電子科大版數(shù)理方程課后習(xí)題答案

1、一準(zhǔn)備（Preliminaries）A幾個(gè)常用的物理定律?單擺的數(shù)學(xué)模型單擺的數(shù)學(xué)模型:牛頓第二定律牛頓第二定律:F=maa—物體加速度物體加速度F—合外力合外力m—物體質(zhì)量物體質(zhì)量虎克定律虎克定律:(1)f=–kxf—彈力彈力k—彈性系數(shù)彈性系數(shù)x—彈簧伸長彈簧伸長(2)p=YuxY—楊氏模量楊氏模量ux—彈性體相對伸長彈性體相對伸長付里葉熱傳導(dǎo)定律付里葉熱傳導(dǎo)定律:Q—熱量熱量T—溫度溫度κ—熱導(dǎo)率熱導(dǎo)率牛頓冷卻定律牛頓冷卻定律:q

2、=k(u|S–u0)q—熱流密度熱流密度u0—外界溫度外界溫度u|S—物體溫度物體溫度B幾個(gè)有用的積分公式2()()()222(cossin)cosRe()sinIm()cossinsinsincoscosbixxbaabixxbaabixxbaabxxxbbaaabbbaaabbbaaacxeexixdxieexdxieexdxiexeexdxxxxxxdxxxxxxdxedxc????????????????????????????

3、?????????????????????????????????????C函數(shù)的Fourier展開是正交函數(shù)系??(21)()sin2nnXxxL???????????sin22mgdtdmL??dTQdx????????????xLnxXn?sin)((()())()xxttxxxxttxxxttTxuxuTuTuuLxguguu???????????P22ex2邊界條件(Boundaryconditions)00|0xx???端固

4、定，u()()()0ttxxLuFtSYuLtFt????????對端做受力分析Lu(Lt)O0|0xxLu????初值條件(initialcondition)u(xt)u(xdxt)xxdxLO0()()()()(1)xxtTxdxTxTxconstTxSYuuk??????受力分析水平方向注意(2)(00)0(0)uuLb??解一階ODE的邊值問題(boundaryvalueproblem)(1)(2)得0|tbuxL??0|0tt