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- What actually is a differential? - Mathematics Stack Exchange
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 around, but none o
- What exactly is a differential? - Mathematics Stack Exchange
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 adding and multiplying rational numbers Then you ask me "But what are the rational numbers?" The answer is: They are anything that obeys those rules Now in order for that to make sense, we have to know that there's at least
- Linear vs nonlinear differential equation - Mathematics Stack Exchange
2 One could define a linear differential equation as one in which linear combinations of its solutions are also solutions
- Proving uniqueness of solution of a differential equation
Proving uniqueness of solution of a differential equation Ask Question Asked 3 months ago Modified 3 months ago
- 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
- The logic subtlety behind solving differential equations.
The basic logic of solving ordinary differential equations is then that to derive certain conditonal equations from a starting equation, where the conditions are imposed on the domain of the variables, the slogan being: “If I start with something that looks like this here, I also end up with something that looks like this there ” and
- What is exponential map in differential geometry
It's worth noting that there are two types of exponential maps typically used in differential geometry: one for Riemannian manifolds, which you refer to in your question, and one for Lie groups, which Spivac is referring to The expression $\exp (u)\exp (v)=\exp (u+v+ [u,v]+\dots)$ is known as the BCH formula and applies specifically to Lie groups
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