Articles for: derivatives

The Pantheon of Derivatives – Part V
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Important Theorems - biased, of course
Implicit Function Theorem [1]
Jacobi Matrix (Chain Rule).
Let ## (x_0,y_0 ) ## be a point in$$U_1…

The Pantheon of Derivatives – Part IV
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Lie Derivatives
A Lie derivative is in general the differentiation of a tensor field along a vector field. This allows several applications…

The Pantheon of Derivatives – Part III
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Some Topology
Whereas the terminology of vector fields, trajectories, and flows almost by itself suggests its origins and physical relevance,…

The Pantheon of Derivatives – Part II
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Generalizations Beyond ##\mathbb{R}## and ##\mathbb{C}##
As mentioned in the section on complex functions (The Pantheon of Derivatives - Part…

The Pantheon of Derivatives – 5 Part Series
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Differentiation in a Nutshell
I want to gather the various concepts in one place, to reveal the similarities between them, as they are often…

Some Conceptual Difficulties in the Roles of Variables and Constants
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1. Variables and Constants
When is a constant not a constant? When it varies.In the standard equation ##y=ax+b##, we are used to thinking of x and…