Category: Applets

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 […]melbapplets.ms.unimelb.edu.au/2024/04/05/basesandcoordinatesinr2

Visualising the GramSchmidt Algorithm
This applet demonstrates the GramSchmidt algorithm performed in $\mathbb R^3$. The GramSchmidt 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 […]melbapplets.ms.unimelb.edu.au/2024/04/05/visualisingthegramschmidtalgorithm

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 appletmelbapplets.ms.unimelb.edu.au/2024/03/25/visualisinglineartransformationsinr2

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 […]melbapplets.ms.unimelb.edu.au/2024/03/25/visualisinglineartransformationsinr3

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 appletmelbapplets.ms.unimelb.edu.au/2024/02/28/cylindricalcoordinatesengineeringmaths

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 appletmelbapplets.ms.unimelb.edu.au/2024/02/28/sphericalcoordinatesvisualengineeringmaths

Solution of the heat equation
This applet shows a solution of the heat equation, a partial differential equation from MAST20029 Engineering Mathematics.melbapplets.ms.unimelb.edu.au/2023/05/26/solutionoftheheatequation

Visualising the span of two vectors
This applet visualises the span of two vectors in R3 using linear combinations.melbapplets.ms.unimelb.edu.au/2023/02/01/visualisingthespanoftwovectors

Vector equations of lines in R2
This applet shows a line in R2 and the vector form of its equation.melbapplets.ms.unimelb.edu.au/2023/02/01/vectorequationsoflinesinr2

Vector equations of planes in R3
This applet shows a plane in R3 and the vector form of its equation.melbapplets.ms.unimelb.edu.au/2023/02/01/vectorequationsofplanesinr3
Number of posts found: 54