2015年7月13日 · 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 …

2016年11月3日 · 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. …

2018年7月21日 · 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 …

See this answer in Quora: What is the difference between derivative and differential?. In simple words, the rate of change of function is called as a derivative and differential is the actual …

2013年3月18日 · Please explain me the idea of differentiating differential forms (tensors). Example: compute d(xdy + ydx) The answer is known, we should have 0. What's the rule?

2017年11月18日 · I'm taking an undergraduate differential geometry class, and because either because the professor has chosen to forgo rigor (as a background in analysis isn't required …

2019年10月3日 · I am a bit confused about differentials, and this is probably partly due to what I find to be a rather confusing teaching approach. (I know there are a bunch of similar questions …

2015年9月8日 · Spivak's Comprehensive introduction to differential geometry is one source I remember. .. Or maybe try guilleman and pollack's differential topology, or even Marsden and …

2018年3月6日 · The voltage of a capacitor can be described with the differential equation $ \frac {du} {dt} + \frac {1} {RC} u = 0$ where the voltage is u (t) at the time t. Solve the differential …

Say I take an embedded submanifold of $\\Bbb R^n$, like the sphere. Any differential form on $\\Bbb R^n$ can be restricted to the sphere. My question is this: is any differential form on the …