Is there an ordinary differential equation with no solutions? Precisely, I mean 1) not in the IVP context, just a simple ODE without IVP conditions, 2) not an ODE with complex solutions but no real
Boundary value problems and integro-differential equations lie at the heart of modern applied mathematics, providing robust frameworks to model phenomena across physics, engineering and beyond. These ...
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A differential form is (technically) a function that we can calculate value at a point and AFAIK it has nothing to do with infinitesimals nor tends to anything. A course in precalculus, calculus, or even real analysis almost never gives an answer to "What is dx?". It is only until differential geometry, one gets to learn what it is. One should not learn these from Wikipedia but from a ...
derivatives - What is the difference between a differential and a ...
Anyone who sees calculus in application is likely to encounter both derivatives and differentials. The two concepts have confusingly similar notation. For that reason, this post is a very important contribution.