Overview JSXGraph Examples

In the section you will find some examples demonstrating JSXGraph in linear algebra and calculus. Related HELM Workbooks will be added.

Complex Numbers

Linear Mapping \(\mathbb{R}^2\to \mathbb{R}^2\) and coordinate unit vectors Just see the effect of setting the image of the unit vectors.
Linear Mapping \(\mathbb{R}^2\to \mathbb{R}^2\) and Matrices (HELM Workbook 8 Matrix solution of Equations 8.2, 8.3)
Linear Mapping \(\mathbb{R}^2\to \mathbb{R}^2\) and Matrices Demonstrated at a circle.
Linear Mapping \(\mathbb{R}^2\to \mathbb{R}^2\) and Matrices Demonstrated at a polygon.
Rotation in \(\mathbb{R}^2\) Rotation of a polygon, matrix is displayed.
Eigenvectors of a linear Mapping \(\mathbb{R}^2\to \mathbb{R}^2\) (HELM WB 22 Eigenvalues and Eigenvectors, 22.1.2)
Triple Product Given by three points a volume can be constructed. This applet shows the idea of the contstuction.

Sequences in 1d (HELM WB 16 Sequences and Series 1.)
\(\epsilon-\delta\)-criterion for continuous functions
Uniform continuity of functions
Definition of Area functions The idea of the area function is shown.
h-Method and Sine The influence of the parameters of the damped sine function are demonstrated. (HELM Workbook 11 Differentiantion 1.,4. )
Tangent and osculating circle (numerical) For a given function the tangent and the osculating circle is drawn. The derivatives are approximated numericaly. (HELM Workbook 11 Differentiantion 1.,4. )
Tangent and osculating circle (symbolic) For a given function the tangent and the osculating circle is drawn. The derivatives are computed symbolicaly. (HELM Workbook 11 Differentiantion 1.,4. )

Sequences in 2d (HELM WB 16 Sequences and Series 1.)
Piecewise curve and tangent A piecewise curve depending on sliders and the tangent of the curve are shown.
Areas with function limits Show 2D integration area with functions as limits
Function plot: Plot a function provided in input box. (HELM Workbook 18 Functions of Several Variables, 18.1)
Function and Tangent Plane: Given function an sliders (HELM Workbook 18 Functions of Several Variables, 18.3)
Function and Tangent Plane: Function assigned in an input field. (HELM Workbook 18 Functions of Several Variables, 18.3)
Function and Taylor 2nd order Given function an sliders
Function and Taylor 2nd order Function assigned in an input field.

Curvilinear bounded domain (functions of \(y\)) You are given a domain and you have to reconstruct this domain by setting up four functions. (HELM Workbook 27 Multiple Integration 27.2)
Curvilinear bounded domain (functions of \(x\)) You are given a domain and you have to reconstruct this domain by setting up four functions. (HELM Workbook 27 Multiple Integration 27.2)
Curvilinear bounded domain You are given a domain and you have to reconstruct this domain by setting up four functions.

Polar coordinates (HELM Workbook 27 Multiple Integration 27.2.3, 27.4)
Spherical coordinates (HELM Workbook 27 Multiple Integration 27.4.3)
Spherical coordinates One set is hard coded in the applet, now try to fit the other on. (HELM Workbook 27 Multiple Integration 27.4.3)

Slope Field Slopefield of a function \(f:\mathbb{R}^2\to\mathbb{R}\) like \(y'(x)=f(x,y)\) is plotted, a trajectory thru \((x,_0,y_0)\) is plotted. The function can be modified by an input field.
Vector Field 2d given by a function \(V:\mathbb{R}^2\to\mathbb{R}^2\), a trajectory thru \((x,_0,y_0)\) is plotted. The vector field can be modified by an input field.
Vector Field 3d given by a function \(V:\mathbb{R}^3\to\mathbb{R}^3\), a trajectory thru \((x,_0,y_0)\) is plotted. The components of vector field can be modified by input boxes.
Vector Field 3d and curl given by a function \(V:\mathbb{R}^3\to\mathbb{R}^3\) the curl \(\nabla\times V\) is computed and shown. The components of vector field can be modified by input boxes.
Vector Field 3d at function plot Given a function \(f:\mathbb{R}^2\to\mathbb{R}\) and the vectorfield \(V:\mathbb{R}^3\to\mathbb{R}^3\), the vectofield is plotted at the graph of the function \(f\).
Vector Field 3d at surface Surface given by a function \(s:[-1,1]^2\to\mathbb{R}^3\) and the vectorfield \(V:\mathbb{R}^3\to\mathbb{R}^3\), the vectofield is plotted at the surface.
Vector Field 3d at curve Curve given by a function \(c:[-1,1]\to\mathbb{R}^3\) and the vectorfield \(V:\mathbb{R}^3\to\mathbb{R}^3\), the vectorfield is plotted at the curve.
Vector Field 3d with slider Curve can be manipulated by sliders, the vectorfield as well. Both is hard coded in the applet.