本文来自一个学生的提问。 当时想了想，预感有这样的处处可导，但导函数又不黎曼可积的函数，可不知如何构造。若不要求导函数有界，则有很多例子，但若...

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...

周次: 10 日期: April 29, 2022 节次: 2 In today’s lecture, we are going to look at three typical applications of first-order differential equations. Analyzes an object moving along a straight line while subject to a force opposing its motion. A model of population growth which takes into account factors in the environment placing limits on growth. A...

周次: 10 日期: April 27, 2022 节次: 1 In this lecture, we talk briefly on the numerical method for solving an initial value problem for a general first order differential equation. The method is called Euler’s Method, it is the most simplest numerical method for solving a differential equation. Secondly, we will look at how to sketch graphical...

周次: 9 日期: April 22, 2022 节次: 2 In this lecture, we would like to give several examples on solving differential equations. Three examples will be shown. And Euler’s method for numerical solution for the initial value problem of differential equations will also be explored. Solving Linear Equations We solve the equation $$ \dfrac{dy}{dx} + P(x), y =...

周次: 9 日期: April 20, 2022 节次: 1 In this lecture, we introduce some basic concept for differential equations, how to think of them, how to describe them and how to solve them. The most important thing is to know how to solve a differential equation. We will solve typical separable differential equations as well as the first-order linear differential equations. Chapter 9. Further...