周次: 16 日期: June 9, 2022 节次: Extra1 In this lecture, we estimate the error of Taylor polynomial to the generating function. The result provides a criteria for the convergence of Taylor series. A lot of common functions can be expanded to Taylor series according to this result. And without the proof, we will see that more common functions can be represented by power...
周次: 16 日期: June 8, 2022 节次: 1 In this lecture, we show that the convergent power series represents a function $f(x)$. The coefficient of the power series can be presented in turn by the function. This opens a new page for the application of power series, for we can associate power series to any infinitely differentiable functions. To see the power series derived...
周次: 15 日期: June 1, 2022 节次: 1 In this lecture, we will continue the discussions on the power series. A radius of convergence of a power series is emerging from the ratio test for the absolute convergence. We will discuss the basic operations, like differentiation and integrations on a power series, and the multiplication of two power series as well. When a power...