query: When is separation of variables an acceptable assumption to solve a PDE?
positive_passages.docid: 119763
positive_passages.text: Why separation of variables works in PDEs?
negative_passages.docid: 53616
negative_passages.text: Boundary condition with spatial derivative is ignored by NDSolve
negative_passages.docid: 66919
negative_passages.text: When/why does the principle of least action plus boundary conditions not uniquely specify a path?
negative_passages.docid: 68896
negative_passages.text: Why should a solution to the wave equation be finite?
negative_passages.docid: 37337
negative_passages.text: Minimizing a functional with a free boundary condition
negative_passages.docid: 131786
negative_passages.text: Why are second order linear PDEs classified as either elliptic, hyperbolic or parabolic?
negative_passages.docid: 138766
negative_passages.text: Nondimensionalizing a differential equation
negative_passages.docid: 89863
negative_passages.text: 2D Heat equation: inconsistent boundary and initial conditions
negative_passages.docid: 58960
negative_passages.text: Time dependent Schrödinger equation with time independent potential and separation of variables
negative_passages.docid: 45363
negative_passages.text: Show that both mixed partial derivatives exist at the origin but are not equal
negative_passages.docid: 125026
negative_passages.text: When does order of partial derivatives matter?
negative_passages.docid: 4199
negative_passages.text: Evans PDE Problem 5.15: Poincaré inequality for functions with large zero set
negative_passages.docid: 23495
negative_passages.text: Replacing solution NDSolve
negative_passages.docid: 17501
negative_passages.text: Optimal resolution of a wave equation
negative_passages.docid: 31845
negative_passages.text: When not to treat dy/dx as a fraction in single-variable calculus?
negative_passages.docid: 43294
negative_passages.text: Solution to 2nd order PDE
negative_passages.docid: 130974
negative_passages.text: Complex valued 2+1D PDE Schrödinger equation, numerical method for `NDSolve`?