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• 4. 下列何者為微分方程式 x²y''+3xy'+2y=0 的通解(general solution)? (A) y = [Acos(lnx)+Bsin(lnx)
• 5. 下列何者為非齊次微分方程式 y''−2y'+2y=的通解(general solution) ? (A) y =,其中A、B為常數 (B) y =,其
• 4.=？ (A)ln 2 (B)(C)(D)
• 2. What is the , for a non-ideal gas whose state can be expressed as the virial equation: (V=molar v
• 6. 下列的一階常微分方程,何者不符合正合(exact)微分方程式的定義? (A) (y² +3)dx+(2xy - 2)dy = 0 (B) (y+cosx)dx+(x+siny)dy
• 3. Which valence bond wavefunction for He is not a proper wavefunction because it violates the Pauli
• 4. We can construct three sp2 hybrid orbitals (i.e., φun = 1,2,3) as follows:φ1=a1(2s)+b1(2pz)φ2=a2(
• 5. 如圖(二)，求兩曲線y=x與y=-5x-x2所圍區域面積 =？(A)(平方單位) (B)(平方單位) (C)(平方單位) (D)(平方單位)
• 5. According to the selection rules in the atomic spectra, which of the following transition is NOT
• 7. 已知拉氏轉換(Laplace transform),反拉氏轉換(inverse Laplace transform)為下列何者? (A) (B) (C) (D)
• 6.f(x)=，則f(x)在下列哪一區間為增函數？ (A)(-1, 1) (B)(-∞, 1) (C)(0,∞) (D)(1,∞)
• 6. Two metal blocks with the same mass at different temperatures (T1 and T2) are contacting each oth
• 7.f(x)=sin (1-2x)，則=？ (A)(B) 0 (C)(D)
• 8. 已知 f(t) = 、g(t)=cos2t,求 L{f(t)*g(t)} =? [其中 f(t)*g(t)表函數f(t)與g(t)的褶積(convolution)] (A) (B)
• 9. 已知週期函數f(x)=1-3cos²x,其週期為π,傅立葉級數(Fourier series)可表示為 f(x) =,則下列敘述何者正確? (A) A₀ = 0 (B)= 0, n = 1
• 8.y=，則=？ (A)(B)(C)(D)
• 9. 已知g(2)=2，g'(2)=-1，g(3)=-2， g'(3)=2，且f(3x)=x2g(2x3)，則f'(3) =？ (A)-2 (B)(C)1 (D)3
• 10. 已知函數f(x)= |x|, -π＜x＜π,若函數f(x)的傅立葉級數(Fourier series)可表示為 f(x) = A₀ + A₁cosx + A₃cos3x + A₅cos5x+…
• 7. The first few spherical harmonics(θ, Φ) responsible for the angular parts of the hydrogen wavefun
• 10.f(x)=，則f(x)在x=π的切線斜率為何？ (A)-1(B)1-π (C) 1 (D)1+π
• 11. 若向量,則向量內積=? (A) 0 (B) 16 (C) 38 (D) 68
• 11.f(x)=，則f(x)在x=0的泰勒級數為何？ (A)(B)(C)(D)
• 8. An unnormalized wavefunction of the hydrogen atom is given by r2e(3 cos2 θ - 1). What are the thr
• 12. 已知三維空間中一向量= ＜2, 3,−2＞,其與座標軸(X,Y,Z)夾角分別為 α、β、γ,則 cosγ = ? (A) (B) 0 (C) (D)
• 12.=？[提示：利用羅必達法則(L'Hospital's Rule)] (A) 1 (B)(C) 0 (D) 不存在