Analysis and Linear Algebra K, Kf, Bt, part A, 2004

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

Theory

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,) 19.22ab

Matlab

Goal:
Write a program for the fixed point iteration.

Reading:

Activity plan:

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