τ-Tilting modules over one-point extensions by a simple module at a source point

Let B be an one-point extension of a finite-dimensional k-algebra A by a simple A-module at a source point i. In this paper, we classify the tau-tilting modules over B. Moreover, it is shown that there are equations vertical bar tau-tilt B vertical bar = vertical bar tau-tilt A vertical bar + vertical bar tau-tilt A/< e(i)>vertical bar and vertical bar s tau-tilt B vertical bar = 2 vertical bar s tau-tilt A vertical bar + vertical bar s tau-tilt A/< e(i)>vertical bar. As a consequence, we can calculate the numbers of tau-tilting modules and support tau-tilting modules over linearly Dynkin type algebras whose square radical are zero.