Notes in Classification of PDEs

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Status	Last Update	Fields
Published	05/03/2024	What is the order of \(u_{xx} + u_{xxtt} = 1\)
Published	05/03/2024	What is the order of \(u_x + u_{tt} = u^3 + x^5\)
Published	05/03/2024	What does it mean for a PDE to be homogeneous
Published	05/03/2024	What does it mean for a PDE to be inhomogeneous
Published	05/06/2024	State the recipe for hyperbolic PDEs
Published	05/06/2024	State the recipe for elliptic PDEs
Published	05/06/2024	What can the dot product be used to tell us?
Published	05/06/2024	What is the term \(Q(y_{1}, y_{2},..., y_{n})\) known as?
Published	05/06/2024	How to distinguish homogeneous and inhomogeneous PDEs?
Published	05/06/2024	What is a key feature of linear PDEs?
Published	05/15/2024	What is the defining quality of a quasi-linear PDE?
Published	05/06/2024	What is a defining property of semi-linear PDEs?
Published	05/06/2024	What is the PDE hierarchy?
Published	05/06/2024	What must be stated during the classification of PDEs?
Published	05/06/2024	How do we determine the type of a PDE in the form below? \(A(x,y)u_{xx} + 2B(x,y)u_{xy} + C(x,y)u_{yy} + D(x,y,u,u_{x}, u_{y}) = Q(x,y)\)
Published	05/06/2024	Which coefficients of a PDE are responsible for the "type" of the PDE (hyperbolic, parabolic,...)?
Published	05/06/2024	What happens if \(B^2 - AC\) changes sign in \(xy \) space?
Published	05/06/2024	State the recipe for parabolic PDEs
Published	05/06/2024	What can non-mixed, second order, semi-linear PDEs always be turned into?
Published	05/06/2024	How many initial conditions are required for a PDE with k time derivatives?
Published	05/06/2024	For a second order PDE where are linear combinations of the condition on \(u\) and its normal derivative required?
Published	05/06/2024	What are dirichet boundary conditions characterised by?
Published	05/06/2024	What are neumann boundary conditions?
Published	05/06/2024	What is the most general form for boundary conditions (including higher dimensional version)?
Published	05/06/2024	What are Robin Boundary conditions?
Published	05/06/2024	What do dirichlet and neumann conditions arise from?
Published	05/06/2024	What does a space-time diagram illustrate?
Published	05/06/2024	How is a periodic function defined mathematically?
Published	05/06/2024	What is the (prime) period?
Published	05/06/2024	How do we define an even function?
Published	05/06/2024	How do we define an odd function?
Published	05/06/2024	What is a piecewise continuous function?
Published	05/06/2024	What is a singularity?
Published	05/06/2024	When is a function classed as discontinuous at a point?
Published	05/06/2024	What is a periodic extension of a function?
Published	05/06/2024	What can we make a periodic function out of?
Published	05/06/2024	What is the definition of the inner (dot) product?
Published	05/06/2024	What three conditions must inner products satisfy?
Published	05/06/2024	How is the inner product defined for real functions?
Published	05/06/2024	When are two functions orthogonal?
Published	05/06/2024	For what fucntions does \(\int_{-L}^Lf(x)dx = 0\)?
Published	05/06/2024	How is a fourier series of a fucntion \(f(x): [-L,L] \rightarrow \mathbb{R} \) defined?
Published	05/06/2024	State dirchlet's theorem
Published	05/06/2024	If \(f:[-L,L] \rightarrow \mathbb{R}\) is an even fucntion, what value does \(b_{n}\) take in its fourier series?
Published	05/06/2024	If \( f:[-L,L] \rightarrow \mathbb{R}\) is an odd function, what value does \(a_{n}\) take in its fourier series?
Published	05/06/2024	What is a half range series?
Published	05/06/2024	State the sine series for a function defined in \([0,L]\)
Published	05/06/2024	State the cosine series for a fucntion defined in \([0,L]\)
Status	Last Update	Fields