Hi to all, i am new italian user of this FORUM and i have a problem for you.
I search for a function from a single variable, ( i.e. the time t), with this characteristics:
Let (V, h, P, dc) three value that i knows,( with V >= h), my function f(t) must to satisfy this condition:
1) In t=0 f(t=0)=P.
2) The integrals of f(t) from the interval t = [0,dc] must be equal to h.
3) The function must be integrable also over dc because as long as the dT time when is integral is equal to V.
4) In the t=[0,+inf] the function f(t) must be with a derivate f'(t)<0. She's not have a minimum or maximum on this interval, and in this interval she must be only positive.
5)The integral of f(t) in t=[0,+inf] must be obviously a function F(t) growing.
I try more function, also polynomial function like
f(t) = a1*t^n1+a2*t^n2+....+aq*t^nq ( general expression ) but i am not capable to estimate the polinomial coefficients (a1,...,aq) from my initial conditions.
If anyone have a solution to my research i am very gratefully with you, also if anyone want tell me a book where i can found a response it's ok for me, but i am not a mathematical.
Many thanks to all.