Improved Taylor formula and its numerical simulation;

Taylor Formula Applied in Deciding the Covergence and Divergence of Infinite Series and Improper Integral;

We use the Taylor expansion to analyze the signature space,which is obtained from calculating the input-output cross-correlation of the DUT(Device Under Testing),to get the delay time of signature-pair.

We can popularize real analysis to complex analysis by the Taylor expansion of analytic function and Laurent expansion in function of the complex variable.

Used method of data collection,"Tyler model" and China s Sports New Curriculum for the collection,clear both their intrinsic significance,discovered "Tyler model," Curriculum to give teachers a lot of room for New Curriculum sports and physical education teachers were given more rights.