Ordinary Differential Equations Homework 6 Solution

Fourier Series:


    1. Section 37: Problem 3

    2. Section 37: Problem 5

    3. Section 38: Problem 1

    4. Section 38: Problem 4

    5. Section 38: Problem 7

    6. Let V be a real inner product space and let v, w ∈ V be non-zero.

        a) Let J(t) = ∥v − tw∥2 for t ∈ R. Find the value of t (in terms of v, w) that minimizes J.

        b) What does your result from part (a) tell you about the projection PW (v) = ∥w,vw∥2 w of v onto W (the span of w)?





















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