浅谈Dirichlet函数在微积分中的作用

Role of Dirichlet Function in Calculus Teaching

反例在数学理论中占据着极为重要的地位,它的影响和作用并不比那些著名的定理差.该文论述了微积分教学中Dirichlet函数在函数、函数周期、极限、连续、导数、积分等概念的澄清方面起到突出的反例作用。

Counter-examples occupy an extremely important place in the mathematical theories,they are more or less of the same influence and significance as those famous theorems.this paper points out that in calculus teaching Dirichlet function plays an outstanding role of counter-example in clarifying the concepts of function,function cycle,limit,continuity,derivative and integral,and meanwhile it gives the limit expression of Dirichlet function.