Differential Operator in Matlab in 1 Dimension
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In common, the differential operation is defined as "dy/dx" which means differentiate y with respect to x and in matlab it's defined by "diff()". But how can we define "d/dx" which means differentiate with respect to x. Basically it shows an operation in 1 dimension rather 2. This definition is used in many fields such as Einstein theories and geometry. For example, If we have a scalar as [a1] in initial point and [a2] at the secondary position, d/dx denotes how much a2 changed with respect to a1. Does Matlab has a specific operator for this or any way that we can define it so that it can be used in higher order differential equations?
There was a post here:
But there was no correct answer.
I'd appreciate any opinions!
More Answers (1)
Chris on 12 Dec 2021
Edited: Chris on 12 Dec 2021
I'm not a math major so there's probably something technically wrong about this statement, but "d/dx" is essentially "dy/dx", replacing y with an arbitrary function of x. The only operators Matlab has by default are listed here. Most everything else is a function, which means the code it operates on likely needs to be enclosed in parentheses.
If you're using the symbolic toolbox, I believe the diff function should suffice for what you're asking. You could also define an inline function to describe exactly the derivative you want.
syms y(x,z) x z
y = x^2 + 5*z;
diff(y) % d/dx
diff(y,z) % d/dz
ddz = @(a) diff(a,z); % Inline d/dz
There is also the numerical (vs. symbolic) diff, which might work for the situation you describe:
h = 2; % Step size
aa = [5,10,14]; % Vector of values
ddx = diff(aa)/h