## Session 2, 2015

### CDF demonstrations

Below are links to Mathematica-produced CDF demonstrations, as used in the DMTH137 and MATH332 lectures. To get the best from these interactive modules, you will need to download the free CDF player from the Wolfram Inc. website.

## DMTH137 Session 2, 2015

#### Lectures in Week 1

- M-shape, using coordinates or vectors
- letter shapes, parametrised by design features
- rotating letter shapes
- skewed, using basis vectors
- points along a line

#### Lectures in Week 2

#### Lectures in Week 3

- Matrix Multiplication
- Linear Transformations in ℝ
^{2}- Reflect in
*x*-axis - Reflect in
*y*-axis - Reflect through the origin/Rotate about the origin
- Reflect in line: swap
*x*and*y*coordinates - Dilation/Contraction
- Expansion/Compression in
*x*-direction - Expansion/Compression in
*y*-direction - Shear in
*x*-direction - Shear in
*y*-direction - Rotation
- Shearing of letter ‘M’
- Use of Homogeneous Coordinates
- Translation & Shearing using Homogeneous Coordinates
- Multiple Transformations using Homogeneous Coordinates

- Reflect in

#### Lectures in Week 4

#### Lectures in Week 6

- Induction example: sums of odd numbers
- Induction example: sums of successive integers

## MATH136/235 any year

#### Lectures in Week 1

- Geometry/Algebra: 2x2 Determinant
- Geometry/Algebra: Eigenvalues of a 2x2 matrix