The gradient of time is in a physics mind the "time''s elasticity in the space referential". This analytic method allows us to solve partials differentials equations as these of Navier/Stokes in fluids mechanics , this of Schrodinger in quantum mechanics , this of Fourier about heat propagation ,or these of Maxwell and many others... Our technic gives to physicists, some advantages in the elaboration of the good physics theories ,which explain each equation''s solution. In effects , all partials differentials equation have "waves" as solutions. The gradient of time let us believe that, all wave is in space and time , a progressive sum of dilatations and contractions of our universe. This book has been written , to present and proove that the gradient of time in its theory and principle , is a good and right technic to solve in a physics and in a mathematics minds , all the partials differentials equations.