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Autores: María Tarazona, Edwin Velázquez & Ernesto Rodríguez
Formulario
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TEOREMA DE GREEN
$$\vec{F}\left(x,y\right)=P\left(x,y\right)\widehat{\imath}+Q\left(x,y\right)\widehat{\jmath}$$$$\oint_{\partial D^+} \vec{F}\cdot\, d\vec{r} = \iint\limits_{D} \left( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right) \,dA$$
TEOREMA DE LA DIVERGENCIA DE GAUSS
$$\def\ooint{{\bigcirc}\kern-11.5pt{\int}\kern-6.5pt{\int}} \def\oooint{{\bigcirc}\kern-12.3pt{\int}\kern-7pt{\int}\kern-7pt{\int}}\ooint_{\partial Q}\vec{F}\cdot\vec{n}\,dS=\iiint\limits_{Q}\nabla\cdot\vec{F}\,dV$$
TEOREMA DE STOKES
$$\oint_{\partial D^+} \vec{F}\cdot\, d\vec{r} = \iint\limits_{D} \left(\nabla\times\vec{F}\right)\cdot\vec{n} \,dA$$
FÓRMULA DE EULER
$$
$$ $$e^{i\mathsf{\varphi}}=cos\left(\mathsf{\varphi}\right)+isen\left(\mathsf{\varphi}\right)$$ $$e^{i\mathsf{\pi}}+1=0$$
INTEGRAL DE CAUCHY
$$
$$ $$\oint\limits_{\mathsf{\Gamma}}\frac{f\left(z\right)}{\left(z-z_0\right)^{n+1}}\,dz=\frac{2\mathsf{\pi}i}{n!}f^{n}\left(z_0\right)$$
ECUACIÓN DE LAPLACE
$$\nabla^{2}u\left(x,y\right)=0$$ $$u_{xx}+u_{yy}=0$$
ECUACIONES DE CAUCHY-RIEMANN
$$f\left(x+iy\right)=u\left(x,y\right)+iv\left(x,y\right)$$ $$u_x=v_y \thinspace\thinspace\thinspace\thinspace\thinspace\thinspace\thinspace\thinspace u_y=-v_x$$
FACTOR INTEGRANTE
$$$$ $$$$ $$\mu\left(x\right)\left(dy+\left[P\left(x\right)y-Q\left(x\right)\right]dx=0\right)$$ $$\mu\left(x\right)=e^{\int P\left(x\right)\,dx}$$
"Las matemáticas puras son, en su forma, la poesía de las ideas lógicas" -Albert Einstein
CALCULADORA GRÁFICA
RECURSOS TEXTUALES
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