1. MATH 175: Numerical Analysis II
Lecturer: Jomar Fajardo Rabajante
2nd Semester AY
IMSP, UPLB

2. COMPARTMENT MODELS

3. TANK-MIXING PROBLEM 60% A B 20%
Consider the following tanks: (amt of fluid per unit of time)
60% A B
20%

4. TANK-MIXING PROBLEM
We can model the flow of fluid by the following System of ODE: (Homogeneous and closed system)

5. TANK-MIXING PROBLEM 5L 60% A B 20% 4L
Consider the following tanks: (amt of fluid per unit of time) 5L
60% A B
20% 4L

6. TANK-MIXING PROBLEM
We can model the flow of fluid by the following System of ODE: (Non-homogeneous and open system)

7. B A

8. EXERCISE (laboratory assignment)
Consider two tanks where initially each tank contains 100 gal of fresh water. A salt solution with concentration 1 lb/gal is pumped into Tank 1 at the rate of 3 gal/min, and the solution in Tank 1 is pumped to Tank 2 at a rate of 4 gal/min. The solution in Tank 2 is pumped back into Tank 1 at a rate of 1 gal/min and also to the outside at a rate of 3 gal/min. Assume that initially each of the two tanks have 3 lb of salt. What is the system of ODE (IVP) that would represent the flow of salt.

9. 2S+E ES E+P REACTION KINETICS k1 k2 k–1 LAW OF MASS ACTION
the rate of a reaction is proportional to the product of the concentrations of the reactants.
Consider: k1 k2
2S+E ES
E+P
Reversible reaction
k–1

10. REACTION KINETICS
The reaction can be represented by a system of ODE:

11. MICHAELIS-MENTEN REACTION KINETICS
For your research pleasure: Determine the system of ODE that represents Michaelis-Menten Reaction Kinetics What is the solution to that system of ODE?

12. Other Compartment Models
Epidemics Model (SIR)
Rumor Model
These two were discussed in the laboratory.
Next meeting, we will start discussing Numerical Methods for solving ODEs.