Calendar

Topics:

1- scalar fields

2- position vector

3- gradient

4- potential

Download the slides here

Download the introduction slides here

Exercises on gradient, directional derivative, parameterization of curves.

You can download the slides here

Topics of this week:

• Line integrals (linjeintegralen)
• Conservative vector fields and circulation (konservativt vektorfältet och cirkulationen)
• Flux integrals (Flödesintegralen och Ytintegralen)

Download the slides here

Exercises on line integrals, potential, flux integral

You can download the slides here

Topics of this week:

• divergence (divergensen)
• Gauss' theorem
• curl (rotationen)
• Stokes' theorem
• The Green formula in the plane
• curl free field (virvelfria fält) and scalar potential
• solenoidal field (solenoidalt eller källfritt) and vector potential

You can download the slide here.

You can download the exercises and some slides about the cylindrical and spherical coordinates here

Topics of this week:

• curvilinear coordinate systems (kroklinjiga koordinatsystem)
• cylindrical coordinates
• spherical coordinates
• gradient, divergence and curl in a curvilinear coordinate system
• Laplace's equation and its solution assuming spherical symmetry.

You can download the slides here.

Formulas for curvilinear coordinates: here

You can download some exercises here

Download some exercises (with no solution) here.

Topics of this week:

• Nablaoperatorer
• Nablaräkning
• Integralsatser
• Kartesiska tensorer
• Indexräkning

You can download the slides here.

You can download some exercises here.

Download some exercises (with no solution) here

Topics of this week:

1. Some special vector fields:
   • Point source and the Gauss' law
   • The dipole
   • Vortex source and the Stoke's law
2. Laplace's and Poisson's eqautions:
   • Solution of Laplace's equation for planar, cylindrical and spherical symmetry
   • Dirichlet boundary conditions and the uniqueness theorem
   • Neumann's boundary conditions

Download the slides here.

Download some exercises with the solutions here.

Download some exercises here (with no solution).

The exam starts at 9.00am sharp.

Please, arrive some minuts earlier.

• Room L21: GROUP A
• Room L22: GROUP B
• Room L41: GROUP C
• Room L42: Four students from each group will sit in room L42. These students will be randomly selected by the teachers.

At the exam, students can use:

•  the BETA book,
•  the vector algebra formulas  (the sheet handed out in class).
•  the curvilinear coordinate formulas (the sheet handed out in class).

Nothing else is allowed.