User:Eml5526.s11.team01.roark/Mtg09

[[media: Fe1.s11.mtg9.djvu| Mtg 9]]: Fri, 21 Jan 11 [[media: Fe1.s11.mtg9.djvu| Page 9-1]]
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G1DM1.0: [[media: Fe1.s11.mtg4.djvu| p. 4-4]] G = General
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1D = 1-dimenional

M1 = Model 1

.0 = “simple” boundary conditions

PDE = [[media: Fe1.s11.mtg4.djvu| (1) p. 4-4]]

Boundary conditions:

Essential Boundary condition = [[media: Fe1.s11.mtg4.djvu| (3) p. 4-4]]

Natural Boundary condition = [[media: Fe1.s11.mtg4.djvu|(4) p. 4-4]]


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G1DM1.0 /D1

(D1 – Dataset 1)




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$$\displaystyle \text{ }\Omega \text{ }=\left] 0,\underbrace{1}_{L=1} \right[$$
 *  (1)
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$$\displaystyle {{a}_{2}}\left( x \right)=2+3x$$
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$$\displaystyle f\left( x,t \right)=5x$$
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$$\displaystyle \frac{{{\partial }^{s}}u(x,t)}{\partial {{t}^{s}}}=0$$ Meaning static or steady state. $$\displaystyle {{\text{ }\!\!\Gamma\!\!\text{ }}_{\text{g}}}=\left\{ 1 \right\},\text{g}=4$$
 *  (4)
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$$\displaystyle u\left( x=1 \right)=4$$ [[media: Fe1.s11.mtg9.djvu| Page 9-2]]
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$$\displaystyle {{\text{ }\!\!\Gamma\!\!\text{ }}_{\text{h}}}=\underbrace{\left\{ 0 \right\}}_{x=0},h=12$$
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$$\displaystyle \underbrace{n(0)}_{-1}\underbrace{{{a}_{2}}(0)}_{2}\frac{\partial u(x=0)}{\partial x}=12$$ I.e., Solve the following problem:
 *  (2)
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$$\displaystyle \frac{d}{dx}\left[ \left( 2+3x \right)\frac{du}{dx} \right]+5x=0~\forall x\in \left] 0,1 \right[,u\left( 1 \right)=4,~\,-2\frac{du(x=0)}{dx}=12$$
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HW 2.4:
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Show
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$$\displaystyle \mathop{\int }^{}\frac{1+x}dx=\frac{2}-x+\log \left( 1+x \right)+\underbrace{k}_{Const}$$ End HW 2.4
 *  (4)
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 * 1) $$\displaystyle \mathop{\int }^{}logxdx=xlogx-x$$ (hint: Integration by parts)
 * 2) $$\displaystyle \mathop{\int }^{}logxdx=\frac{1}{2}{{x}^{2}}\left[ logx-\frac{1}{2} \right]$$
 * 3) Find $$\displaystyle \int{\frac{({{x}^{2}}dx)}{(1+cx)}}$$ in particular c=1 => (4)
 * 4) Find $$\displaystyle \mathop{\int }^{}\frac{{{x}^{2}}dx}{a+bx}\text{ }\!\!~\!\!\text{ }$$
 * 1) Find $$\displaystyle \mathop{\int }^{}\frac{{{x}^{2}}dx}{a+bx}\text{ }\!\!~\!\!\text{ }$$

[[media: Fe1.s11.mtg9.djvu| Page 9-3]] Note: Demo Wolfram Alpha (WA) e.g. (debt usa)/(gdp usa) integrate logx, etc. Link WA computational results in HW reports. Avoid plagiarism.