# Theory

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.

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, 22.6abcd, 22.7, 22.8, 22.9, 22.10abc

Project:
Project f(x)=0 , including modeling, solver implementation, application to model equations, analysis and conclusions, presentation.
Wamlings eq's, version 2001
Öhrströms eq's, version 2001
Example report

# Matlab

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.

Excercises:
20.23, 20.24

# Activity plan:

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.

/Kenneth