wrathmann

JSXGraph Example collection

Calculus (univariate)

• Derivative of a function (h-method)
• Osculating circle
• Osculating circle (input)

Calculus (multivariate)

The development of these applets where supportet by ERASMUS+ project KA226 IDIAM.

• Tangentplane
• local 2nd order approximation

Calculus (symbolic)

In these examples the function js.manipulate was used to the derivatives in a symbolic way. The examples are part of the talk Examples using the CAS of JSXGraph held at the JSXGraph2024

• Osculating circle on a graph
• Taylor polynomial
• Curl of a vector field
• Orbitals of H atom

See the list below or look at the Examples there.

Probability Distributions

• Binomial Distribution
• Exponential Distribution
• Gamma Distribution
• Normal Distribution
• Poisson Distribution
• Uniform Distribution

In the following examples one can highlight probalities $P(a<=X<=b)$.

• Binomial Distribution
• Exponential Distribution
• Gamma Distribution
• Normal Distribution
• Poisson Distribution
• Comparison Poission and Binomial Distribution

Differential Equations

scalar ODEs

• LR current
• 1d heat equation (booundary value problem)
• Exponential decay/growth

System of ODEs

• Show 2D vectorfields In this applet the vectorfield can be edited via input fields.
• Lotka-Voltera
• 2x2 System over time
• 2x2 System tracectory
• 2x2 System tracectory ODE (Euler, Heun, RK4)
• Phasenportrait (inhomogenous)
• System of non-autonomous ODE
• System of non-autonomous ODE (trajectory and time)
• Heat equation (stationary, 1D)

Interactive Digital Assessement in Mathematics

The following applets were supported by the ERASMUS+ project IDIAM KA-226. At idamath.github.io one will find STACK questions as well. The links will direct to the IDIAM page.

Complex Numbers

• Complex numbers (polar coordinates)
• Complex numbers (addition) (HELM WB 10 Complex Numbers, 10.1.2, 10.2.1, )
• Complex numbers (multiplication)
• Roots of Complex numbers

Linear Algebra

• 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
• 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 \(\mathbb{R}^2\to \mathbb{R}^2\)
• Triple Product Given by three points a volume can be constructed. This applet shows the idea of the contstuction.

Integration 1d

• Riemann Sums

  Calculus 1d

• Sequences in 1d
• \(\epsilon-\delta\)-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.
• Tangent and osculating circle (numerical) For a given function the tangent and the osculating circle is drawn. The derivatives are approximated numericaly.
• Tangent and osculating circle (symbolic) For a given function the tangent and the osculating circle is drawn. The derivatives are computed symbolicaly.

  Elementary functions

• Definition Sine and Cosine
• Sine and Cosine (functiongraph)

Calculus 2d

• Sequences in 2d
• 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.
• Function and Tangent Plane: Given function an sliders
• Function and Tangent Plane: Function assigned in an input field.
• Function and Taylor 2nd order Given function an sliders
• Function and Taylor 2nd order Function assigned in an input field.

Integration domains 2d

• Curvilinear bounded domain (functions of \(y\)) You are given a domain and you have to reconstruct this domain by setting up four functions.
• Curvilinear bounded domain (functions of \(x\)) You are given a domain and you have to reconstruct this domain by setting up four functions.
• Curvilinear bounded domain You are given a domain and you have to reconstruct this domain by setting up four functions.

Coordinate Transformations

• Polar coordinates
• Spherical coordinates
• Spherical coordinates One set is hard coded in the applet, now try to fit the other on.

Vector Fields

• 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.