Comments on: BetterExplained Calculus Course Now Available (Public Beta)

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Wed, 22 Jan 2020 23:23:57 +0000

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By: navneet

navneet — Wed, 09 Apr 2014 20:29:26 +0000

hi khalid....,,, i have thought of a small intuitive idea on "laplace transform" need your suggestions on it....
Laplace transform are basically used to solve differential equation. we know that derivative of e^x =e^x the same function.... so if we can express a function f(t) in terms of e^x all the D operators will vanish... and we will get a simple picture ... something like watching a function wearing exponential glasses .. and how do we do that... by division...like how many 2 are there in 10 ??? =10/2=5 .... likewise how much (scaling factor) of e^xt in f(t)..??= f(t)/e^xt.... but since the function f(t) is extending in time ,so we have to integrate to get real expression of f(t) in e^xt. thus we get L{f(t)} =integration f(t)*e^-xt dt..
i also think the term "s" used to denote variable in laplace transform is misleading... it should be "sigma" (i don't know how to write its symbol :D :D)...
my textbook uses s>o ,s<k like terms where s is complex variable...and i have learned that complex variables do not have ordering property (i.e they can't be compared by equality or inequality ) and that confused me .... i even had a argument with the teacher....
need some intuitive lessons on complex integration and analytic functions....help to rescue

By: kalid

kalid — Tue, 11 Feb 2014 06:39:15 +0000

Hey Tim, thanks for the comment. Great point. There's something neat that a curve holds so much information in the derivative -- it's almost like a hologram (or a cell in a body) where any tiny portion contains information about the greater whole. The equation for each derivative can be used to create the parent curve.

By: Tim McGrath

Tim McGrath — Sat, 08 Feb 2014 18:21:19 +0000

K--

In learning the Maclaurin series, I was struck by how the description of a whole curve--or at least the seeds of that description--could be contained in something as nebulous as the nth derivative. It reminded me of fractal geometry, where the concept of self-similarity can be found on every scale, from the smallest to the largest.