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| − | [[Image:Example7.jpg]][[Category:math]] | + | [[Image:Example7.jpg]] |
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[[Category:tutorial]] | [[Category:tutorial]] | ||
| − | =Divergence and Gradient Theorems= | + | == Divergence and Gradient Theorems == |
| + | by Kilian Cooley | ||
| + | |||
| + | '''INTRODUCTION''' | ||
| + | |||
| + | |||
| + | |||
| + | <pre> Contents | ||
| + | - Divergence and Gradient in 1D: The Fundamental Theorem of Calculus | ||
| + | - Divergence Theorem in 2D | ||
| + | - Conservation of Mass for Moving Fluids | ||
| + | - Gradient Theorem in 2D | ||
| + | - Proof of Archimedes' Principle | ||
| + | - A Warning About Coordinate Systems | ||
| + | - References | ||
| + | </pre> | ||
| + | ---- | ||
| + | |||
| + | ==Divergence and Gradient in 1D: The Fundamental Theorem of Calculus== | ||
| + | |||
| + | |||
| + | ---- | ||
| + | |||
| + | ==Divergence Theorem in 2D== | ||
| + | |||
| + | ---- | ||
| + | |||
| + | ==Conservation of Mass for Moving Fluids== | ||
| + | |||
| + | ---- | ||
| + | |||
| + | ==Gradient Theorem in 2D== | ||
| + | |||
| + | ---- | ||
| + | |||
| + | ==Proof of Archimedes' Principle== | ||
| + | |||
| + | ---- | ||
| + | |||
| + | ==A Warning About Coordinate Systems== | ||
| + | |||
| + | ---- | ||
| + | |||
| + | ==References== | ||
| + | |||
| + | ---- | ||
| + | |||
<math>\int_0^1\int_0^4\int_{-1}^7\nabla\phi {dV} = \frac{\partial u}{\partial x}\hat{e}_x</math> | <math>\int_0^1\int_0^4\int_{-1}^7\nabla\phi {dV} = \frac{\partial u}{\partial x}\hat{e}_x</math> | ||
Revision as of 10:47, 11 March 2013
Contents
Divergence and Gradient Theorems
by Kilian Cooley
INTRODUCTION
Contents - Divergence and Gradient in 1D: The Fundamental Theorem of Calculus - Divergence Theorem in 2D - Conservation of Mass for Moving Fluids - Gradient Theorem in 2D - Proof of Archimedes' Principle - A Warning About Coordinate Systems - References
Divergence and Gradient in 1D: The Fundamental Theorem of Calculus
Divergence Theorem in 2D
Conservation of Mass for Moving Fluids
Gradient Theorem in 2D
Proof of Archimedes' Principle
A Warning About Coordinate Systems
References
$ \int_0^1\int_0^4\int_{-1}^7\nabla\phi {dV} = \frac{\partial u}{\partial x}\hat{e}_x $
$ \int\int\int_{\partial \Omega} {\mathbb R} $
