- #1

Saladsamurai

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## Homework Statement

I am learning about PDE classification from a text on CFD (by Anderson). This section is not complete enough to be able to extend his example problems into more general cases. I read that to classify a

**system**of PDEs as being parabolic, elliptic, or hyperbolic, I need to do some crazy stuff with Cramer's rule. However, the examples that he has shown are 1st order PDEs and like I said, are *systems* of PDEs. Now I have been asked to show that the 1D heat equation is parabolic and I am not sure how to apply what I have learned since a) it is 2nd order and b) it is only 1 eqaution:

[tex]\frac{\partial T}{\partial t} = \alpha \frac{\partial^2 T}{\partial x^2} \qquad(1)[/tex]

## Homework Equations

Cramers rule

## The Attempt at a Solution

I thought that I could form a system by forming the total differential of T(x, t)

[tex] dT = \frac{\partial T}{\partial x} \,dx + \frac{\partial T}{\partial t} \,dt \qquad(2)[/tex]However I am not sure if this is helpful. Any hints?