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My choice would be Boundary Value Problems and Green's Functions by Ivar Stakgold. It have an introduction to distribution theory and them apply it to finding Green's functions.

It includes:

  • ODE
  • PDE with initial conditions
  • PDE with boundary conditions.

I found a preview here

Cheers

show/hide this revision's text 1

My choice would be Boundary Value Problems and Green's Functions by Ivar Stakgold. It have an introduction to distribution theory and them apply it to finding Green's functions.

It includes:

  • ODE
  • PDE with initial conditions
  • PDE with boundary conditions.

Cheers