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Научный форум dxdyМатематика, Физика, Computer Science, Machine Learning, LaTeX, Механика и Техника, Химия,Биология и Медицина, Экономика и Финансовая Математика, Гуманитарные науки |
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| Страница 2 из 2 |
[ Сообщений: 21 ] | На страницу Пред. 1, 2 |
12.05.2011, 03:37 
??![$\begin{picture}(400,200)
\bezier(0,150)(50,0)(100,150)
\bezier(50,140)(-50,150)(50,160)
\bezier(50,140)(150,150)(50,160)
\put(83,95){P}
\put(20,147){C: $x^2+y^2=1$}
\put(50,110){$V$}
\put(10,60){$\partial V=$ P+C}
\put(180,150){$ \quad \text{[quote]} \quad \textbf{Stotch}: \quad \displaystyle\iint_P\text{rot} f \cdot \mathbf n dP =?$}
\put(120,100){$ 1)$ \quad \textcolor{blue}{Ostrogradski-Gauss Theorem:}$\quad \displaystyle\iiint\limits_V\left(\nabla\cdot\mathbf{F}\right)dV=\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (\mathbf{F}\cdot\mathbf{n})\,dS .$}
\put(120,70){$2) \quad \displaystyle \iiint\limits_V \nabla \cdot \text{ rot} f \ dV= \iint\limits_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (\text{rot} f) \cdot\mathbf{n} \ d(\partial V) = \iint\limits_{P+C}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (\text{rot} f) \cdot\mathbf{n} \ d\langle P^{_+}C\rangle $}
\put(120,40){$ \hspace{100pt} = \displaystyle\int\limits_P \text{rot} f \cdot\mathbf{n} \ dP+ \displaystyle\int\limits_C \text{rot} f \cdot\mathbf{n} \ dC $}
\put(120,10){$3) $ \quad \text{[quote]}: \quad \textcolor{blue}{\textbf{svv}: \quad $\operatorname{div} \operatorname{rot} a =\nabla \cdot \text{rot a}= 0 \ \Rightarrow \ \displaystyle \iiint\limits_V \nabla \cdot \text{ rot} f \ dV =0$.}}
\end{picture}$](https://dxdy-01.korotkov.co.uk/f/4/0/5/405a5904a4e64d1d5d6988b64afd1e4982.png "$\begin{picture}(400,200)
\bezier(0,150)(50,0)(100,150)
\bezier(50,140)(-50,150)(50,160)
\bezier(50,140)(150,150)(50,160)
\put(83,95){P}
\put(20,147){C: $x^2+y^2=1$}
\put(50,110){$V$}
\put(10,60){$\partial V=$ P+C}
\put(180,150){$ \quad \text{[quote]} \quad \textbf{Stotch}: \quad \displaystyle\iint_P\text{rot} f \cdot \mathbf n dP =?$}
\put(120,100){$ 1)$ \quad \textcolor{blue}{Ostrogradski-Gauss Theorem:}$\quad \displaystyle\iiint\limits_V\left(\nabla\cdot\mathbf{F}\right)dV=\iint\limits_{S}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (\mathbf{F}\cdot\mathbf{n})\,dS .$}
\put(120,70){$2) \quad \displaystyle \iiint\limits_V \nabla \cdot \text{ rot} f \ dV= \iint\limits_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (\text{rot} f) \cdot\mathbf{n} \ d(\partial V) = \iint\limits_{P+C}\!\!\!\!\!\!\!\!\!\!\!\subset\!\supset (\text{rot} f) \cdot\mathbf{n} \ d\langle P^{_+}C\rangle $}
\put(120,40){$ \hspace{100pt} = \displaystyle\int\limits_P \text{rot} f \cdot\mathbf{n} \ dP+ \displaystyle\int\limits_C \text{rot} f \cdot\mathbf{n} \ dC $}
\put(120,10){$3) $ \quad \text{[quote]}: \quad \textcolor{blue}{\textbf{svv}: \quad $\operatorname{div} \operatorname{rot} a =\nabla \cdot \text{rot a}= 0 \ \Rightarrow \ \displaystyle \iiint\limits_V \nabla \cdot \text{ rot} f \ dV =0$.}}
\end{picture}$")
