Resumo de Edps

Ψ(t) = Ψ'(t) = λ Ψ(t)\nC₁(0) = 0, ψ(0) = 0\n1º CASO λ > 0 , λ = μ²\nk = μ\nC₁ - C₂ = 0 C₁ + C₂ = 0\nC₁ = C₂\n\nλ = 0 → reduce trivial\nC₂ = 0\n2º CASO λ = 0\nΨ(1) = 0\nA(1) + B = 0\nC₁ = 0\nE = 0\n3º CASO λ < 0 λ = -μ²\nλ = -μ λ = (-mπ/2)²\nΨ(t) = (m²/4π²)(Ψ(t))\nE_m = ∫f(π/2t)\nΨ(t) = C₁cos(mπ/2t) + C₂sin(mπ/2t)\nM(0) = 20/11\nM(λ) = 0\nM₀(t) = nπx\nE_m = \nM(x) = ∑m(π/2)x\nM = 8a(1)^2\n\nM(x,t) = \n\{M_{tt} = C_{tt} + U_α\nM_x(0,t) = M_{tt}(1,t) = 0\nM_{tt}(x,0) = nπx\nM_t(λ,0) = 0\nM_t(λ,0) = 0 λ > 0 , λ = -μ²\nλ < 0 , λ = -μ\nV = μ\nk = ±μ\nΨ(0) = C₁μ + C₂e^{-μ}\nΨ(0) = 0 = C₁ + C₂\nC₁ = C₂ = 0 → indeterminate\nλ = 0\nΨ(0) = A(0) + B = 0\nC₁ = 0\nC₁ = 0\nΨ(1) = A(1) + B = 0\nA - B = 0\nΨ(1) = C₁cos(μt) + C₂sin(μt) = 0\n\nC₁ = C₂ → reduce to trivial\nλ = 0 Ψ(λ) = A_n(ω) + B_n(Ψ)\n• \nM(λ) = Max\nM_x(0) = 0\nM_x(1) = 1\nM(Ψ)(λ) = 0\nΨ(λ)(λ) = λ\nΨ(λ)(λ) = (Eλ)\n•\nB_m = 𝑐/𝜋\nm(1,7),(cos(𝑚𝜋𝑥)dx)\n\n• \nS.Eterno\n\nBm = ∫ 𝑓(𝑥)𝑐𝑜𝑠(𝑚𝜋𝑥)dx\n\nΨ(λ) = (λ''(λ) = λ)\nΨ(λ)(E(λ)) = (λ(0) = 0)\nλ(0)≤λ0 λ = -μ²\n\n(l)'(1) = -λ(m(λ)) + (C2 sin(λ))\nC(μ)(𝑡) = 0\n\nλ≤0 λ= -μ²\nC(λ(1)) = 0\nC(λ(1) =C(1/cos(λ ))=0\nM = (m+λ)\n\n 𝑓𝑖𝑛𝐷(𝜆)(𝑠𝑏𝑐𝑜𝑠[(m+λ/2)𝜋𝑥]\nM(λ)(𝑡) = 𝑓\03360𝑓𝜆(𝜆)\nM(λ) = 𝑓𝑚(λ) = 2𝑀_m\nM(λ) = 1\n= ∑(m=0)𝑓𝑐𝑜𝑠[λ(m+λ)𝜋𝑥]e^{-λ(m)^2t}\nM(λ)(0) = 1+βn\n\nAm = 𝑓/1\n\nAm = 2/∫ f)(.cos[λ(m+k)πx]dx\nAm = 2/∫(cos[m(λ+𝑘)πx]dx\nAm = 2(t-1)/(m+λ)π \nM(1,2) = ∑(2t-1)/(λ(m+k)π)e^{-λ(m+k)²τ} \n\ny