**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.

**Reading:**

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.

**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.

25.3, 25.4, 25.5.

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

Last modified: Tue Aug 15 15:18:36 MET DST 2000