导函数是否一定黎曼可积？
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...
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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...
W1s1 Volume by Slicing
W1-S1 Volumes by Slicing and Rotation About an Axis 周次: 1 日期: February 23, 2022 节次: 1 In this semester, we will be beginning with the applications of definite integrals. Today’s course is the contents in section 6.1 (Volumes by Slicing and Rotation About an Axis). Outline Review: Riemann sums & Definite Integral Definite integral is dealing with...
写在比赛结束之后
比赛结束了，结果没有出线。虽然这是想要的结果，可是没有在竞争中胜出，总是有些不开心。总结其中的得失，没有讲完是最大的遗憾，其实在选题的时候，...