Derivatives Articles

Tag Archive for: derivatives

deriitive5

The Pantheon of Derivatives – Important Theorems (V)

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Implicit Function Theorem [1] Jacobi Matrix (Chain Rule). Let ## (x_0,y_0 ) ## be a point in$$U_1 \times U_2 = \{x \in \mathbb{R}^k\,\vert \,||x-x_0||<…
deriitive4

The Pantheon of Derivatives – Lie Derivatives And Others (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…
deriitive3

The Pantheon of Derivatives – Sections, Pullbacks And Pushforwards (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,…
deriitive2

The Pantheon of Derivatives – Manifolds And Vector Fields (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…
deriitive

The Pantheon of Derivatives – The Direction (I)

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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…
variables

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…