Equations of love

This is really the ultimate. Copied word for word, symbol for symbol from my maths lecture notes.

excerpt:

We all know that many(most) relationships have their ups and downs. Let's try to model this fact.

Romeo love Juliet but Juliet believes in a more subtle approach and finds Romeo's excessive enthusiasm rather repulsive - the more he loves her, the less she likes him. On the other hand, when he loses interest, she fears losing him and begins to see his good side. Romeo is more straightforward; his love for Juliet increases when she is warm to him and decreases when she is cold. Let R(t) represent Romeo's feelings and J(t) Juliet's. We can model the lovers' feelings by

where a,b are positive constants and alpha and beta represent their feelings when they first meet. This is a system of simultaneous first order ODEs. In this case, the equations are linear, so it is easy to solve them. Put , as a TRIAL,

where lamda could turn out to be complex - if so, we will as usual interpret the exponential to mean that we are really dealing with sine and cosine functions. [ The final solutions for R and J must be real - the feelings are real, not complex!]

End exceprt

If only love were to be so simple to understand!

On a different note, I really really ought to be sleeping but I happen to chance upon on this one interesting piece of lecture material to share with those who are interested. Oh ya, I have maths lectures first thing in the morning erm..today. YAY!