What do I need to know before studying PDE?

[pyfgcr]

Hi, I'm really interesting of PDE, but I don't really know what I have to learn before start with PDE.
I have learn multivariable calculus and ODE, but are there something need to learn before PDE?
Thanks in advance.

 

[jedishrfu]

How about vector analysis? PDEs appear in a lot vector analysis problems path, surface volume inegrals, Javier stokes eqn...

 

[pyfgcr]

I have bought a PDE book by Evan and I don't understand even the notion and inequalities in the appendix such as measure, support, Lipschitz continuous, convolution, norm,... and many other things.
I wonder where I can learn all this stuff.

 

[jedishrfu]

what about the beginning chapters? I wouldn't judge a book by reading what's in the appendix. That stuff is there in case you need it and isn't a prerequisite to understanding PDEs.

 

[MathematicalPhysicist]

For basic PDE You need to know basic Functional Analysis (i.e for stuff like Fourier coefficients in problems of Sturm-Liouville in separation of variables). Other than that also ODE and Multivariable and Vector calculus are essential.

The more advanced you get in the book the more you need to know more results from Analysis. It's up to you if you want to understand the methods to understand the theory behind them. It's a long road, that's for sure...

 

[Unstable]

You should ask yourself what is your interest on PDEs? Theoretical properties, numerical issues, modeling of e.g. biological phenomena, … ?

What was your interest when studying ODEs?

 

[sokrates]

Pick a practical PDE, like one of those already suggested ( say, Poisson Equation in 2D)

and try to solve it numerically.

Yes, numerical attempt will be like designing an experiment and you will learn a lot along the way.

Once you solve it numerically, in order to make sure you did correctly, try to get an analytical 1D solution with no y-variation and see if you solved it correctly.Thing is, I had been educated for more than 10 years in different schools, in different contexts, but when I had to solve a PDE correctly,

that's when I learned all that is necessary. My 2 cents. Good luck.

 

[Unstable]

That’s it!

People, especially pure math orientated have to understand that Des (ODE, PDE, DDE,…) are more than just objects to study from a mathematical point of view. Unfortunately, until now most math courses about Des are about theoretical properties. No doubt, this is important, but these guys (most of them are really not able to this) have to show students what one could do with these Des.

I am talking to you as a math PhD.

To start with Des either from a numerical point of view or a modeling point of view, it is much more important in order to understand the power of this tool than just concentrating on mathematical properties.

To understand why the solution of an ODE exists and is unique is important for the examination but it has nothing to do with the real value of an ODE.

As an example, I know money exists and it is important to have, but what you could do with it is a complete different field. The same with Des….

 

[Number Nine]

That’s it!

People, especially pure math orientated have to understand that Des (ODE, PDE, DDE,…) are more than just objects to study from a mathematical point of view. Unfortunately, until now most math courses about Des are about theoretical properties. No doubt, this is important, but these guys (most of them are really not able to this) have to show students what one could do with these Des.

I am talking to you as a math PhD.

To start with Des either from a numerical point of view or a modeling point of view, it is much more important in order to understand the power of this tool than just concentrating on mathematical properties.

To understand why the solution of an ODE exists and is unique is important for the examination but it has nothing to do with the real value of an ODE.

As an example, I know money exists and it is important to have, but what you could do with it is a complete different field. The same with Des….

Eh, in my experience most courses/texts devote so much time to numerical methods and applications that student's walk away without understanding how to solve any equation that doesn't precisely match one that they're seen before. If anything, intro courses should be far more theoretically oriented.

 

[Unstable]

Wow… that is different to my course… I learned only theoretical stuff!

Nevertheless, I want to say that I am an expert in ODE modeling with biological background and we have to go back to the basics.

The traditional ideas of DES are what?

 

[Unstable]

EDIT:

DEs are the perfect example where theoretical math fails (for students and most users, don't get me wrong theoretical stuff
is important but should not be only thing)

The question is not why my car is red and has 4 wheels (and not 7 maybe), the question is why I could drive from A to B with this (maybe perfect) car under several circumstances!