Meetkunde en Natuurkunde - 2007-2008

The RuG page with information on the course is here.

The grade for the course is determined only by the final exam.

Office hours: Fridays, 10:00-12:00.

Lesson 1 (15/11/2007)

Definition of derivatives for maps $f:R^n->R^m$ and their properties (sec. 1.3.1). Vector fields, velocity vectors, differential equations and curves (sec. 2.2.1).

Lesson 2 (16/11/2007)

Vector fields as derivations (sec. 2.2.1.2). The inverse and implicit function theorems (sec. 1.3.2).

Lesson 3 (22/11/2007)

Submanifolds of R^n (sec. 2.1).
Exercises on manifolds.

Lesson 4 (23/11/2007)

Tangent spaces (sec. 2.2.2).
Exercises on manifolds and tangent spaces.

Lesson 5 (29/11/2007)

Vector fields on manifolds (sec. 2.2.3). Dual spaces (sec. 1.2).
Exercises on vector fields.

Lesson 6 (30/11/2007)

Differential forms (sec 2.3.1.1). Closed and exact forms, and the Poincaré lemma (sec. 2.3.1.2).
Exercises on 1-forms.

Lesson 7 (06/12/2007)

Gradient (sec. 2.3.1.3). Transformation rules (sec. 2.3.1.4).
Exercises on 1-forms.

Lesson 8 (07/12/2007)

Integration of 1-forms (sec. 2.4.1).
Exercises on 1-forms.

Lesson 9 (13/12/2007)

Definition of k-forms (sec. 3.1.1). Interior product (def. 3.7 and prop. 3.8).
Exercises on k-forms.

Lesson 10 (14/12/2007)

Transformation of k-forms (sec. 3.1.3). Exterior derivation and Poincaré lemma (sec. 3.2.1-3.2.3). Definition of div and rot (sec. 3.2.4 without the examples).
Exercises on k-forms.

Lesson 11 (20/12/2007)

Integration of k-forms. Definition of k-cubes, k-chains and boundary (sec. 3.3.2 until proposition 3.24).

Lesson 12 (21/12/2007)

Proof of the Stokes theorem (the rest of sec. 3.3.2).
Exercises on k-chains and integration.

Lesson 13 (10/01/2008)

Green, Gauss, Stokes (sec. 4.2). Hamiltonian systems (sec. A.4.1, A.4.2.1). Definition of Lie derivatives (see the exercises).
Exercises on Hamiltonian systems.

Lesson 14 (11/01/2008)

Exercises.

17/01/2008

Canceled.

Lesson 15 (18/01/2008)

Exercises.

Lesson 16 (24/01/2008)

Exercises.