Jul 13, 2015 · The right question is not "What is a differential?" but "How do differentials behave?". Let me explain this by way of an analogy. Suppose I teach you all the rules for adding and multiplying …

The first answer is using so many other complex mathematical terms that it does not help in any way. Unless you are a genius in advanced linear algebra ( at that point, you would not even need a …

Jun 8, 2013 · How to distinguish linear differential equations from nonlinear ones? I know, that e.g.: $$ y''-2y = \\ln(x) $$ is linear, but $$ 3+ yy'= x - y $$ is nonlinear. Why?

Next semester (fall 2021) I am planning on taking a grad-student level differential topology course but I have never studied differential geometry which is a pre-requisite for the course. My plan i...

Jan 27, 2015 · Sometimes it arrives to me that I try to solve a linear differential equation for a long time and in the end it turn out that it is not homogeneous in the first place. Is there a way to see direc...

I was wondering if anyone could recommend some books for studying topics such as abstract manifolds, differential forms on manifolds, integration of differential forms, Stokes' theorem, de Rham

I know this is a subjective question, but I need some opinions on a very good book for learning differential equations. Ideally it should have a variety of problems with worked solutions and be ...

The differential form $\omega$ is a (smooth) collection of multilinear functions $\omega_p$ on each tangent space $T_pM$ at each point $p\in M$. The form $\omega$ is ...

Dec 16, 2022 · This question shows research effort; it is useful and clear

Feb 19, 2019 · This definition is from the book Neron Models. I want to understand what this definition is saying in the affine case. Suppose $X = \\operatorname{Spec} B, S ...