Trying to fix another typo, seeing disparities between visual studio markdown and...

diff --git a/Swift-Hohenberg-Solver/README.md b/Swift-Hohenberg-Solver/README.md
index 3c3be0c87f0e8e0f450a6b84799c35c3ef8687fb..eba572e540377579edc80fde38b0073760c99824 100755 (executable)
--- a/Swift-Hohenberg-Solver/README.md
+++ b/Swift-Hohenberg-Solver/README.md
@@ -53,7 +53,8 @@ $$\begin{aligned}
             1 + \Delta & -1\r
         \end{pmatrix}\r
         \begin{pmatrix}\r
-            U_n\\ V_n\r
+            U_n\\\r
+                   V_n\r
         \end{pmatrix} &= \begin{pmatrix}\r
             U_{n-1} + kg_1U_{n-1}^2 - kU_{n-1}^3\\\r
                0\r
@@ -61,13 +62,18 @@ $$\begin{aligned}
 \end{aligned}$$\r
 \r
 As usual, we multiply each side of the equation by a\r
-test function $\overrightarrow\varphi_i = \begin{pmatrix}\r
+test function \r
+\r
+$$\overrightarrow\varphi_i = \begin{pmatrix}\r
     \phi_i\\ \psi_i\r
-\end{pmatrix}$\r
+\end{pmatrix}$$\r
+\r
+to get the equation\r
 \r
 $$\begin{aligned}\r
     \begin{pmatrix}\r
-            \phi_i\\ \psi_i\r
+            \phi_i\\ \r
+                \psi_i\r
         \end{pmatrix}\cdot\begin{pmatrix}\r
             1 - kr & k(1 + \Delta)\\\r
             1 + \Delta & -1\r
@@ -75,7 +81,8 @@ $$\begin{aligned}
         \begin{pmatrix}\r
             U_n\\ V_n\r
         \end{pmatrix} &= \begin{pmatrix}\r
-            \phi_i\\\psi_i\r
+            \phi_i\\\r
+               \psi_i\r
         \end{pmatrix}\cdot\begin{pmatrix}\r
             U_{n-1} + kg_1U_{n-1}^2 - kU_{n-1}^3\\\r
                0\r
@@ -86,7 +93,8 @@ and then expand our solution vector in this basis
 \r
 $$\begin{aligned}\r
     \sum_j u_j\begin{pmatrix}\r
-            \phi_i\\\psi_i\r
+            \phi_i\\\r
+               \psi_i\r
         \end{pmatrix}\cdot\begin{pmatrix}\r
             1 - kr & k(1 + \Delta)\\\r
             1 + \Delta & -1\r
@@ -94,7 +102,8 @@ $$\begin{aligned}
         \begin{pmatrix}\r
             \phi_j\\\psi_j\r
         \end{pmatrix} &= \begin{pmatrix}\r
-            \phi_i\\\psi_i\r
+            \phi_i\\\r
+               \psi_i\r
         \end{pmatrix}\cdot\begin{pmatrix}\r
             U_{n-1} + kg_1U_{n-1}^2 - kU_{n-1}^3\\\r
                0\r