Teacher: Andrea Valente (aaue.dk/~av)
Book: David C. Lay: Linear Algebra and its applications
Article: The fire tower
Course plan:
| Lecture nr | Date | Topic | Comments |
|---|---|---|---|
| 1 | ??? feb - time - room | Intro
What is linear algebra, what do we need it for, ... Systems of linear equations
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... |
| 2 | date - time - room | Ch. 1.2 Row reduction and Echelon Form
Solve systems with python: example. |
Ex. Ch. 1.2: 1, 3, 7, 9, 13, 15, 17, 33 |
| 3 | date - time - room | Ch. 1.3 Vector equations
Example of radar diagram, to visualize RN vectors. |
Ex. Ch. 1.3: 1, 3, 5, 9, 11, 13, 25 |
| 4 | date - time - room | Ch. 1.4 The Matrix Equation + Ch. 1.8 Introduction to linear transformations | Ex. Ch. 1.4: 1, 3, 9, 11, 13, 15, 21
Ex. Ch. 1.8: 1, 3, 9, 13, 19, 25 |
| 5 | 11/mar - 8:30 - room | Ch. 1.5 Solution Sets of Linear Systems + Ch. 1.6 | Ex. Ch. 1.5: 1, 3, 5, 15, 25 |
| 6 | date - time - room | Ch. 1.7 Linear independence + Ch. 1.10 (applications of linear systems) | Ex. Ch. 1.7: 1,3, 5, 7, 11, 17 |
| 7 | date - time - room | (Ch. 1.8) Ch. 1.9 The matrix of linear transformation. Python program to try 2D transformations out (here) | Ex. Ch. 1.9: 1, 3, 5, 17, 19, 25, 27
Given the line L defined by y = k * x, where k is any real number, find a linea transformation T that projects points, using the line as symmetry axis. A point P will the projected by T, into a point P' so that: 1- a line passing by P and P' will be hortogonal to L. 2- the distance between P and L is the same as the distance of P' to L. Calculate the matrix for T. |
| 8 | date - time - room | Ch. 2.1 Matrix Operation (+ Ch. 2.7) | Check out these slides
on 2D affine transformations.
Implementation of 2D transforms, and
interactive, visual solution to last lecture problem (here).
|
| 9 | date - time - room | Ch. 2.2 The inverse of a Matrix.
Linear algebra in Python: Scipy examples. |
Ex. Ch. 2.2: 1, 3, 5, 7, 9, 31
John D. Barrow Pi in the Sky: Counting, Thinking, and Being |
| 10 | date - time - room | Ch. 2.3 Characterizations of invertible matrices (+ Ch. 2.7 Applications to Computer Graphics)
IFS fractals: python code here. |
Ex. Ch. 2.3: 1, 3, 11, 17, 21 |
| 11 | date - time - room | Presentation of article | ... |
| 12 | date - time - room | ... | ... |
| 13 | date - time - room | ... | ... |
| 14 | date - time - room | ... | ... |
| 15 | date - time - room | ... | ... |
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More material: online lectures on Linear Algebra (youtube).
EXAM DATE: see here
[MAT2C er som MAT1B - Bestået/Ikke bestået - mundtlig eksamen med forudkendte opgaver]