1. Review of MA3264 Exam matters –Time: 25 April 2011, Wednesday, PM Paper (1:00—3:00pm) –Venue: Cinnamon Chua TP Hall (U-Town) –Style: open book exam; bring a calculator with basic function!! Some tips: –Read the problem, think a few seconds, then write! –All equations and formula developed in class can be used except that you are requested to derive them. –In general, no very tedious computation.

2. Exam paper 5 problems with 20 marks each Most of them are similar with those problems in homework and/or tutorials except the last one Distribution –Optimization model: 1 problem –Probabilistic & discrete model: 1 problem –Continuous model: 1 problem –Applications: 2 problems

3. Review Chapter 1 Introduction Required: –Models for the examples –Their solutions Not required: –Definition of model, model history –Procedure of modeling, model classification

4. Review Chapter 2 Optimization models Required: –One variable optimization: Model and solution –Multivariables optimization Model and solution, Lagrange multiplier method –Models for linear programming Not required: Simplex method

5. Review Chapter 3 Discrete models Required: –Build discrete models –Solutions –Steady states & asymptotically stable Not required –Proof of stability

6. Review Chapter 4 Continuous models Required: –First order ODE models –System of ODE models –Nondimensionlization –Solution of first ODE –Phase plane portrait –Steady states and asymptotically stable –Basic numerical methods – Euler methods

7. Review Not Required –Bifurcation –Runge-Kutta method –Solution structure, –Direction field –Existence & uniqueness theorem

8. Review Chapter 5 Probability models Required: –Build models –Transition matrix –Long term behavior Not Required –Biology applications

9. Review Chapter 6 Models for population Required –Malthus model, Logistic model, Harvest models –Lotka-Volterra model –Nondimensionization, solution, applications Not required –Age-dependence models –Delay models

10. Review Chapter 7 Models for waves and oscillations Required –Variable gravitational acceleration –Pendulum models –Mechanical vibrations –Solutions of 2 nd ODE Not required –Numerical methods

11. Review Chapter 8 Applications Required –Chemical reaction –Model for infection disease –Design a Pneumatic pump Not required –Michaelis-Menten theory

12. Thank & apology Thank you –For your cooperation –For your hard work –For you patience & understanding Apology –Typos in lecture notes –Some problems in homework are hard and tedious –Cannot finish more applications –……

13. Good Luck in your Final Exam!!!