Computer sessions

The following computer sessions are part of the Body and Soul educational program. The sessions are a natural part of any course following the Body and Soul educational program.

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
C4. Linear Algebra in R^n

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)

E1. The Integral
E2. How small is the error?
E3. The Exponential Function
E4. Sin and Cos
E5. My ODE Solver Part I
E6. My ODE Solver Part II
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 *