The differential-algebra tag has no wiki summary.
64
votes
6answers
4k views
How can you prove that a function has no closed form integral?
I've come across statements in the past along the lines of "function $f(x)$ has no closed form integral", which I assume means that there is no combination of the operations:
addition/subtraction
...
4
votes
0answers
33 views
If $D:A\to A$ is a derivation, what can be said about the range of $D$?
What can be said about the relation between the domain and range of a derivation as a function?
If $A$ is the domain, any space of functions, what does $D(A)$ look like, where $D$ is a derivation? ...
3
votes
3answers
318 views
What is the connection between Grothendieck's Differential Operators and Hochschild Cohomology
For a given commutative algebra $A$ over a field $\mathbb{K}$(with char=0) the algebra of differential operators on $A$ is the set of endomorphism $D$ of $A$ such for some $n$ we have that for any ...
3
votes
1answer
70 views
Trace and Norm maps on differential extensions
I'm working through a proof which is rather algebraic, and my abstract algebra is probably only basic to intermediate. I have a differential extension $E/K$ of a differential field $K$, and the proof ...
3
votes
2answers
229 views
Determination of inverse laplace transform using primitive functions
In How can you prove that a function has no closed form integral?, the accepted answer points to http://www.sci.ccny.cuny.edu/~ksda/PostedPapers/liouv06.pdf where one can find a corollary by Liouville ...
2
votes
1answer
91 views
Confusion about commutative differential algebra
Here we read the following
Let $(A,d)$ be a commutative differential graded algebra such that $H^0(A,d)=\mathbb Q$, $H^1(A,d)=0$ and $\dim H^p(A,d)<\infty$ for each $p$. There exists then a ...
2
votes
1answer
161 views
Introduction to Elementary Functions
I'm looking for an introductory text on algebraic treatment of elementary functions. Really short and easy-going. Video lectures are even better.
I want to learn basic ideas (i.e. definitions) behind ...
1
vote
0answers
59 views
Algebras vs. rings in algebraic differential calculus
Vector fields (and differential operators of higher order) on a real manifold are often defined in terms of $\mathbb{R}$-algebra $C^\infty(M)$. However, it is not clear to me why is the ...
0
votes
1answer
73 views
“fluent” functions
In an old mathematics book (Ritt, 1948, p.5) I have come across the notion of "monogenic analytic" and "fluent" functions. These are complex valued functions. Has anyone heard of these terms before? ...
0
votes
3answers
79 views
What is $\lim\limits_{x\to 0}x^2\cos(2/x)$?
I have to evaluate
$$\lim_{x\to 0}x^2\cos(2/x)$$
using one or more of the limit laws.
I am using the multiplication law and I am wondering if I am on the right track here?
I have split it up to: ...
0
votes
0answers
90 views
Exercises in Differential Galois theory
I hope not to re-open a pre-existing question.
I'm stuck into a course about Differential Galois Theory: pretty interesting, but I'm not able to solve any exercise being epsilon-far from trivialites ...
0
votes
0answers
321 views
Matrix differential equation: Putzer, exp(tA), x'=Ax, basis vector
I need a lot of help to this problem ... please solve this step by step and I will be grateful :-).... thanks :-)
$$ A=
\left(\begin{matrix}
-1 & 0 & 1\\
3 & 2 & -1\\
...
