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...

一. 背景介绍 设计3D打印机的热床时，热床的升温能力关乎着打印的成功与否。过低的温度会造成打印件翘曲，导致打印失败。因此，热床是否能升温到所需...

周次: 7 备注: Attendance check 日期: April 8, 2022 节次: 2 In this lecture, we will take a quick glance at the Numerical Integration methods. Numerical integrations are very useful in practice. The methods we are going to learn are Trapezoidal Method and Simpson’s Method. We will learn how to evaluate an integration numerically,...

周次: 7 日期: April 6, 2022 节次: 1 In this lecture, we explore more examples of integration. Trigonometric substitutions and integration by looking up the integration tables are covered. Note that most of these calculations can be done by hands. § 8.5 Three Basic Substitutions The most common substitutions are $x=a\tan\theta$, $a=\sin\theta$, and $x=a\sec\theta$. They can be useful for dealing with the integrals involving...

前几天在电脑上使用 Notability 客户端批量修改笔记名称的时候，曾一度出现了 notability 笔记全部丢失的情况。所幸的是 iPad 上显示一切正常，赶紧把 iPad 的笔记同步到 iCloud 后才松了...