PDE or differentiable manifolds?

[mathmari]

Hello!

I am doing my master in the field Mathematics in Computer Science. I am having a dilemma whether to take the subject Partial differential equations- Theory of weak solutions or the subject differentiable manifolds.

Could you give me some information about these subjects?? (Wondering)

What knowledge is required?? (Wondering)

 

[Fallen Angel]

Hi mathmari,

I don't really know what you could do in PDE's but I had a course called "differentiable manifolds" also, at that course I was supposed to have two linear algebra courses, two differential calculus course, two integral calculus courses, introduction to ODE's, introduction to PDE's, topology, curves and surfaces geometry and a course called "Global theory of surfaces".

In fact I don't remember too much about that course but I remember it was really interesting. I was taught about "inmersions and submersions" (direct translation from Spanish ), bundles, integral curves, local flows, lies derivatives , Frobenius theorem (do not confound with Rouche-Frobenius) and this kind of things.

As always it will depend on who, what and how your professor explain but in my case I remember it was a hard course. (Which is obviously good :p)

 

[mathmari]

I don't really know what you could do in PDE's but I had a course called "differentiable manifolds" also, at that course I was supposed to have two linear algebra courses, two differential calculus course, two integral calculus courses, introduction to ODE's, introduction to PDE's, topology, curves and surfaces geometry and a course called "Global theory of surfaces".

I haven taken subjects like multivariable analysis, differential geometry, ordinary differential equations, linear algebra, introduction to ODE/PDE, etc.

But I haven't taken subjects like topology...

Do you think that these subjects are a good backround for the subject "Differentiable Manifolds" ?? (Wondering)

 

[Fallen Angel]

Hi mathmari,

I just told you what I was supposed to know, of course differential geometry is essential but topology ... I just remember to have used a couple of simple facts at the begginning and maybe some isolated theorem in advance, I mean, if you know the basics you don't need a course on topology, but probably will need to read about some result you didn't know (or maybe not).