in high school Math
Department of Mathematics,
Matsumoto Agatagaoka High School,
Agata ,Matsumoto , 390 , Japan
First I sketch some graphs of one function f(x,y,t)=0 which has a parameter t. Usually there are lines with respect to x,y coordinates, because of avoiding unnecessary difficulties. And I show the animation of these graphs changing the value of parameter. Secondly I sketch some graphs of f(x,y,t)=0 with its envelope. Then I show the animation and overall graphs. Thirdly I solve the problem by traditional hand works. As powerful as the computer is, it is not nearly as powerful as our own intelligence and we will gain experience in using each to expand the power of the other.
I pick up two examples from my ordinary lecture for pre undergraduates classes. One is the Wierstrass’s example that is a continuous function but not differentiable on almost everywhere and founded in 1875. Students are usually given some examples of continuous function but not differentiable on some isolated points. The other is Taylor's Polynomials of nth orders. Students think that trigonometric functions are quite different from polynomial functions. These are in the category of difficult discussions. But I think it is useful for any science class to give such graphical images without strictly discussions. My aim is to give not only some inspirations of how to solve the problems but also some feelings of reality of the problems and some wills of creations.
This report is only ordinary use for high school students to build up their fundamental firm and to make proceed their power of Mathematics. Programs of this report completely depend on Mathematica by means of using some beautiful graphics , animation and pallets and buttons. These graphics and the animation are not so incredible nor excellent, but useful for beginners of science course students. I have had 7 hours lectures of these examples of this report for these three years. Those were very good times for me and students.