ex1: errata

exercise1/exercise1.typ

@@ -42,20 +42,14 @@ this document was created using
 
 == a)
 
-#[#show math.equation: set text(size: (FONT_SIZE * 0.60))
+#[#show math.equation: set text(size: (FONT_SIZE * 0.56))
   #rotate(
     -90deg,
     reflow: true,
     table(
       $bold(u(x, y, t))$, $bold(u_y)$, $bold(u_t)$, $bold(u_(x x))$, $bold(u_(x y))$, $bold(u_(y x))$,
 
-      $t^4 - cos(x y)$,
-      $x sin(x y)$,
-      $4 t^3$,
-      $y^2 cos(x y)$,
-      $x y cos(x y)$,
-      $x
-      y cos(x y)$,
+      $t^4 - cos(x y)$, $x sin(x y)$, $4 t^3$, $y^2 cos(x y)$, $x y cos(x y) + sin(x y)$, $x y cos(x y) + sin(x y)$,
 
       $-sin(t x y)$,
       $- t x cos(t x y)$,
@@ -456,5 +450,13 @@ $
   frak(O) := {1/a, x/b, (x^2 - 1/3)/c}
 $
 
-where $a & = sqrt(2), b & = sqrt(2/3)$ and $c & = sqrt(2/5)$.
+where $a & = sqrt(2), b & = sqrt(2/3)$ and $c & = sqrt(8/45)^(dagger)$.
+
+#[#show math.equation: set text(size: FONT_SIZE * 0.75, gray.darken(50%))
+  $
+    dagger: inner(x^2-1/3, x^2-1/3) & = integral_(-1)^1 (x^2 - 1/3)^2 dd(x) \
+                                    & = integral_(-1)^1 (x^4 - 2/3 x^2 + 1/9) dd(x)
+                                      = 8/45
+  $
+]