diff --git a/surface_generation.nb b/surface_generation.nb
index 8b13789..a554d30 100644
--- a/surface_generation.nb
+++ b/surface_generation.nb
@@ -1 +1,26 @@
+Visualize how gradients relate to surfaces
+The Points (x, y, z) satisfying w = f (x, y, z) = u x^2 + v y^2 + z^2 for a particular value of w form the the surface shown. As the w varies, the surface deforms along the normals defined by the vector field 
+gradient f = f_x i + f_y j + f_z k
+represented by the arrows.
 
+S1[u_, v_, w_] := 
+ S1[u, v, w] = 
+  ContourPlot3D[
+   u*x^2 + v*y^2 + z^2 == w, {x, -3, 3}, {y, -3, 3}, {z, -3, 3}, 
+   Boxed -> False, Axes -> False]
+   
+S2[u_, v_] := 
+ S2[u, v] = 
+  VectorPlot3D[{u*2 x, v*2 y, 2 z}, {x, -3, 3}, {y, -3, 3}, {z, -3, 
+    3}, Boxed -> False, Axes -> False]
+    
+Manipulate[
+ Show[{S1[u, v, w], S2[u, v]}, ImageSize -> {400, 400}],
+ {u, -3, 3, Appearance -> "Labeled"},
+ {v, -3, 3, Appearance -> "Labeled"},
+ {w, 0, 2, Appearance -> "Labeled"},
+ (*the evaluation will not time out*)SynchronousUpdating -> False,
+ SaveDefinitions -> True]
+ 
+ 
+