﻿ Casyopee - Creating a function by a formula, calculating, graphing, tabulating, solving

What they say:   I used Casyopée to help students solve optimisation problems. It allowed me to present students very open tasks. Students explored and found results that they had to prove afterward. Casyopée also helped students reuse basic strategies for solving.
What they say:   Casyopée is faster and more convenient than a calculator.... We have the geometric and algebraic side of the problem at the same time. It is easier to see how a function "reacts." It's useful and interesting.
What they say:   Casyopée makes it easy to calculate a derivative, to factor, to calculate zeros... and have a graph of the function next to it in the same window. It allows on a geometric problem to be able to establish variables that can then be used to study the problem by way of functions...
What they say:   Casyopee is a powerful application that can prove useful to both students and teachers It allows you to use various exploration and modeling tools, with the purpose of studying or teaching mathematical functions.
What they say:   Casyopee comes with lots of features. One of these features is the help provided for proving a function. There is also a feature for writing HTML reports that include the mathematical functions. Casyopee is guaranteed to improve the mathematical knowledge of its users.
What they say:   Besides the concept of number, the concept of function is the most important one in mathematics
What they say:   The notion of function is present in all scientific disciplines, and also in everyday life. Our experience as a teacher shows every day that it is a problem for many students. Situations with Casyopée can also be used outside of a technological environment and everyone will be able to reflect on her professional practice.

We wish to define the function of repartition for the normal law and to know the critical value for the 0,95 threshold

We shall use the first item by formula of the entry Create function in the Algebra menu.

As a difference with Figure 3 - Expression creation box, the dialog box includes a button for entering the independent variable identifier. Note that several identifiers can be chosen, x being proposed as a default. Note also that, optionally, like for expressions, it is possible to ask Casyopée to check whether the function defined by the formula is actually defined for all real numbers (check box Check Existence).

 Figure 31 - Create function by formula

After the function has been defined, the Calculate button offers three additional calculations, specific for the functions. We try here the entry “anti-derivative” whose result is the standard normal cumulative distribution with a constant difference. Since the function obtained is null for t=0, we define a function g by adding ½. (Create function / by formula then enter the formula 1/2+If(t)).

Note the buttons at the bottom of the graphic tab that allow graphing functions and calculating limits. In the tool bar at the top of the tab, several zooming are accessible with one button. Here, to correctly frame the curve, it has been necessary to zoom in y several times, and to zoom in x once. Axis have also been moved simply by dragging the graph with the mouse. Framing would also have been possible by entering numbers by way of the W button or by dragging the axis unit arrows. Another possibility is via a “zoombox”. Maintain the Ctrl key down, click a corner of the rectangle you want to zoom in, and drag towards the opposite corner. After confirming, the graph will fit into your rectangle.

Figure 32 - Functions, graphs and limits

Tabulating the functions is done by way of the  button. The button allows copying the table into the clipboard (separators: tabulations and line breaks). It is then possible to paste the data into a text processor or a spreadsheet.

Figure 33 - Tabulating a function

We now approach the critical value of the standard normal law at the level of 0.95.  For a graphical study one can enter a constant function h and point the intersection of the graphs in order to move a cursor and to read approximate values.

Figure 34 - Graphical study

 Casyopée also allows to enter an equation g(t)=h(t) and to solve in exact or approximate mode.  Approximate mode is adequate here. Casyopée applies the Newton method, starting from the cursor position. Figure 35 - Equation and approximate solution

Creation date : 22/11/2014 - 10h40
Category : - help