## Computer sessions

The following computer sessions are part of the Body and Soul educational program. This material is not to be used in courses not using the books.

Students can work in pairs with the computer sessions and each of the sessions should take about two hours to complete. Each session contains some theoretical background that students should be familiar with before the session starts, together with a couple of basic questions that should be answered.

Within each session are presented a number of problems that the students should solve during the session. Each session also contains hints on how to solve the problems, and full answers to all problems.

Sessions with a star (*) are not completed, in some cases older material is provided instead.

### A: Programming

A1. Matlab Programming: Expressions, Functions, Conditionals and Loops

A2. C++ programming *

### B: Calculus Tools

B1. Linear and Polynomial Functions

B2. 3D Geometry

B3. Divergence, Rotation, Laplace *

B4. Multiple Integrals *

B5. Gauss, Green, Stokes *

### C: Solving Ax = b

C1. Vectors and Matrices

C2. Linear Systems

C3. Gaussian Elimination

### D: Solving f(x) = 0

D1. The Bisection Algorithm

D2. The Fixed Point Iteration Algorithm

D3. Linearization, Newton's Method

### E: Solving u'(t) = f(t, u(t)) (ODE)

E7. Adaptive dG0 with Newton iterations

E8. Adaptive dG0 using duality.

E9. f(u) = 0 (Newton's Method for systems)

### F: Solving u' = f(u) (PDE)

F1. Back to Poisson

F2. The heat equation

F3. Convection-diffusion

F4. Reaction-diffusion

F5. Systems of convection-diffusion-reaction equations

F6. Incompressible Navier-Stokes *

F7. Elasticity *

F8. Electromagnetics *