**Goal:**

Understanding vectors and fundamental vector and matrix algebra, including
projections, rotations, reflections etc. Further, linear systems of equations
and a first taste of the important concepts linear dependence/independence
of vectors, and basis.
Understanding the fundamentals of complex numbers and their
arithmetic, and the basic fact that any n'th degree polynomial equation has
exactly n roots.

**Reading:**

AMB&S chap. 20 (Analytic geometri in R2) and 22 (Complex numbers)

**Exercises:**

20.1, **20.3**, 20.4, 20.5, **20.6**, 20.7, **20.8**, **20.9**, **20.10** (note misprint:
..a onto b onto (1,2) with.. should read ..b=(1,2) onto a with..), **20.11**,
20.12 (see 20.13), **20.14**,
20.15, 20.16, 20.17, **20.18**, 20.19, **20.20**, 20.21, **20.22**, 20.25, 20.26, 20.27. Consider bold **first**, then the rest!

**22.1, 22.2, 22.3**, 22.4, **22.5, 22.6abc**d, **22.7, 22.8,
22.9, 22.10a**bc

**Project:**

Project f(x)=0 , including
modeling, solver implementation, application to model equations,
analysis and conclusions, presentation.

Wamlings equations

Öhrströms equations

Example report

**Goal:**

Getting more familiar with the matlab syntax for vectors (lists) and matrices,
and how to use matlab as an elementary vector and matrix calculator,
including solving linear systems of equations.

**Reading:**

**Excercises:**

20.23, 20.24

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

L1: Special lecture, with preparation for understanding the particle-in-box model and Lambert Beers law

S1: Finish work on elementary vector algebra and Experiment with the Vector Calculator and in the Euclids plane lab.

G1: Systems of linear equations. Intro to Gauss elimination method.

L2: Analytical geometry in the plane. Intro to linear systems of equations. Complex numbers. Linear dependence/independence, basis and change of basis.

S2: Start matlab and follow the instructions in matlab linear algebra

L3: Linearization, tangent and the derivative. AMB&S chap. 23.

S3: Start matlab and follow the instructions in inverse, determinant and intro to linearization

Work on project f(x) = 0.

G2: Work on project f(x) = 0.

/Nils

Last modified: Thu Sep 26 22:54:44 MET DST 2002