**Goal:**

Understand the definition of *x ^{r}*, and the concepts fixed point, fixed point iteration, and contraction mapping. Understand the the idea of coupled systems of equations.

Understand elementary vector algebra, including scaling, addition, scalar multiplication and projection of vectors.

**Reading:**

AMBS chapt. 18, 19, 20.

Minimum reading: 18.1-18.5; 19.1,2,3,4,6,7,8,9; 20.4-22;
lecture notes (linear algebra, intro)
postscript
pdf.

**Exercises:**

**18.1**, **18.3abd** but simplify 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**, 19.16, (19.17,)

**19.18** but simplify
by considering g(x)=x^2/(10-x) with L=21/81 on [-1 1] instead of g(x)=x^4/(10-x)^2,

(19.19, 19.21,) **19.22a**b

**Goal:**

Write a program for the fixed point iteration.

**Reading:**

Lecturer: Mats Larson

L1: The power function *x ^{r}*. Fixed point
iteration. Chapt 18, 19.

S1: Extra Matlab Programming Session (including review of diagnostic test).

G1: Solve problems from the book.

L2: Linear algebra. Chapt 20.1-22.

S2: The Fixed Point Iteration Algorithm

G2: Continue working on the problems in the book.

`/stig`