Homogeneous Coordinates
A brief introduction to homogeneous coordinates and their geometric interpretation.
Single variable calculus
Lecture notes from the Integration Workshop at the University of Arizona. The workshop aims to revisit a few select topics of undergraduate mathematics from a graduate perspective. The notes draw from the text “An introduction to real analysis” by John K. Hunter, and we refer the interested reader to section 8.6, 10.1-3 and 12.4 for further details. These notes contain more material than I intend to cover in the lecture. I urge you to go through all of it, even the parts that I don’t get to in the lecture.
Properties of the exponential
complex (1).pdf
For any complex number $z$, $1+z+\frac{z^{2}}{2 !}+\frac{z^{3}}{3 !}+\cdots+\frac{z^{n}}{n !}+\cdots$ converges to a complex value which we shall denote as $e^z$. The function $e^z$ has the following properties
For any complex number $z$, $1+z+\frac{z^{2}}{2 !}+\frac{z^{3}}{3 !}+\cdots+\frac{z^{n}}{n !}+\cdots$ converges to a complex value which we shall denote as $e^z$. The function $e^z$ has the following properties
- $\frac{\mathrm{d}}{\mathrm{d} z} e^{z}=e^{z}, \quad e^{0}=1$
- $e^{z+w}=e^{z} e^{w} \quad\text { for any complex } z, w$
- $e^{z} \neq 0 \quad\text { for any complex } z$
Cubic Spline Interpolation
样条的英语单词spline来源于可变形的样条工具,那是一种在造船和工程制图时用来画出光滑形状的工具. 在中国大陆,早期曾经被称做齿函数.后来因为工程学术语中放样一词而得名.样条插值是使用分段多项式进行插值的方法.由于样条插值可以使用低阶多项式样条实现较小的插值误差,这样可避免使用高阶多项式所出现的龙格现象.
188 post articles, 21 pages.