# Category: Applets

1. ### Bases and Coordinates in R2

This applet demonstrates the concept of coordinate vectors in $\mathbb R^2$ A basis $\mathcal B$ of a vector space $V$ is a linearly independent spanning set. One useful feature of a basis is that it gives rise to a way of writing coordinates on $V$. Any vector $\mathbf v \in V$ can be written uniquely […]
2. ### Visualising the Gram-Schmidt Algorithm

This applet demonstrates the Gram-Schmidt algorithm performed in $\mathbb R^3$. The Gram-Schmidt algorithm converts a basis of an inner product space into an orthonormal basis. It does this by building up the orthonormal basis one vector at a time. For each vector in turn, we remove any component that is parallel to the vectors which […]
3. ### Visualising linear transformations in R2

This applet shows the geometric effect of a linear transformation $T: \mathbb R^2 \to \mathbb R^2$. You can type a matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a triangle are transformed when multiplying by $M$. Other resources: Geogebratube page for this applet
4. ### Visualising linear transformations in R3

This applet shows the geometric effect of a linear transformation $T$ in $\mathbb R^3$. You can type a 3×3 matrix $M$ on the right hand side of the applet, and then click Play to see how the vertices of a cube are transformed when multiplying by $M$. Can you see if the corresponding transformations are […]
5. ### Cylindrical Coordinates Visual (Engineering Maths)

This applet helps visualise the surface generated by cylindrical coordinates using r,θ and z. Click and drag on the sliders on the left to adjust the ranges for r,θ and z. Geogebratube page for this applet
6. ### Spherical Coordinates Visual (Engineering Maths)

This applet visualises surfaces generated by spherical coordinates using r,θ and φ. Click and drag on the sliders on the left to change the values for r,θ and φ. Click and drag on the graph to change/rotate the view. Geogebratube page for this applet
7. ### Solution of the heat equation

This applet shows a solution of the heat equation, a partial differential equation from MAST20029 Engineering Mathematics.
8. ### Visualising the span of two vectors

This applet visualises the span of two vectors in R3 using linear combinations.
9. ### Vector equations of lines in R2

This applet shows a line in R2 and the vector form of its equation.
10. ### Vector equations of planes in R3

This applet shows a plane in R3 and the vector form of its equation.

Number of posts found: 54