basic_tools:calculus:leibniz_integration_formula
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basic_tools:calculus:leibniz_integration_formula [2018/03/12 12:49] jakobadmin |
basic_tools:calculus:leibniz_integration_formula [2018/03/28 12:28] (current) jakobadmin |
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| ====== Leibniz Integration Formula ====== | ====== Leibniz Integration Formula ====== | ||
| + | <tabbox Intuitive> | ||
| + | <tabbox Concrete> | ||
| This tool gives a nice formula to the derivative of a one dimensional integral with dependencies to the varied quantity every where, with $f, a$ and $b$ having the right conditions | This tool gives a nice formula to the derivative of a one dimensional integral with dependencies to the varied quantity every where, with $f, a$ and $b$ having the right conditions | ||
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| $$ | $$ | ||
| + | <tabbox Abstract> | ||
| - | + | <tabbox Why is it interesting?> | |
| - | ** Uses and further concepts** | + | |
| This formula is really nice in one dimenisonal [[basic tools:variational calculus|Variational Calculus]] and | This formula is really nice in one dimenisonal [[basic tools:variational calculus|Variational Calculus]] and | ||
| - | with $a(0) = a$, $b(0) = b$, and for the particle mechanics [[advanced_tools:noethers_theorems|Noether's Theorem]]. For integrals over arbitrary manifolds, it generalizes to the [[|Lie derivative]] of a volume element. | + | with $a(0) = a$, $b(0) = b$, and for the particle mechanics [[theorems:noethers_theorems|Noether's Theorem]]. For integrals over arbitrary manifolds, it generalizes to the [[start|Lie derivative]] of a volume element. |
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| + | </tabbox> | ||
basic_tools/calculus/leibniz_integration_formula.1520855350.txt.gz · Last modified: 2018/03/12 11:49 (external edit)
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