After using of some important limits in Advanced Mathematics,we may choose one of the methods in computation,such as method of improvisation and method of replacement with equivalent infinitesimal and method of Taylor expansion,to g.

Taylor expansion gives proof to the uniqueness theorem and the maximum modules principle, which is simple and clear at a glance, compared with the traditional proo

This paper is devoted to the study of the Taylor expansions of smooth functions on groups of Heisenberg type G , the Taylor expansions of smooth functions onG× R+ , and then existence and uniqueness for viscosity solutions of a kind of partialdifferential equations on groups of Heisenberg type.

By making use of the integral property of geometrically convex functions and geometrical convexity of the two exponential functions,this paper obtains two new estimation formulas of the remainder term in Taylor expansion of ex(x>0) and e-x(x>0),and two new inequalities.

Several enconomical methods in difference computation,which include the method of Taylor expansion, the splitting method, the method of compensated computation in deducted region, the method of self-controled time step, are discussed on the basis of difference scheme of explicit and complete square conservation.

Based on traditional three-order recursive Taylor expansion and four-order Range-Kuttle method,another effective method four-order Taylor expansion was proposed.