Course content
Please familiarise yourself with the course information (link above).
Toepassings van lineêre stelsels. Lineêre transformasies. Projeksie,
rotasie en refleksiematrikse.
(2D/3D). CADtoepassings. Vektorruimtes. Verskilvergelykings. Kleinste
kwadrate benaderings. Eiewaardes en vektore.

Applications of linear equations. Linear
transformations. Projection, rotation and reflection matrices
(2D/3D). CADapplications. Vector spaces. Difference equations. Least
squares approximations. Eigenvalues and vectors.

Lecture summary
Date  Description 
Klasnotas
/ Class notes 
15/09  Motivation: Millau
Viaduct. Linear algebra terminology: matrices, row vectors,
column vectors. Matrix algebra with focus on multiplication (see
also Gilbert Strang's lecturethe link to MIT Open Courseware is
to the side). Matrix zoo. Reminder of identities (order of
multiplication is especially important!). Brief detour: the
meaning of the inverse, and why we don't compute it. 
16/09  Other uses of matrices: predicting the spread of
wildfires. Gaussian elimination: rowreduction as executed by a
computer. Three scenarios: unique solution, no solution or free
variable. Examples: closed economy, balancing of chemical
equations. Homework: traffic network example. 
17/09  Gaussian elimination: currents in an electric
circuit. Overview of LU decomposition
(class example). 
20/09  Linear transformations. Application, reversal
and the existence of. Linearity. Geometrical interpretation
(projection, shear, translation, dilation, rotation). Simple
selftest: addition
 multiplication. 
22/09  Given a description of a linear transformation,
determine the corresponding transformation matrix. The technique
is simple: AI = A = [Ae_{1}
Ae_{2} Ae_{3}] (i.e. if you
can transform the unit axes, then you know A). Derivation of
the rotation matrix in 2D (example
spreadsheet). [Extra: Bullet
Time] 
23/09  A closer look at rotation, projection and reflection
matrices. 
Tutorials
Freely available textbooks
Textbook
Prescribed
textbook, Zill & Cullen (3rd ed).
Outside links