All Questions
10 questions
54
votes
13
answers
90k
views
Good differential equations text for undergraduates who want to become pure mathematicians
Alright, so I have been taking a while to soak in as much advanced mathematics as an undergraduate as possible, taking courses in algebra, topology, complex analysis (a less rigorous undergraduate ...
26
votes
9
answers
14k
views
Graduate ODE textbook
Suppose that a hypothetical math grad student was pretty comfortable with first-year real variables and algebra, and had even studied some other things (algebraic geometry, Riemannian geometry, ...
15
votes
5
answers
12k
views
Beginners text on calculus of variations
I want to begin learning Calculus of Variations. What texts would MathOverflow recommend? Amazon shows up quite a few options.
I work on Machine Learning, and that where I intend to apply this.
...
7
votes
1
answer
494
views
Carleson's lectures at UCLA
It seems that Professor Lennart Carleson gave a series of Lectures at UCLA in 1985. For example, one could find several mentions about these lectures in the book by Garnett & Marshal (see for ...
- 747
7
votes
3
answers
2k
views
Collections of examples and counterexamples in (real, complex, functional) analysis, ODEs and PDEs
What books collect examples and counterexamples (or also "solved exercises", for some suitable definition of "exercise") in
real analysis,
complex analysis,
functional analysis,
ODEs,
PDEs?
The ...
user60665
6
votes
1
answer
309
views
Survey paper on isoperimetry
I am searching for a comprehensive survey article (or more different articles) on the subject of isoperimetric problems from ancient Greece to modern mathematical physics. Could you point out some ...
user60665
5
votes
0
answers
329
views
Could there be something like a Grzegorczyk hierarchy in Analysis?
My most prevalent interest in mathematics has always been hyper-operators. I first learned about them when I was in highschool, and quite frankly, they amazed and dazzled me. For those who've yet to ...
user78249
3
votes
2
answers
579
views
More recently published comprehensive reference on inequalities in the spirit of Hardy-Littlewood-Pólya
Is there a comprehensive reference book on inequalities in the
spirit of the one written by G.H. Hardy, J.E. Littlewood, and G. Pólya(*), but more up-to-date (i.e., published in more recent years and ...
user60665
3
votes
0
answers
141
views
Partially BV vector fields and renormalization
Why does the approach used to prove Theorem 4.1 in the paper by Le Bris and Lions on Renormalized solutions of some transport equations with partially $W^{1,1}$ velocities and applications not work ...
user123672
2
votes
2
answers
317
views
Concrete example of BV function $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative
What are examples of two BV functions $u:\mathbb{R}^2 \to \mathbb{R}$ with singular derivative?
More precisely, I'd like to see an example (and a plot using Mathematica or Matlab) of
a function
$$...
- 839