110年 - 110 國立臺灣大學_碩士班招生考試_農藝研究所生物統計學乙組:工程數學(I)#100772

(a) Write down the system of different equations for the population of lynx and hare using the assumptions above. (5%)

(b) For α = 3,β = 2,γ = 2, ε =1, determine the type and stability of each critical point (10%)

(c)With initial hare population of k, find the population of the hare versus time when the initial lynx population is zero. (5%)

2. Solve the non-homogeneo us ODE (10%)

3. Solve the non-homogeneous ODE (20%),

(a) Formulate the transition probability equations of this Markov chain. (10%)

(b) Calculate the steady state of the population distribution. (10%)

(c) Plot the eigenvectors, and steady state of transition probability matrix on the figure. (10%)

5. Solve the two-dimensional wave equation in polar coordinates. Using, the method of separation of variabies, determine solutions that are radially symmetric. (20%)

110年 - 110 國立臺灣大學_碩士班招生考試_農藝研究所生物統計學乙組:工程數學(I)#100772

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