# Theory

Goal:
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.

AMB&S chap 24 and 25.

Excercises:
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
L1: Differentiation rules. Numerical differentiation.
S1: More on linear systems of equations. Some related exercises
G1: Computing derivatives. Derivatives of products, composite functions etc. Partial derivatives. Some exercises on differentiation.
L2: Applications of derivatives. Newtons method. L'Hopsital rules.
S2: First part: Oral exam f(x)=0. Second part: Newtons method. Make your own implementation of Newtons method!
L3: More on Newton's method for systems. Review of an old final exam.
S3: First part: Oral exam f(x)=0. Second part: Newtons method for systems.
G2: Newtons method and L'Hopitals rules.

/Nils