5/31/2023 0 Comments Infinitesimals in r![]() There is quite a bit (or a lot) of history behind it. What is an infinitesimal? What is a differential? – GlynĪs I noted earlier, the philosophical/logical questions surrounding the infinitesimal are, basically, beyond my expertise. If you are still interested in receiving a copy of my resume, please let me know. It’s been fun exchanging a bit of math with you. Sorry, if I have used too many words to express my thoughts. If we treat dy and dx as infinitesimal quantities such that dx≠0, and yet exceedingly close to zero, then we may treat dy/dx as a fraction. Now, granted ∆y/∆x is indeed a fraction as long as ∆x≠0, which latter condition is the case at all times, anyway. Or, sometimes we write dy/dx=1/(dx/dy) or in the chain rule case: dy/dx = (dy/du) (du/dx).Īnyway, getting back to the point, the symbol dy/dx represents – MORE THAN ANYTHING ELSE – the limit of ∆y/∆x, where ∆y = f(x+∆x) – f(x), as ∆x approaches zero, if the limit exists. As mentioned, this happens, for example, when we want to find the differential of a function f(x) as in dy=f’(x)dx. In fact, when it comes to practicality, we treat dy/dx as if it were a fraction. This area of discussion – as exciting, rigorous and important as it is – is beyond my expertise. But there is and has been a whole lot of philosophical/logical debate as to what an infinitesimal actually is. You can treat them as (infinitesimal) differentials. That’s my point! I did say I could say more. Why do you reject dy/dx as a fraction - a ratio of differentials? You said you could say more on the topic … Cheers, Glyn Hi Albert: I accept your history but not your math. Please feel free to ask further questions. But I will leave it at that at this point. This symbol was invented by Leibniz, the other contemporaneous inventor of the Calculus. So, the symbol dy/dx represents a single idea-the idea of the derivative. The symbol dy/dx represents the derivative of (the function) y with respect to x. The symbol dy/dx … does it represent a fraction or a whole symbol? Please feel free to let me know what you think about my proposal. I’d be glad to email you a copy of my resume. I wonder if I can be of use to your organization. Given my credentials, I can expertly and confidently teach many of the subjects (especially the mathematical ones) in your curriculum. I have two Masters degrees, one in Pure Mathematics and the other in Mathematical Finance, which is equivalent to Quantitative Finance or Financial Engineering. I have been a professor of mathematics for some twenty (20) years in a community college. ![]() ![]() It would be an honor to be associated with a winner such as your company. Your expertise and services, as laid out on your web site, are quite impressive.
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