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: 8 日期: April 15, 2022 节次: 2 In this lecture, we discuss the improper integral of type II, as well as the convergence test for improper integral of type I with non-negative integrands. In the section part, we will talk about the simplest differential equations, the geometric visualization of a differential equation with slope fields, and separable equations. Type II Improper Integrals Definition....
周次: 8 备注: Attendance check 日期: April 13, 2022 节次: 1 In this lecture, we consider integrals when the domain of integration is infinite, or the range of the integrand is infinite. Such cases are not Riemann integrable, therefore, they are called improper integrals. We would like to manage the integrations for these cases, via some limit procedure. Outline Improper Integrals of...