Chapter 6: Parameter estimation #

1. Solve the following ODE in MATLAB using ode45 and report the value of \(y(t=10)\) . Report 4 significant digits of your answer.
   \[ \frac{dy}{dt} = \frac{y+t^2-2}{t+1}; y(0) = 2 \] Ans: 69. 25

2. Using fminsearch in MATLAB, find the minimum of the following function. \[ f(x,y) = x^2y - 2xy^2 +3xy +4 \] Use \([-1.2, 1]\) as the initial guess. Report 2 significant digits of all the values.

   • Report the minimum value.
     Ans: 3.5
   • Report the value of x_min.
     Ans: -1.0
   • Report the value of y_min.
     Ans: 0.5

3. I have a measured set of data points as given in the following table.

   x	y
   500	0.05
   550	0.1
   600	0.2
   650	0.4
   700	0.8

   It is known that y and x are related according to the equation: \(y=A \exp(\frac{−B}{x})\) . Which of the following values of the parameters fit the measured data points well?

   a. A = 1000, B = 5000
   b. A = 900, B = 4500
   c. A = 5000, B = 5500
   Ans: a