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Anyone wants to try answering that?
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yeah ....second order differential (I assume you mean second derivative ) physically represents acceleration of change
second order differential equation models the dynamics (i.e. the WAY it is changing, stability in respects to he eigenvalues in the homogeneous equation) of a physical system.Last edited by RevolutionThroughReason; 07-10-2012, 02:18 AM. Reason: added more explanation for educational value[QUOTE=Afghanistan2010;658085][B]He is no different [COLOR="Red"]than us[/COLOR][/B],[B]he[COLOR="Red"] blindly believes [/COLOR]in the words [COLOR="Red"]of other men[/COLOR][/B],:[/QUOTE]
2010 Admitting he's a blind believer not in God, but what other men says. -
Like dx/dt is velocity v. . . First order rate of change of x which represents lets say displacement in physical sense
Then dv/dt is acceleration a . . . The Second order or rate of change of v
Each with respect to time.Comment
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Toramana here is an answer in layman terms
first order: measures rate of change
second order: measures rate of (rate of change)
e.g.,
x^3 is an odd function
d/dx (x^3) = 3x^2 will give you a parabola
d/dx ( d/dx (x^3) ) = 6x will give you a straight line.
But perhaps this much you already know. Question can be why do you need it? Where is it used? Being a computer science person, I will give you a CS example. You might be familiar with the laplace filters in image processing. You can use it for blurring an image. The way it works is by taking an input mask (which is a sum of a second derivative w.r.t x and a second derivative w.r.t y), and you multiply (correct word = convolve) this filter with the original image. Another example from the same area is edge detection. What is an edge? Don't you think it is the rate of change between two points in an image? If you apply a second derivative to this variation, just identify the zero-crossings and you have your edge :-)
This is also a key component in vector calculus so many examples can be given from world of physics also.Comment
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If you mean
v = dx/dt
a = dv/dt = d²x/dt²
which means,if you derivate the speed,you get the acceleration and if you derviate twice the route you get the acceleration aswell.High achievement always takes place in the framework of high expectation.
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I think toramana knows the acceleration velocity concept fellas, he might after something else here.
Not dabbling in hamiltonian mechanics are you toramana ? stay away from that stuffIt's enough that I know, Our time had a home, In your heart..Was a place..But the glass always breaks..Comment
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Yes, agree with that definition (the most general) i.e., approximates change in "rate of change" ....(very crude eg) My salary was 100 dollars at the end of 2010---got 5 dollars raise in salary for 2011, 8 dollars raise for 2012, 7 dollars 2013,---Originally posted by RevolutionThroughReason View Post
-first deriv
(avg) change in salary over 3 years ---((105-100)+(113-105)+(120-113))/3
-second deriv
(avg) change in salary-raise over 3 years---- ((8-5)+(7-8))/3Last edited by Toramana; 07-10-2012, 06:53 PM.Comment
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Actually, am studying Riemannian geometry in the hope if I could apply it where I want to. But every math is fascinating---I am studying a book "The historical development of the calculus"---nice book describing as how various ideas in calculus originated.Originally posted by Talal View PostLast edited by Toramana; 07-10-2012, 09:40 PM.Comment
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Originally posted by Toramana View Post
really? ....My area of interest right now is Differential Geometry (which Riemannian Geometry is heavily influential as it introduced the concept of Manifolds).
