Abstract: Using the Mathematica software programming，the visualization of the compound Simpson formula for numerical integration is realized，and the dynamic calculation process of an example is presented. The interaction process to solve linear equations by the successive over-relaxation iteration method is designed，and the effect of the relaxation factor changes on the approximate solution is analyzed. A visual display of the special Newton iterative method for nonlinear equation roots is given，and the method of solving process through a numerical example is demonstrated. Using the Mathematica software in the course of numerical analysis，the intuitive and interactive of teaching content are enhanced，and the students′ interests and motivation in learning are stimulated.

Key words: Mathematica software, dynamic visualization, numerical integration, linear equations, nonlinear equation