在 MacOS 上安装 Node.js 与 Slidev (用 Markdown 写 PPT)
为何要使用 Node.js 我并不是程序员，安装 Node.js 其实唯一的目的就是要使用 slidev 这个包，它能方便的将 markdown 转为 ppt. 这样，我在 notion 上写的讲义就可以方便的先转换成 markd...
W3-S2 Work, Fluid Pressure and Forces
周次: 3 日期: March 11, 2022 节次: 2 In this lecture, we’ll give a brief introduction to the concepts of works and fluid pressures. Many examples will be presented. This lecture covers §6.6 and §6.7. Outline Work Work refers specifically to a force acting on a body and the body...
W3-S1 Areas of Surfaces of Revolution and the Theorem of Pappus
周次: 3 日期: March 9, 2022 节次: 1 A curve sweeps out a surface in the space around is called a surface of revolution. The “area” of this surface depends on the length of the rope and the distance of each of its segments from the axis of revolution. In this section, we calculate the area of surface of...
W2-S2 Moments and Center of Masses
周次: 2 日期: March 4, 2022 节次: 2 Outline In this lecture, we discuss moments ( 质量矩）and centers of mass. Two concepts are related. In this lecture, we only deal with one- and two-dimensional problems (Essentially all the problems been dealt with are in one-dimension). Basic Principle for Center of Mass and Moment Definition. (Center of Mass) For...
W2-S1 Lengths of Plane Curves
周次: 2 备注: Attendance check 日期: March 2, 2022 节次: 1 Outline We knew what is meant by the length of a straight line segment, but without calculus, we have no precise notion of the length of a general winding curve. The idea of approximating the length of a curve has no difference with the idea of approximating an area or approximating...
W1-S2 Volumes by Slicing (cont.) , Volumes by Cylindrical Shells
周次: 1 日期: February 25, 2022 节次: 2 Outline For solids of revolution, the volume is relatively easy to find out. In section 6.1 and 6.2, we developed three method for finding volumes. The first two are based on the area of cross-sections, therefore these cases are direct applications of the formula $V = \int_a^b A(x) dx.$ The third case uses cylindrical shells for...