第 38 / 87 页
非代码面试题
显示 20 / 1721 道匹配题目
答题状态：未尝试未正确已正确
ID题目领域难度题型进度权限
3332Relative Decay of the Second Mode to the FirstIf two heat modes start with the same amplitude, \sin x and \sin(2x), what multiplicative factor relates the amplitude of the second to the first after time t?数学中等derivation未尝试面试订阅3333Same Mode, Larger Diffusion CoefficientFor the same initial mode \sin(2x), which system cools faster: \kappa=1 or \kappa=3?数学中等derivation未尝试面试订阅3334Long-Run Dominant Mode in a Two-Mode MixtureIf the initial condition is u(x,0)=5\sin x+\sin(4x) with zero boundary conditions, which mode dominates at long horizons?数学中等derivation未尝试面试订阅3335Time Needed for a Mode to Shrink by a Factor e^-1For the mode \sin(3x) evolving under u t=2u xx , after what time does its amplitude shrink by a factor of e -1 ?数学中等derivation未尝试面试订阅3341Projected Optimum Above the FloorMinimize (x-2) 2 subject to x\ge 0. Using the KKT form g(x)=0-x\le 0, find the optimizer x * and the optimal multiplier .数学简单derivation未尝试面试订阅3345Negative Target, Mildly Active FloorMinimize (x--2) 2 subject to x\ge -1. Using the KKT form g(x)=-1-x\le 0, find the optimizer x * and the optimal multiplier .数学简单derivation未尝试面试订阅3368Midpoint Rule Exact on a LineUsing a single-panel midpoint rule, approximate \int 0 4 (1+x)\,dx.数学简单derivation未尝试面试订阅3369Trapezoid Rule on a Symmetric Convex FunctionUsing a single-panel trapezoid rule, approximate \int -1 1 x 2\,dx.数学简单derivation未尝试面试订阅3370Midpoint Rule Misses a Symmetric BowlUsing a single-panel midpoint rule, approximate \int -1 1 x 2\,dx.数学简单derivation未尝试面试订阅3371Simpson on a CubicUsing one Simpson panel, approximate \int 0 2 x 3\,dx.数学中等derivation未尝试面试订阅3381Degree of Exactness of Two-Point GaussFor two-point Gauss-Legendre quadrature on [-1,1], what is the highest polynomial degree integrated exactly?数学中等derivation未尝试面试订阅3382Two-Point Gauss on x^2+1Using two-point Gauss-Legendre on [-1,1], approximate \int -1 1 (x 2+1)\,dx.数学中等derivation未尝试面试订阅3383Two-Point Gauss on x^4Using two-point Gauss-Legendre on [-1,1], what approximation do you get for \int -1 1 x 4\,dx?数学中等derivation未尝试面试订阅3391Central-Difference Richardson Upgrade 1A second-order central-difference estimate of f'(x) is 1.28 at h=0.2 and 1.22 at h=0.1. Using an O(h 2) Richardson extrapolation, what improved estimate do you get?数学简单derivation未尝试面试订阅3392Second-Derivative Richardson Upgrade 2A second-order estimate of f''(x) is 5.8 at h=0.4 and 5.2 at h=0.2. Assuming an O(h 2) truncation error, what Richardson-extrapolated estimate do you get?数学简单derivation未尝试面试订阅3393First-Order Extrapolation From Two Forward MeshesA first-order one-sided derivative estimate is 2.6 at h=0.1 and 2.45 at h=0.05. Assuming an O(h) bias, what extrapolated estimate cancels the leading error?数学简单derivation未尝试面试订阅3394Recover the Leading O(h^2) Error CoefficientSuppose D h = L + c h 2 + O(h 4). If D 0.3 = 4.18 and D 0.15 = 4.045, what is c?数学简单derivation未尝试面试订阅3395Recover the Limit of a First-Order SchemeA first-order approximation obeys D h = L + c h + O(h 2). If D 0.4 = 1.9 and D 0.2 = 1.6, what is the extrapolated estimate of L?数学简单derivation未尝试面试订阅3410Second-Order Forward Stencil at a BoundaryUse the second-order forward stencil (-3f(0)+4f(h)-f(2h))/(2h) with h=0.1, f(0)=1, f(0.1)=1.24, and f(0.2)=1.52. What derivative estimate do you get at 0?数学中等derivation未尝试面试订阅3416Entropy of a One-Heavy Rest-Uniform Source 1A discrete source has one special symbol of probability 0.5 and 4 other symbols sharing the remaining probability uniformly. What is the entropy in bits?数学简单derivation未尝试面试订阅