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我在讲公式δ′(a~(1/2))=1/2δ′a时采用以下的方法: 問学生:若x为近似数,δ′x~2=? 答:δ′x~2=2δ′x. (*) 又問:若x~2等于已知数a,x=? 答:x=a~(1/2),(取算术根) 再問:若以x~2=a,x=a~(1/2)代入(*)式,結果怎样? 答:δ′a=2δ′(a~(1/2)),δ′(a~(1/2))=1/2δ′a.随着就可以告訴学生。最后的結果就是課本中65頁第10行所说的事实,即:近似数平方根的相对誤差界,等于被开方数的相对誤差界的一半。这样通过几次問答,完全可以使学生下費力气地接受这部分的知識。至于近似数高次方根的誤差問題,也可以很自然地得到結論。如
I use the following method when formulating δ′(a 1/2)=1/2δ′a: Ask the student: If x is an approximate number, δ′x~2=? A: δ′x~2 =2δ′x. (*) Q: If x~2 is equal to the known number a, x=? A: x=a~(1/2), (take arithmetic root) Then ask: if x~2= a, x=a~(1/2) is substituted into (*), what is the result? Answer: δ′a=2δ′(a~(1/2)),δ′(a~(1/2))= 1/2δ’a. You can tell students. The final result is the fact that the line on page 65 in the textbook says that the relative error bound of the square root of the approximate number is equal to half of the relative error bound of the squared number. In this way, through several questions and answers, you can make students fully accept this part of the knowledge. As for the error problem of the approximate number of higher-order square roots, it is also natural to draw conclusions. Such as