IVLE8: [MA1506] Final Exam

• Q1(a) Separable equation.
• Q1(b) Building model from the last sentense: "Assume that ...".
  
• Q2(a) cos^2 x - sin^2 x = cos 2x
• Q2(b) Second Order Linear ODE with constant coefficients (IVP).
  
• Q3(a) First-order ODE.
• Q3(b) Logistic model and Harvesting model, with their equilibrium point B/s and beta_2 respectively.
  
• Q4(a) Use the equation in the hint, and move y'' to left-hand-side, then integrate twice, with initial value y(0)=0 and y'(0)=0. (Answer: PL^3/(3EI)? )
• Q4(b) Unit step function, same as past-year papers.
  
• Q5(a) Partial fraction.
• Q5(b) Complicated Laplace...
  
• Q6(a) You can do Laplace one by one, or do them together. (Similar to Tutorial 9 Q1, and the two methods can be find in A./P. Leung's solution and Official solution.)
• Q6(b) Complicated Markov... But you can solve it like this (can finish in less than 3 min)
  http://www.mediafire.com/?yjwbwb2myvj.
  After you learnt Advanced mathematics, don't forget the primary mathematics.
  
• Q7(a) Remember: trace = sum of eigenvalues. So easy to get the last eigenvalue.
• Q7(b) Similar to the tutorial questions.
  
• Q8(a) You have seen this question in Mid-term and tutorial already.
• Q8(b) The easiest part of this paper.