(D) Photon detectors were used in UV-Vis spectrophotometer while thermal detectors were used in IR spectrometer.(5分)

V. Essay Writing (30%)Scott Young is widely known for his remarkable learning projects. Most notably, he completed the equivalent of MIT’sfour-year computer science program in only one year without being enrolled as a regular student. Instead, he relied primarily onself-directed learning and online resources.Some people believe that formal classroom instruction remains the most effective way to learn, while others argue thatmotivated learners can achieve equal or even better results through independent study.Which approach do you think is more effective: formal classroom learning or self-directed learning? Explain your opinionwith specific reasons and examples. Your essay should be 200-250 words in length.

1. Find the solution by separating variables method. (20%) \[ \frac{\partial u}{\partial x} = \frac{\partial u}{\partial y} \] B.C.: \( u(0, y) = 2e^{-4y} \)

2. \( z^2 + z + 1 - i = 0 \), find the solution. (20%)

(a) Calculate the determinant for A (5 %)

(b) Calculate A5 -A =? (10 %)

(c) Calculate AT +A =? (5 %)

(a) y+xy′=0 (5%)

(b) y′′ + y = t , y(0) = 1 , y′(0) =0 (using Laplace transform method) (15%)

(a) Calculate the Laplace Transform of f(t) (10%)

(b) Calculate the Fourier Transform of f(t) (10%)Hint: The Heaviside function H(t) and shifted Heaviside function

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