3. Solve    y" + 4y = r(t)

             r(t) = |t|, -π ≤ t ≤ π, r(t) = r(t + 2π)

(a)Find the steady-state solution

(b)  Solve u(x, t) (hint: you may want to transform the given heat problem by v(x, t) = u(x, t) - )

1. 相較於他們父母的世代，現今年輕人享受較多的自由和繁榮。

2. 但是在這個快速改變的世界中，他們必須學習如何有效地因應新的挑戰。

二 、英文作文 （ 占 2 0 分 ）說明︰1.依提示在「答案卷」上寫一篇英文作文。2.文長至少120個單詞（words）。提示︰你認為家裡生活環境的維持應該是誰的責任?請寫一篇短文說明你的看法。文分兩段，第一段說明你對家事該如何分工的看法及理由，第二段舉例說明你家中家事分工的情形，並描述你自己做家事的經驗及感想。

Kinmen Kaoliang is a strong liquor distilled from fermented sorghum. The principal supplier KKL Inc. is proud to keep strictly its tradition in kaoliang making, including the annual breeding of koji in open air. This allows random microbes to grow into koji, producing subtle variations in flavor of the liquor each year.As a young scientist willing to understand what underlies the variation in flavors of the Kaoliang, please elaborate a 3-year strategic plan to characterize and compare the composition of kojis from different years. If you wish, you may plan in studies of the sorghum and water as well. (40%)

You find a superior batch of koji that produces the most desirable traits of Kaoliang. How would you preserve this unique batch, so it could be used consistently and unlimited in the future? (25%)

Many Kinmen natives are renowned for their capacity of kaoliang consumption. Do you think there could be a special genetic background for higher alcohol tolerance in Kinmen natives? If yes, how would you test it? If not, what do you think could be the reason behind this general conception? (25%)

Kaoliang's unique aroma and intensity stands out from the broad spectrum of liquors. How likely do you think it could be to promote the culture of kaoliang to a foreign community, for example, to France? (10%)Please note, technical details are welcomed but not required for answering the above questions. Your thinking and strategic proposals are what we would like to understand. Do feel free to use diagrams or drawings to make explicit your ideas.

1. 求取該處土壤之有效覆土應力、初始孔隙比及過壓密比。(5%)

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