1u1(x, t) + A2u2(x, t) a) Sketch the graph of the function (0.3) on the interval...

   

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1u1(x, t) + A2u2(x, t) a) Sketch the graph of the function (0.3) on the interval (0,2) where (0.3) f(x)=xif 0 < x≤ 1, f(x) = -x + 2 if 1<x< 2. b) Sketch the graph of the function f(x) in (0.3) as (an extended) even func th 3) a) Given the heat equation with k> 0 a constant. Determine the solution to the (insulated rod) heat equation problem L(u) = 0 with u(0, t) = 0, u(2, t) = 0, t ≥ 0, (0.4) (0.5) f(x) = u(x, 0), where f(x) is given in (0.3). b) Determine limt→∞u(x, t). 4) a) Determine for every real λ the general real valued solutions yes(x) t 1u1(x, t) + A2u2(x, t) a) Sketch the graph of the function (0.3) on the interval (0,2) where (0.3) f(x)=xif 0 < x≤ 1, f(x) = -x + 2 if 1<x< 2. b) Sketch the graph of the function f(x) in (0.3) as (an extended) even func th 3) a) Given the heat equation with k> 0 a constant. Determine the solution to the (insulated rod) heat equation problem L(u) = 0 with u(0, t) = 0, u(2, t) = 0, t ≥ 0, (0.4) (0.5) f(x) = u(x, 0), where f(x) is given in (0.3). b) Determine limt→∞u(x, t). 4) a) Determine for every real λ the general real valued solutions yes(x) t