Differentiation cheat sheet
This post serves as a cheat sheet for differentiation. It just includes the most basic of the rules to be remembered when computing derivatives. First a little reminder on the notation being used in differentiation. Leibniz’s notation for the first derivative of a function f(x) is Newton’s notation for the first derivative of a function [...]
On critical points of functions
There is a really large number of applications in engineering, in which the identification of critical points of a function is crucial for the analysis and modeling of a process or a system. Generally, one may identify three kinds of critical points, that is (a) maxima, (b) minima and (c) saddle or stationary inflection points. [...]
Functions and graphs primer
A function is a rule that maps each of the elements in a domain to one and only one element in a range. The set of all possible elements in the input is the domain D of a function; the set of all possible elements in the output is the range R of a function. [...]
Handy & powerful differentiation...
Formally stated, the derivative of a function of the form with k a constant and with respect to an independent variable x, is simply, I find this to be extremely handy in all cases. Consider the simple case in which, In the same way, In a more complex example, In an even more complex example, [...]
A short note on functionals, conserva...
The thing starts with invariance, conservation and symmetry… Invariant is something that is unchanged by a coordinate transformation. Conserved is something that is unchanged by a process within a given coordinate system. Symmetry could be considered a broader property of some ‘universe’ in which some entity of interest remains the same under a specific operation. [...]