Motivation .For a given function f(),find its root(s),i.e.: =find x (or r=root)such that f(x)=0 ·BVP:dipping of suspended power cable.What isλ？ 入cosh 50-λ-10=0 (Some)simple equations=solve analytically 6x2-7x+2=0c0s3x-c0s7x=0 (3x-2)(2x-1)=02sin5xsin2x=0 x= x=,暨，n∈Z Copyright©2011，NAOYin Last Modification:Oct.2011 3 Motivation • For a given function f(x), find its root(s), i.e.: ⇒ find x (or r=root) such that f(x) = 0 • BVP: dipping of suspended power cable. What is λ? λ cosh 50 λ − λ − 10 = 0 • (Some) simple equations ⇒ solve analytically 6x 2 − 7x + 2 = 0 cos 3x − cos 7x = 0 (3x − 2)(2x − 1) = 0 2 sin 5x sin 2x = 0 x = 2 3 , 1 2 x = nπ 5 , nπ 2 , n ∈ Z Copyright c 2011, NAYin Last Modification: Oct. 2011 3