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3340Why Diffusion Forgets Fine Initial DetailsWhy does long-time heat evolution remember coarse mass distribution more than fine initial details?数学中等essay未尝试面试订阅4941Infer Constant Forcing From Midpoint 1Let y solve y'' = c on [0,1] with y(0)=0 and y(1)=3. If y(1/2)=1.25, what constant c is implied?数学简单数值题未尝试面试订阅4942Infer Constant Forcing From Midpoint 2Let y solve y'' = c on [0,1] with y(0)=1 and y(1)=2. If y(1/2)=2, what c is implied?数学简单数值题未尝试面试订阅4943Infer Constant Forcing From Midpoint 3Let y solve y'' = c on [0,1] with y(0)=-1 and y(1)=1. If y(1/2)=-0.75, what c is implied?数学简单数值题未尝试面试订阅4944Infer Constant Forcing From Midpoint 4Let y solve y'' = c on [0,1] with y(0)=2 and y(1)=4. If y(1/2)=2.8125, what c is implied?数学简单数值题未尝试面试订阅4945Infer Constant Forcing From Midpoint 5Let y solve y'' = c on [0,1] with y(0)=0.5 and y(1)=1.5. If y(1/2)=1.25, what c is implied?数学简单数值题未尝试面试订阅4946Infer Interval Length From Mixed Boundary Data 6Let y solve y''=0 on [0,L] with y(0)=1 and y'(0)=2. If y(L)=4, what interval length L is implied?数学简单数值题未尝试面试订阅4947Infer Interval Length From Mixed Boundary Data 7Let y solve y''=0 on [0,L] with y(0)=5 and y'(0)=-1.5. If y(L)=2, what L is implied?数学简单数值题未尝试面试订阅4948Infer Interval Length From Mixed Boundary Data 8Let y solve y''=0 on [0,L] with y(0)=2.2 and y'(0)=0.4. If y(L)=3.4, what L is implied?数学简单数值题未尝试面试订阅4949Infer Interval Length From Mixed Boundary Data 9Let y solve y''=0 on [0,L] with y(0)=-1 and y'(0)=1.2. If y(L)=2, what L is implied?数学简单数值题未尝试面试订阅4950Infer Interval Length From Mixed Boundary Data 10Let y solve y''=0 on [0,L] with y(0)=4.5 and y'(0)=-0.5. If y(L)=3.9, what L is implied?数学简单数值题未尝试面试订阅4951Infer Domain Length From First Dirichlet Eigenvalue 11For y'' + lambda y = 0 on [0,L] with y(0)=0 and y(L)=0, the first positive eigenvalue is lambda 1 = (pi/L) 2. If lambda 1 = 4*pi 2, what is L?数学中等数值题未尝试面试订阅4952Infer Domain Length From First Dirichlet Eigenvalue 12For y'' + lambda y = 0 on [0,L] with Dirichlet endpoints, the first positive eigenvalue is lambda 1 = (pi/L) 2. If lambda 1 = pi 2/4, what is L?数学中等数值题未尝试面试订阅4953Boundary Eigenvalue 3For y'' + λ y = 0 on [0,1] with y'(0)=0 and y(1)=0, what is the 1-th positive eigenvalue?数学中等数值题未尝试面试订阅4954Boundary Eigenvalue 4For y'' + λ y = 0 on [0,1.5] with y(0)=0 and y(1.5)=0, what is the 2-th positive eigenvalue?数学中等数值题未尝试面试订阅4956Infer Poisson Forcing From Arc Maximum 13Let y solve y'' = -c on [0,1] with y(0)=0 and y(1)=0. If the maximum value of y on the interval is 0.25, what c is implied?数学中等数值题未尝试面试订阅4957Infer Poisson Forcing From Arc Maximum 14Let y solve y'' = -c on [0,2] with y(0)=0 and y(2)=0. If max y = 2.5, what c is implied?数学中等数值题未尝试面试订阅4958Infer Poisson Forcing From Arc Maximum 15Let y solve y'' = -c on [0,3] with y(0)=0 and y(3)=0. If the maximum value is 1.6875, what c is implied?数学中等数值题未尝试面试订阅4959Infer Poisson Forcing From Arc Maximum 16Let y solve y'' = -c on [0,1.5] with y(0)=0 and y(1.5)=0. If max y = 1.125, what c is implied?数学中等数值题未尝试面试订阅4961Shooting Method Diagnostic 18Why does the shooting method for a second-order BVP usually search over one missing initial slope rather than over an entire function?数学困难essay未尝试面试订阅