## ALA-A, 2004, week 6

### Theory

Goal:
The definition of the derivative. To understand the different "rules of differentiation", for example for the power functions x^r, sums and products, and for composite and inverse functions. Further, to understand Newtons method, both for a scalar equation and systems of equations.

AMBS chap 23, 24 and 25.

Excercises:
23.1, 23.2, 23.6, 23.7
24.1, 24.2, 24.4 hint: use the fact that 2^(x+h)-2^x=2^x(2^h-1) (why?), 24.5.

### Matlab

Goal:
Understanding that computer arithmetic is not exact, and how this relates for example to computations of derivatives.
To learn how to use matlab to handle linear systems of equations.

Exercises:
25.3, 25.4, 25.5.

### Activity plan:

L=Lecture, S=Studio, G=Group work

Lecturer: Nils Svanstedt

L1: Chapter 23.

G1: Computing derivatives. Derivatives of products, composite functions etc. Partial derivatives. Some exercises on differentiation.

L2: Chapter 24.

L3: Chapter 25.

S3: Continue with A9. Linearization, Newtons Method

G2: Newtons method and L'Hopitals rules.

Matlab consultation: Thursday 17-19, room KD1, tutor: David Heintz.

/stig