設多項式 使 。
估計絕對誤差 在區間 (0.5,1) 上的上限。 (more…)
學校圖書館檢來一本舊教科書，名為 Applied Numerical Analysis。
If you worked for a mining company the following might be a typical problem:
There are two intersecting mine shafts that meet at an angle of 123, as shown in the figure above. The straight shaft has a width of 7 feet, while the entrance shaft is 9 feet wide. What is the longest ladder that can be negotiate the turn? You can neglect the thickness of the ladder members, and assume it is not tipped as it is maneuvered around the corner. Your solution should provide for the general case in which the angle, A, is a variable, as well as the widths of the shafts. (more…)
數值法解方程的題目，通常會提供 initial guess。但有時就算沒有提供，我們也可以約略估計，比如解
To find the definite integral of a polynomial of degree less than 4, we can use the following formula.
Nothing special, it is just something about Simpson’s rule.
Just discuss an easy AL Applied Mathematics (II) Question with students.
Let be twice differentiable functions such that .
(a) Let , where . Show that .
(b) Using (a), or otherwise, find Taylor’s expansion of the function about , up to the term in . (more…)