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Questions in category: 应用数学 (Applied Mathematics)
应用数学
2. (课程)应用数学中的PDE
Posted by haifeng on 2017-02-28 16:33:31 last update 2017-02-28 16:44:41 | Answers (0) | 收藏
http://web.stanford.edu/class/math220b/
Course of Stanford University
Math 220B
Partial Differential Equations of Applied Mathematics
Summer 2003
参考书:
Partial Differential Equations: An Introduction by Walter Strauss (适合本科生阅读)
Partial Differential Equations by Lawrence Evans. （适合研究生阅读）
3. 古埃及分数
Posted by haifeng on 2013-01-08 22:29:07 last update 2021-06-20 18:11:53 | Answers (2) | 收藏
观察
\[
\frac{153}{1001}=\frac{1}{8}+\frac{1}{36}+\frac{1}{14415}+\frac{1}{346305960},
\]
\[
\frac{153}{1001}=\frac{1}{7}+\frac{1}{101}+\frac{1}{11234}+\frac{1}{1135768634}+\frac{1}{227153727}+\frac{1}{257994078222798918}.
\]
因此 $\frac{153}{1001}$ 在计算机中也可以表示为 $(8,36,14415,346305960)$. 当然这并不比表示成 $153/1001$ 强多少.
首先不妨验证一下, 其次思考如何用计算机列出所有的表示方法, 即表示为 $\frac{1}{a_1}+\cdots+\frac{1}{a_n}$ 的形式.
这里涉及到的是古埃及分数. 详细可参考 Richard K. Guy 著 Unsolved Problems in Number Theory. 《数论中未解决的问题》. D11.
Remark (on 2021-06-20)
上面两个等式参见 [1] P.183. 第二个等式似乎并不正确.
References:
[1] Raymond Séroul, Programming for Mathematicians, Translated from the French by Donal O'Shea. Springer.