Mainly my interest is to understand spatial curvature of objects over large distances. But I m also getting introduced to synthetic differential geometry now which deals primarily with the study of shape operators and curvature without a metric space. This is fascinating; it employs more Abstract Algebraic concepts of set relationships and topology than Riemannian stuff; sometimes it's hard to wrap my head around how exactly it can be "Differential" Geometry when we are not dealing with metric spaces.[QUOTE=Afghanistan2010;658085][B]He is no different [COLOR="Red"]than us[/COLOR][/B],[B]he[COLOR="Red"] blindly believes [/COLOR]in the words [COLOR="Red"]of other men[/COLOR][/B],:[/QUOTE]
2010 Admitting he's a blind believer not in God, but what other men says.Comment
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Originally posted by Afghanistan2010 View Post
and if you derivate twice the route? what are you saying? LOL[QUOTE=Afghanistan2010;658085][B]He is no different [COLOR="Red"]than us[/COLOR][/B],[B]he[COLOR="Red"] blindly believes [/COLOR]in the words [COLOR="Red"]of other men[/COLOR][/B],:[/QUOTE]
2010 Admitting he's a blind believer not in God, but what other men says.Comment
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Thanks for the clue. I want to study RG and related topics as deeply as time allows me. Could you recommend a good book on differential geometry and differential synthetic geometry? Shape operators etc. are the things I am interested in.Originally posted by RevolutionThroughReason View Post
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Originally posted by Toramana View Post
well honestly; for synthetic differential geometry; I highly recommend you tackle fundamentals of theoretical mathematics first like Abstract Algebra , topology Algebraic Topology first or it will seem like an alien language; in fact it almost is.
Well I'm not sure which level of differential geometry you are but these are the books I started with for Classical Differential Geometry
Elementary Differential Geometry by Pressley
Elementary Differential Geometry by O'Neill
Lectures on Classical Differential Geometry by Struik
all these are amazing
now for more advanced stuff which emphasizes Riemannian Geometries and Manifolds
Differential Geometry of Curves and Spaces by DoCormo this is THE BEST book but it is advanced, Try one of the earlier books first
Comprehension Introduction to Differential Geometry by Spivak is amazing, but it's extremely rigorous; and there are volumes; I don't own it, but I have seen it it is very expensive.
Differential Geometry - Curves-Spaces-Manifolds by Kuhnel, I used this one for my course, it's ok but I like DoCormo better.
for Synthetic Differential Geometry; I don't have any specific book; just various pamplets people who are experts in that field send to me.[QUOTE=Afghanistan2010;658085][B]He is no different [COLOR="Red"]than us[/COLOR][/B],[B]he[COLOR="Red"] blindly believes [/COLOR]in the words [COLOR="Red"]of other men[/COLOR][/B],:[/QUOTE]
2010 Admitting he's a blind believer not in God, but what other men says.Comment
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Those are some solid books. You seem like you know your stuff.Originally posted by RevolutionThroughReason View Post
Even Adobe Photoshop can't change me.
A line[Durrand line] of hatred that raised a wall between the two brothers -Hamid Karzai
For generations, the Hindus of India prayed for deliverance from "the venom of the cobra, the teeth of the tiger and the vengeance of the Afghan."
The men of Kábul and Khilj also went home; and whenever they were questioned about the Musulmáns of the Kohistán (the mountains), and how matters stood there, they said, "Don't call it Kohistán, but Afghánistán; for there is nothing there but Afgháns and disturbances." Thus it is clear that for this reason the people of the country call their home in their own language Afghánistán, and themselves Afgháns. The people of India call them Patán; but the reason for this is not known. But it occurs to me, that when, under the rule of Muhammadan sovereigns, Musulmáns first came to the city of Patná, and dwelt there, the people of India (for that reason) called them Patáns—but God knows!
-Ferishta, 1560–1620Comment
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truthfully I have barely touched the tip of the ice berg .....when I first started I wasn't even interested, but then I met a guy and asked him what he was doing his research on and I got swayed into it.Originally posted by Admin Khan View PostThose are some solid books. You seem like you know your stuff.[QUOTE=Afghanistan2010;658085][B]He is no different [COLOR="Red"]than us[/COLOR][/B],[B]he[COLOR="Red"] blindly believes [/COLOR]in the words [COLOR="Red"]of other men[/COLOR][/B],:[/QUOTE]
2010 Admitting he's a blind believer not in God, but what other men says.Comment
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