Matematiska vetenskaper, Chalmers Tekniska Högskola och Göteborgs Universitet

### ALA-A, week 3, 2005

[home, week 1, week 2, week 3, week 4, week 5, week 6, week 7]

### Theory

Goal: Understand the definition of xr, and the concepts fixed point, fixed point iteration, and contraction mapping. Understand the the idea of coupled systems of equations.

AMBS 15, 16, 18, 19
Minimum reading: 15.1-15.8; 16.1; 18.1-18.5; 19.1,2,3,4,6,7,8,9

### Matlab

Reading: Matematik med Matlab - en handledning: Section 3.

Excercises:

### Teaching

Lecture 3.1: AMBS 15

Studio 3.1: The Bisection Algorithm

Exercise 3.1:
David's solutions - week 3.
Demo: 15.2b, 15.6, 15.11c, 15.12, 15.15b,
Basic: 15.2, 15.3, 15.5, 15.11, 15.14, 15.15, 15.16, 15.18, 15.19, 15.23, 15.24

Lecture 3.2: AMBS 16, 18, 19 lecture notes.

Studio 3.2: The Bisection Algorithm (again)

Exercise 3.2:
Demo: 18.1c, 18.3c, 19.3a, 19.4a, 19.19a
Basic: 18.1, 18.3abd but simplify the problem by considering 1/(2+x^2) instead of 1/(1+x^2),
19.1, 19.2a, 19.3b, 19.4, 19.10, 19.11, 19.12, 19.13, 19.14, 19.18 but simplify the problem by considering g(x)=x^2/(10-x) with L=21/81 on [-1 1] instead of g(x)=x^4/(10-x)^2,
19.21a, 19.22