More equations as figures

Author: jussienko

numpy/broadcast-rotation/README.md

@@ -11,7 +11,7 @@ R =
 \end{pmatrix}
 --->
 
-![img](http://quicklatex.com/cache3/9c/ql_ee4015bef241c06a5119104118f9a19c_l3.png)
+![img](../img/rotation-matrix.png)
 
 where θ is the angle of rotation (in radians). Start from the x-y coordinates
 in the file points_circle.dat and rotate them by 90°. Utilize broadcasting for

numpy/heat-equation/README.md

@@ -5,7 +5,7 @@ Heat (or diffusion) equation is
 <!-- Equation
 \frac{\partial u}{\partial t} = \alpha \nabla^2 u
 --> 
-![img](https://quicklatex.com/cache3/d2/ql_b3f6b8bdc3a8862c73c5a97862afb9d2_l3.png)
+![img](../img/heat-equation.png)
 
 where **u(x, y, t)** is the temperature field that varies in space and time,
 and α is thermal diffusivity constant. The two dimensional Laplacian can be
@@ -17,22 +17,22 @@ discretized with finite differences as
  &+ \frac{u(i,j-1)-2u(i,j)+u(i,j+1)}{(\Delta y)^2}
 \end{align*}
 --> 
-![img](https://quicklatex.com/cache3/2d/ql_59f49ed64dbbe76704e0679b8ad7c22d_l3.png)
+![img](../img/nabla.png)
 
 Given an initial condition (u(t=0) = u0) one can follow the time dependence of
 the temperature field with explicit time evolution method:
 
 <!-- Equation
 u^{m+1}(i,j) = u^m(i,j) + \Delta t \alpha \nabla^2 u^m(i,j) 
 --> 
-![img](https://quicklatex.com/cache3/9e/ql_9eb7ce5f3d5eccd6cfc1ff5638bf199e_l3.png)
+![img](../img/heat-time-propagation.png)
 
 Note: Algorithm is stable only when
 
 <!-- Equation
 \Delta t < \frac{1}{2 \alpha} \frac{(\Delta x \Delta y)^2}{(\Delta x)^2 (\Delta y)^2}
 -->
-![img](https://quicklatex.com/cache3/d1/ql_0e7107049c9183d11dbb1e81174280d1_l3.png)
+![img](../img/heat-stability.png)
 
 Implement two dimensional heat equation with NumPy using the initial
 temperature field in the file [bottle.dat](bottle.dat) (the file consists of a