diff options
Diffstat (limited to 'mne')
| -rw-r--r-- | mne/n1.lyx | 4 | ||||
| -rw-r--r-- | mne/n2.lyx | 18 | ||||
| -rw-r--r-- | mne/n3.lyx | 8 | ||||
| -rw-r--r-- | mne/n4.lyx | 28 | ||||
| -rw-r--r-- | mne/n5.lyx | 12 |
5 files changed, 35 insertions, 35 deletions
@@ -182,7 +182,7 @@ Como teorema \series default , si -\begin_inset Formula $D:=[a,b]\times\mathbb{R}$ +\begin_inset Formula $D\coloneqq [a,b]\times\mathbb{R}$ \end_inset , @@ -301,7 +301,7 @@ Si el polinomio interpolador de \end_inset , llamamos -\begin_inset Formula $f[x_{0},\dots,x_{n}]:=a_{n}$ +\begin_inset Formula $f[x_{0},\dots,x_{n}]\coloneqq a_{n}$ \end_inset . @@ -106,7 +106,7 @@ paso \end_inset con -\begin_inset Formula $t_{i}:=a+hi$ +\begin_inset Formula $t_{i}\coloneqq a+hi$ \end_inset , aunque esto se suele calcular como @@ -134,11 +134,11 @@ El método de Euler \series default viene dado por -\begin_inset Formula $\omega_{0}:=x_{0}$ +\begin_inset Formula $\omega_{0}\coloneqq x_{0}$ \end_inset y -\begin_inset Formula $\omega_{i+1}:=\omega_{i}+hf(t_{i},\omega_{i})$ +\begin_inset Formula $\omega_{i+1}\coloneqq \omega_{i}+hf(t_{i},\omega_{i})$ \end_inset . @@ -204,7 +204,7 @@ Teorema de convergencia del método de Euler: \end_inset , -\begin_inset Formula $h:=\frac{b-a}{n}$ +\begin_inset Formula $h\coloneqq \frac{b-a}{n}$ \end_inset , @@ -241,7 +241,7 @@ con para dicho problema con redondeo, dado por \begin_inset Formula \[ -\left\{ \begin{aligned}\omega_{0} & \mid =x_{0}+\delta_{0},\\ +\left\{ \begin{aligned}\omega_{0} & :=x_{0}+\delta_{0},\\ \omega_{i+1} & :=\omega_{i}+hf(t_{i},\omega_{i})+\delta_{i+1}, \end{aligned} \right. @@ -258,7 +258,7 @@ con cada \end_inset , y -\begin_inset Formula $x_{i}:=x(t_{i})$ +\begin_inset Formula $x_{i}\coloneqq x(t_{i})$ \end_inset para cada @@ -451,7 +451,7 @@ Como \end_deeper \begin_layout Enumerate -\begin_inset Formula $y_{i}:=2\xi_{2i}-\omega_{i}$ +\begin_inset Formula $y_{i}\coloneqq 2\xi_{2i}-\omega_{i}$ \end_inset es un método de paso fijo @@ -517,11 +517,11 @@ El método de Euler es el método de Taylor de orden 1. \begin_layout Standard Dado un método de paso fijo de la forma -\begin_inset Formula $\omega_{0}:=\alpha$ +\begin_inset Formula $\omega_{0}\coloneqq \alpha$ \end_inset , -\begin_inset Formula $\omega_{i+1}:=\omega_{i}+hØ(t_{i},\omega_{i})$ +\begin_inset Formula $\omega_{i+1}\coloneqq \omega_{i}+hØ(t_{i},\omega_{i})$ \end_inset , llamamos @@ -222,7 +222,7 @@ teorema \end_inset , sean -\begin_inset Formula $h:=h_{i}$ +\begin_inset Formula $h\coloneqq h_{i}$ \end_inset y @@ -338,7 +338,7 @@ Dar