Useful math - Revision history

Apm: wikipedia: Functional derivative

2023-09-19T11:27:34Z

wikipedia: Functional derivative

← Older revision		Revision as of 13:27, 19 September 2023
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	Maybe the most powerful weapon against '''dependency hell''' and all its various workaround hacks.		Maybe the most powerful weapon against '''dependency hell''' and all its various workaround hacks.

	== Notes ==		== Notes / Misc ==

	* Not to confuse "Holomorphic function" and "Holonomic constraints"		* Not to confuse "Holomorphic function" and "Holonomic constraints"

			* Wikipedia [[https://en.wikipedia.org//wiki/Functional_derivative Functional derivative]]

	== Related ==		== Related ==

Apm: /* Related */ added link to Exotic math

2023-09-19T11:25:38Z

Related: added link to Exotic math

← Older revision		Revision as of 13:25, 19 September 2023
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	----		----
	* [[Pages with math]]		* [[Pages with math]]
			----
			* [[Exotic math]]


	[[Category:Pages with math]]		[[Category:Pages with math]]
	[[category:Information]]		[[category:Information]]

Apm: added Category:Information

2023-07-11T11:02:28Z

added Category:Information

← Older revision		Revision as of 13:02, 11 July 2023
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	[[Category:Pages with math]]		[[Category:Pages with math]]
			[[category:Information]]

Apm: /* Related */

2023-06-27T17:48:59Z

← Older revision		Revision as of 19:48, 27 June 2023
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	* [[Atomic orbitals]]		* [[Atomic orbitals]]
	* [[Hartree-Fock method]]		* [[Hartree-Fock method]]
			----
			* [[Pages with math]]

	[[Category:Pages with math]]		[[Category:Pages with math]]

Apm: /* Some multi-purpouse misc math */ made into a sub-chapter: === Basic higher dimensional higher order derivatives ===

2022-12-05T10:45:23Z

Some multi-purpouse misc math: made into a sub-chapter: === Basic higher dimensional higher order derivatives ===

← Older revision		Revision as of 12:45, 5 December 2022
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	* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]		* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]

	'''Basic higher dimensional higher order derivatives~~:'''~~		'''Generalized functions (1D):'''
			* [https://en.wikipedia.org/wiki/Dirac_delta_function Dirac delta function] … derivative of Heaviside function
			* [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside step function] … antiderivative of Dirac delta function

			=== Basic higher dimensional higher order derivatives ===

	* [https://en.wikipedia.org/wiki/Gradient Gradient] … First order derivative of a scalar field		* [https://en.wikipedia.org/wiki/Gradient Gradient] … First order derivative of a scalar field
	* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative] … gradient projected into direction vector at specific point		* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative] … gradient projected into direction vector at specific point
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	* See: [[Beautiful differentiation (Conal Elliott)]]		* See: [[Beautiful differentiation (Conal Elliott)]]

	'''For a transformation of a coordinate system into an other coordinate system~~:'''~~		'''Other uses of the Jacobian matrix:'''
	* Jacobian matrix … for locally linear transformations – unless generalized derivatives are allowed (like multidimensional analogs to Dirac-deltas)		* For a transformation of a coordinate system into an other coordinate system. <br> For locally linear transformations – unless generalized derivatives are allowed (like multidimensional analogs to Dirac-deltas)
			* For [https://en.wikipedia.org/wiki/Propagation_of_uncertainty propagation of uncertainty] in scientific measurements near sigma limit
	~~'''Generalized functions (1D):'''~~
	* [https://en.wikipedia.org/wiki/~~Dirac_delta_function Dirac delta function] … derivative~~ of ~~Heaviside function~~
	* [https://en.wikipedia.org/wiki/Heaviside_step_function Heaviside step function] ~~… antiderivative of Dirac delta function~~

	=== Useful for analysis of selfassembly and dissipation ===		=== Useful for analysis of selfassembly and dissipation ===

Apm: /* Some multi-purpouse misc math */ added link to page Beautiful differentiation (Conal Elliott)

2022-12-05T10:31:37Z

Some multi-purpouse misc math: added link to page Beautiful differentiation (Conal Elliott)

← Older revision		Revision as of 12:31, 5 December 2022
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	'''For a taylor series of a vector field:'''		'''For a taylor series of a vector field:'''
	* First derivative of a scalar field: Jacobian matrix		* First derivative of a scalar field: Jacobian matrix
	* Second derivative: ~~Uunamed~~ three index tensor		* Second derivative: unnamed three index tensor

			'''For a taylor series of a tensor fields of arbitrary rank (all derivatives):'''
			* See: [[Beautiful differentiation (Conal Elliott)]]

	'''For a transformation of a coordinate system into an other coordinate system:'''		'''For a transformation of a coordinate system into an other coordinate system:'''

Apm: /* Some multi-purpouse misc math */ added stuff regarding higher order multidimensional derivatives

2022-12-05T10:26:40Z

Some multi-purpouse misc math: added stuff regarding higher order multidimensional derivatives

@@ Line 117: / Line 117: @@
 * [https://en.wikipedia.org/wiki/Lagrange_multiplier Lagrange multipliers] – finding extrema under geometric side constraints
 * [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]
-Very basic:
-* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative]
+'''Basic higher dimensional higher order derivatives:'''
 === Useful for analysis of selfassembly and dissipation ===

Apm: /* Some multi-purpouse misc math */ added wikipedia page "directional derivative"

2022-12-05T09:35:33Z

Some multi-purpouse misc math: added wikipedia page "directional derivative"

← Older revision		Revision as of 11:35, 5 December 2022
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	* [https://en.wikipedia.org/wiki/Lagrange_multiplier Lagrange multipliers] – finding extrema under geometric side constraints		* [https://en.wikipedia.org/wiki/Lagrange_multiplier Lagrange multipliers] – finding extrema under geometric side constraints
	* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]		* [https://en.wikipedia.org/wiki/Implicit_function#Implicit_differentiation Implicit differentiation]
			Very basic:
			* [https://en.wikipedia.org/wiki/Directional_derivative Directional derivative]

	=== Useful for analysis of selfassembly and dissipation ===		=== Useful for analysis of selfassembly and dissipation ===

Apm: added: Category:Pages with math

2022-10-05T10:00:50Z

added: Category:Pages with math

← Older revision		Revision as of 12:00, 5 October 2022
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	* [[Atomic orbitals]]		* [[Atomic orbitals]]
	* [[Hartree-Fock method]]		* [[Hartree-Fock method]]

			[[Category:Pages with math]]

Apm: /* Useful algorithms in computer graphics */ added "Walk on spheres"

2022-07-31T07:43:00Z

Useful algorithms in computer graphics: added "Walk on spheres"

← Older revision		Revision as of 09:43, 31 July 2022
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	* GJK algorithm (collision detection)		* GJK algorithm (collision detection)
	* Raymarching		* Raymarching and more general "Walk on Spheres" <br> (also useful.for physical simulations)
	* Octree and more advanced subdivision algorithms		* Octree and more advanced subdivision algorithms
	* Marching cubes (for ugly triangulations – somehow this is everyone's favorite though)		* Marching cubes (for ugly triangulations – somehow this is everyone's favorite though)