- 2, 5, 8, 10, 13
Section 7.5 (13/3):
- 3, 7, 8, 11
Section 7.6 (13/3):
- 1, 6, 8, 11, 14

Chapter VIII:

Section 8.1 (20/3):
- 2, 5, 11, 15
Section 8.2 (20/3):
- 5, 9, 14
Section 8.3 (20/3):
- 2, 3, 9, 18
Section 8.4 (20/3):
- 3, 4, 10, 11
Section 8.6 (3/3 and 20/3):
- 1, 2, 3, 4
- 6-11

Exam material (26/3/2003, 13:30-15:30):

Chapter II: Sect.'s 2.1 thru 2.6 (gradient and directional derivative)

Chapter IV: Sect.'s 4.1 thru 4.4

Chapter V: no homework of this section was assigned. In Sect.'s 5.1 thru 5.5 the notion of double and triple integrals is explained. The calculation of double and triple integral will be required for the exam.

Chpater VII: Sect.'s 7.1 thru 7.6

Chapter VIII: Sect.'s 8.1 thru 8.4 and Sect. 8.6!!! The main Theorem of Stokes is explained in Sect. 8.6. Using the theory of differential forms the special cases of Gauss, Green and Stokes are derived (Sect. 8.1 thru 8.4). Flux and applications to fluids can be skipped.

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