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- What is a differential form? - Mathematics Stack Exchange
69 can someone please informally (but intuitively) explain what "differential form" mean? I know that there is (of course) some formalism behind it - definition and possible operations with differential forms, but what is the motivation of introducing and using this object (differential form)?
- real analysis - Rigorous definition of differential - Mathematics . . .
What bothers me is this definition is completely circular I mean we are defining differential by differential itself Can we define differential more precisely and rigorously? P S Is it possible to define differential simply as the limit of a difference as the difference approaches zero?: $$\mathrm {d}x= \lim_ {\Delta x \to 0}\Delta x$$ Thank you in advance
- Find the solution of the differential equation $xdx+ydy+\frac {xdy-ydx . . .
Further, one of the newly formed differential equations is exact and the other one is not, and then solving each of those newly formed differential equations and then adding in order to equate them to an arbitrary constant and claiming that to be the required solution of the given differential equation to avoid such erroneous results solutions
- How to derive a differential equation of an ellipse
I am quite new to differential equations and derivatives I want to derive an differential form for equation of an ellipse If i start with an ordinary ellipse equation \\begin{equation} \\frac{x^2}
- Newest differential-geometry Questions - Mathematics Stack Exchange
Differential geometry is the application of differential calculus in the setting of smooth manifolds (curves, surfaces and higher dimensional examples) Modern differential geometry focuses on "geometric structures" on such manifolds, such as bundles and connections; for questions not concerning such structures, use (differential-topology) instead Use (symplectic-geometry), (riemannian
- Why does the differential solid angle have a $\sin\theta$ term in . . .
But I'm puzzled why you need to multiply the differential solid angle by $\sin\theta$ It would seem it's because the chunks at the north south pole are "worth less" than the chunks at the equator
- Understanding the differential $dx$ when doing $u$-substitution
I just finished taking my first year of calculus in college and I passed with an A I don't think, however, that I ever really understood the entire $\\frac{dy}{dx}$ notation (so I just focused on
- ordinary differential equations - What exactly is steady-state solution . . .
In solving differential equation, one encounters steady-state solutions My textbook says that steady-state solution is the limit of solutions of (ordinary) differential equations when $t \rightarrow \infty$
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