Applied Mathematics 2270A/B Lecture Notes - Lecture 26: Orthogonal Functions, Dot Product
18 Dec 2018
School
Department
Professor
Document Summary
In this section i"m going to give you definitions and demonstrate how to use it in 12. 2" Def: two functions f1 and f2 are orthogonal on an interval {a, b} if f1(x) *f2(x) dx = 0. "this is the equivalent property for functions to vectors where you took the dot product of two vectors and found it equal to be 0. We have a set of orthogonal functions [ n] if on an interval [a, b] N m dr = 0 for n m. 2 dx = || n||2 is called the squared norm of n on [a, b] 2 dx = || n||2 is called the norm of n on [a, b] I care about cos(nt) and sin(mt) n = 0, 1, 2, 3 on [- , ] = m=n cos(mt) sin(nt) dt = 0 m n cos(mt) sin(nt) dt = 0 m n cos(mt) sin(nt) dt = 0 m n. So {cos(nt), sin(nt)} n = 1, 2, 3,
