I've already covered some differential equations (1st/2nd order, Cauchy/Euler's equation, Chebyshev's equation, Frobenius method, system of differential equations, Sturm Liouville problems) and basic Hilbert space theory (orthogonal projection, orthonormal systems, generalized Fourier series) Laplace and Fourier transforms . now i am trying to learn how to solve the 3 famous equations of mathematical physics : the heat, wave and Laplace equations in 1 and 2 dimensions with different types of initial/boundary condition.
I've checked some PDE books but they're too vast and for now since I don't have much free time I prefer to limit myself to those particular equations.
is there some books that focus mainly on those 3 equations ?
Have you tried Farlow? PRetty user friendly.
IF that is still too long, take a look at Kreyszig Engineering Mathematics. (I am familiar with the 5th edition, but they are all probably similar). Only a single chapter on PDEs and just covers the high spots with emphasis on the big 3. Might fit you well.