Differential Forms in Mathematics: Uses & Applications

altcmdesc
Messages
64
Reaction score
0
I'm just wondering: in what field of mathematics are differential forms frequently used by professional mathematicians?
 
Mathematics news on Phys.org
If you mean proffessional mathematicians as in researchers then geometers.. in various areas of differential, algebraic, Riemannian, noncommutative geometry etc. or mathematical phycisists involved in general relativity and string theory, or differential topologists.. there might be other people that use them every now and then.. for example you could try doing e.g. stochastic analysis on manifolds in which case you'd probably need them
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

I What is this form of concavity called?
Replies
1
Views
1K
I Modeling Asteroid Rotation Using Quaternions: Seeking Guidance on Init
Replies
3
Views
1K
B What is a closed form solution?
Replies
1
Views
1K
I Integral and differential forms of field equations
Replies
16
Views
938
I What are the applications of inverses of vector functions?
Replies
17
Views
3K
MHB First Approach to Differential Forms
Replies
10
Views
4K
I What do applied mathematicians deal with?
Replies
4
Views
2K
MHB Degree of Freedom: Maths Definition & Differential Equations
Replies
1
Views
1K
I Can Intuition be Used in Mathematics to Overcome Limit Laws and Norms?
Replies
3
Views
2K
Classification of mathematical objects
2
Replies
68
Views
5K

Hot Threads

Recent Insights

Back
Top