IDIAMath

Tutorials (Question Examples)

The following tutorials are written to illustrate concrete questions that could be given to students in higher education. We aim to discuss the STACK and JSXGraph features used as well as the motivation for the question, but there is room for improvement, so please give feedback.

Each tutorial will provide the Moodle XML code for the question, so that you can easily import it in your own server and test it, as well as the discussing of the design.

The questions are not really indended to be ready for use.
We reckon that most teachers will want to tailor the questions to their students and use the questions primarily as examples to build on.

Visualising functions in two variables

• Question match-properties. Give an arbitrary function with given properties, with visual aid.
• Question Tune 3D Function Tune parameters of a function to match another function visually
• Question Tune 3D polynomoial Minimal working example of question using jsxgraph

Sketches (questions under construction)

Visualising functions in two variables

• Question 1 Interpret partial derivatives
• Question 6 Select matching function
• Question 7 Select matching partial derivative

Calculus of functions in two variables

Functions of two variables

• Question Find the function term when the graph is drawn

  Differentiation / stationary points / Hessian

• Question select-extremal Select maxima/minima on a plot

In the following questions the tangent plane is shown

• Question stationary point based on trig function
• Question stationary point based on Legendre polynomial

In optimization the local 2nd order behavior of a function hast to be analysed. This is addressed by these questions

• Question Hessian positive definit
• Question Hessian negative definit

Integration Domains in 2D

• Question Polar Coordinates (Matching) (fit the reference volume by entering intervals for \(r\) and \(\phi\)
• Question Area bounded by two functions Find the formulation of the functions that bound the integration domain. Type 1 means that functions depends on \(x\).

Integration Domains in 3D

• Question Cylindrical Coordinates (Matching) (fit the reference volume by dragging sliders)
• Question General Coordinate Transformation (this is like a template for 3D Transform)
• Question Spherical Coordinates (Matching) (fit the reference volume by dragging sliders)
• Question Spherical Coordinates (Rotating) (fit the reference volume by entering parameter intervals)

Visualising curves in 3D

• Question Circular curve: Find the parameters of \(t \mapsto \begin{pmatrix} r \cdot \cos(t) \\ r \cdot \sin(t) \\ h \cdot \cos(n \cdot t - \phi) \end{pmatrix}.\)

• Question Elliptical curve (helix): Find the parameters of the curve given by \(t \mapsto \begin{pmatrix} x_0+ a \cdot \cos(t) \cdot \cos(\alpha) - b \cdot \sin(t) \cdot \sin(\alpha) \\ y_0+ a \cdot \cos(t) \cdot \sin(\alpha) + b \cdot \sin(t) \cdot \cos(\alpha) \\ h \cdot t \end{pmatrix}.\)

• Question Elliptical curve: Find the parameters of the curve given by \(t \mapsto \begin{pmatrix} x_0+ a \cdot \cos(t) \cdot \cos(\alpha) - b \cdot \sin(t) \cdot \sin(\alpha) \\ y_0+ a \cdot \cos(t) \cdot \sin(\alpha) + b \cdot \sin(t) \cdot \cos(\alpha) \\ h \cdot \cos(t)\end{pmatrix}.\)

• Question Rotating a curve about two axis This question trains the imagination of rotating objects around two axis of the coordinate system.

Visualising solids in 3D

• Question 8 3d-cube-transformations

Vector fields in 3D

• Question Curl of a vector field Given is a vector field (as formula and plotted). The student has to choose the right representation for the curl. The filed is selected from a list of given fields.

• Question Vector field of given curl Given is a curl of a vector field (as formula and plotted). The student has to choose the right representation for a vector field, that is fits to the curl. The filed is selected from a list of given fields.

Adaptive Questions

• Question Rotating a curve about two axis This question trains the imagination of rotating objects and guides the student through the topic.
• Question Curl of a given vector field This question trains the computation of the curl of a vector field. This implementation demonstrates the usaga of a single JSXGraph object in an adaptive setting.

Additional Material

Here will find applets demonstrating JSXGraph in different applications. JSXGraph Examples This material is usefull for the HELM material as well.

A huge collection you will find at the JSXGraph homepage and the example data base there.

HTML test

• Test of html-link with jsxgraph

Notes

• JSXGraph sandbox

Documentation from Other Sources

• JSXGraph in Moodle