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: 14 日期: May 27, 2022 节次: 2 In this lecture, we will continue the discussion of absolute and conditional convergence, give the absolute convergence test to show any absolutely convergent series itself must converge. We also look at the difference between absolute and conditional convergences by showing that an absolute convergent series remains the same even after the rearrangement of the terms. However,...
周次: 12 日期: May 13, 2022 节次: 2 In this lecture, we will talk about series, we introduce the sigma notation, and utilize limit to define the sum of a series. Primarily, there are two types of series whose sums can be found directly, by definition. Those are called Geometric Series and Telescoping Series. To study a divergent series, we introduce the $n$th term...
周次: 11 日期: May 6, 2022 节次: 2 In this lecture, we will discuss series and sequences, these are new concept and very important ones. Before talking about series, we will talk about sequences. Overview In this chapter we study how to add together infinitely many numbers. This is a subject of the theory of infinite series. It is clear that infinite sum sometimes...