un paso con \begin_layout Enumerate Obtener el error -\begin_inset Formula $E:=\frac{2^{k}}{2^{k}-1}\Vert Y-\omega_{i+1}\Vert\approx\Vert z_{i}(t_{i+1})-\omega_{i+1}\Vert$ +\begin_inset Formula $E\coloneqq \frac{2^{k}}{2^{k}-1}\Vert Y-\omega_{i+1}\Vert\approx\Vert z_{i}(t_{i+1})-\omega_{i+1}\Vert$ \end_inset . @@ -374,11 +374,11 @@ Para ajustar el paso: \begin_layout Enumerate Calcular -\begin_inset Formula $q:=\left(\frac{\varepsilon h}{2E}\right)^{1/k}$ +\begin_inset Formula $q\coloneqq \left(\frac{\varepsilon h}{2E}\right)^{1/k}$ \end_inset y -\begin_inset Formula $q':=\min\{4,\max\{0.1,q\}\}$ +\begin_inset Formula $q'\coloneqq \min\{4,\max\{0.1,q\}\}$ \end_inset , y hacer @@ -321,7 +321,7 @@ Consideremos un método multipaso de paso fijo que, para un problema en un \end_inset dada por -\begin_inset Formula $\tau(h):=\max_{i=0}^{n_{h}}\Vert\tau_{i}(h)\Vert$ +\begin_inset Formula $\tau(h)\coloneqq \max_{i=0}^{n_{h}}\Vert\tau_{i}(h)\Vert$ \end_inset , el método es @@ -385,7 +385,7 @@ estable \end_inset , sea -\begin_inset Formula $(t_{i},\omega_{i})_{i=0}^{n}:=(t_{hi},\omega_{hi})_{i=0}^{n_{h}}$ +\begin_inset Formula $(t_{i},\omega_{i})_{i=0}^{n}\coloneqq (t_{hi},\omega_{hi})_{i=0}^{n_{h}}$ \end_inset , si se puede generar una solución @@ -393,7 +393,7 @@ estable \end_inset con -\begin_inset Formula $\tilde{\omega}_{i}:=\omega_{i}$ +\begin_inset Formula $\tilde{\omega}_{i}\coloneqq \omega_{i}$ \end_inset para @@ -468,7 +468,7 @@ Demostración: \end_inset los coeficientes del método y -\begin_inset Formula $\varepsilon_{i}:=h\tau_{i}(h)$ +\begin_inset Formula $\varepsilon_{i}\coloneqq h\tau_{i}(h)$ \end_inset , como @@ -561,11 +561,11 @@ teorema \end_inset dado por -\begin_inset Formula $\omega_{0}:=x(t_{0})$ +\begin_inset Formula $\omega_{0}\coloneqq x(t_{0})$ \end_inset y -\begin_inset Formula $\omega_{i+1}:=\omega_{i}+hØ(t_{i},\omega_{i},h)$ +\begin_inset Formula $\omega_{i+1}\coloneqq \omega_{i}+hØ(t_{i},\omega_{i},h)$ \end_inset con @@ -594,11 +594,11 @@ Fijado \end_inset dados por -\begin_inset Formula $\omega_{i+1}:=\omega_{i}+hØ(t_{i},\omega_{i},h)$ +\begin_inset Formula $\omega_{i+1}\coloneqq \omega_{i}+hØ(t_{i},\omega_{i},h)$ \end_inset y -\begin_inset Formula $\tilde{\omega}_{i+1}:=\tilde{\omega}_{i}+hØ(t_{i},\tilde{\omega}_{i},h)+\varepsilon_{i+1}$ +\begin_inset Formula $\tilde{\omega}_{i+1}\coloneqq \tilde{\omega}_{i}+hØ(t_{i},\tilde{\omega}_{i},h)+\varepsilon_{i+1}$ \end_inset para ciertos @@ -641,7 +641,7 @@ Con esto, como \end_inset , llamando -\begin_inset Formula $M:=(1+hL)^{n}$ +\begin_inset Formula $M\coloneqq (1+hL)^{n}$ \end_inset , @@ -806,7 +806,7 @@ donde los polinomio característico \series default de la ecuación es -\begin_inset Formula $P(\lambda):=\lambda^{m}-a_{m-1}\lambda^{m-1}-\dots-a_{1}\lambda-a_{0}$ +\begin_inset Formula $P(\lambda)\coloneqq \lambda^{m}-a_{m-1}\lambda^{m-1}-\dots-a_{1}\lambda-a_{0}$ \end_inset . @@ -840,7 +840,7 @@ Dados un método multipaso de paso fijo \end_inset y -\begin_inset Formula $\omega_{i}:=\alpha_{i}$ +\begin_inset Formula $\omega_{i}\coloneqq \alpha_{i}$ \end_inset para @@ -950,11 +950,11 @@ begin{sloppypar} \end_inset Dados un método implícito -\begin_inset Formula $\omega_{i}:=F(t_{i},h,\omega_{i-1},\dots,\omega_{i-m})$ +\begin_inset Formula $\omega_{i}\coloneqq F(t_{i},h,\omega_{i-1},\dots,\omega_{i-m})$ \end_inset y uno explícito -\begin_inset Formula $\omega_{i}:=G(t_{i},h,\omega_{i},\dots,\omega_{i-m})$ +\begin_inset Formula $\omega_{i}\coloneqq G(t_{i},h,\omega_{i},\dots,\omega_{i-m})$ \end_inset , el @@ -1072,7 +1072,7 @@ Sean \begin_layout Standard El método es de paso variable, ajustando el paso como en los métodos de paso fijo pero con error -\begin_inset Formula $E:=\frac{19}{270}\Vert\beta_{i}-\omega_{i}\Vert$ +\begin_inset Formula $E\coloneqq \frac{19}{270}\Vert\beta_{i}-\omega_{i}\Vert$ \end_inset . @@ -186,7 +186,7 @@ En general, con los métodos de un paso fijo en \end_inset , esto es -\begin_inset Formula $Q(x):=\sum_{i=0}^{n}\frac{x^{i}}{i!}$ +\begin_inset Formula $Q(x)\coloneqq \sum_{i=0}^{n}\frac{x^{i}}{i!}$ \end_inset . @@ -362,7 +362,7 @@ El polinomio \end_inset tiene como única raíz -\begin_inset Formula $\beta:=\frac{1}{1-h\lambda}$ +\begin_inset Formula $\beta\coloneqq \frac{1}{1-h\lambda}$ \end_inset , y si @@ -383,7 +383,7 @@ El polinomio \end_deeper \begin_layout Standard Para implementarlo, sea -\begin_inset Formula $F(\omega):=\omega-\omega_{i-1}-hf(t_{i},\omega)$ +\begin_inset Formula $F(\omega)\coloneqq \omega-\omega_{i-1}-hf(t_{i},\omega)$ \end_inset , se trata de resolver @@ -400,7 +400,7 @@ Para implementarlo, sea \end_inset , dada por -\begin_inset Formula $\omega_{i}^{0}:=\omega_{i-1}$ +\begin_inset Formula $\omega_{i}^{0}\coloneqq \omega_{i-1}$ \end_inset y @@ -549,11 +549,11 @@ Dado un método a \end_inset llamamos -\begin_inset Formula $\rho(z):=z^{m}-a_{m-1}z^{m-1}-\dots-a_{1}z-a_{0}$ +\begin_inset Formula $\rho(z)\coloneqq z^{m}-a_{m-1}z^{m-1}-\dots-a_{1}z-a_{0}$ \end_inset y -\begin_inset Formula $\sigma(z):=b_{m}z^{m}+\dots+b_{1}z+b_{0}$ +\begin_inset Formula $\sigma(z)\coloneqq b_{m}z^{m}+\dots+b_{1}z+b_{0}$ \end_inset . |