diff --git a/README.md b/README.md
index 762722f..e8cddd0 100644
--- a/README.md
+++ b/README.md
@@ -30,7 +30,9 @@ everybody", this package was renamed from `physics` to `physica`.
 
 See the [manual](https://github.com/Leedehai/typst-physics/blob/master/physica-manual.pdf) for more details.
 
-![demo](https://user-images.githubusercontent.com/18319900/236073825-e91b4601-7e92-490b-a7e4-e9e405a2147b.png)
+![demo1](https://github.com/Leedehai/typst-physics/assets/18319900/b0e2753e-ba72-46d4-809f-d6a12d8d1d6d)
+
+![demo2](https://user-images.githubusercontent.com/18319900/236073825-e91b4601-7e92-490b-a7e4-e9e405a2147b.png)
 
 ## Using physica in your Typst document
 
@@ -44,21 +46,21 @@ See https://github.com/typst/packages.
 
 ```typst
 // Style 1
-#import "@preview/physica:0.8.0": *
+#import "@preview/physica:0.8.1": *
 
 $ curl (grad f), tensor(T, -mu, +nu), pdv(f,x,y,[1,2]) $
 ```
 
 ```typst
 // Style 2
-#import "@preview/physica:0.8.0": curl, grad, tensor, pdv
+#import "@preview/physica:0.8.1": curl, grad, tensor, pdv
 
 $ curl (grad f), tensor(T, -mu, +nu), pdv(f,x,y,[1,2]) $
 ```
 
 ```typst
 // Style 3
-#import "@preview/physica:0.8.0"
+#import "@preview/physica:0.8.1"
 
 $ physica.curl (physica.grad f), physica.tensor(T, -mu, +nu), physica.pdv(f,x,y,[1,2]) $
 ```
@@ -76,7 +78,7 @@ CLI Version:
 
 ```sh
 $ typst --version
-typst 0.8.0 (360cc9b9)
+typst 0.9.0 (7bb4f6df)
 ```
 
 To regenerate the manual, use command
diff --git a/physica-manual.pdf b/physica-manual.pdf
index 3517ea7..f50089b 100644
Binary files a/physica-manual.pdf and b/physica-manual.pdf differ
diff --git a/physica-manual.typ b/physica-manual.typ
index c3912a5..2e044fb 100644
--- a/physica-manual.typ
+++ b/physica-manual.typ
@@ -23,7 +23,7 @@
 
 #align(center)[
   Version #version, October 25, 2023 \
-  Doc updated: October 25, 2023
+  Doc updated: November 21, 2023
 ]
 
 #set par(justify: true)
@@ -55,12 +55,12 @@ With `typst`'s #linkurl("package management", "https://github.com/typst/packages
 #import "physica.typ": *
 
 ```typst
-#import "@preview/physica:0.8.0": *
+#import "@preview/physica:0.8.1": *
 
-$ curl (grad f), tensor(T, -mu, +nu), pdv(f,x,y,[1,2]) $
+$ curl (grad f), pdv(,x,y,[1,2]), tensor(Gamma,+k,-i,-j) = pdv(vb(e)_i,x^j)vb(e)^k $
 ```
 
-$ curl (grad f), tensor(T, -mu, +nu), pdv(f,x,y,[1,2]) $
+$ curl (grad f), pdv(,x,y,[1,2]), tensor(Gamma,+k,-i,-j) = pdv(vb(e)_i,x^j)vb(e)^k $
 
 = The symbols
 
@@ -413,7 +413,7 @@ xmat(2, 2, #g)`)
   [`mel`],
   [
     `mel(n, diff_nu H, m)` \ #sym.arrow $mel(n, diff_nu H, m)$ \
-    `mel(n,vec(U,V),m)` #sym.arrow $mel(n,vec(U,V),m)$
+    `mel(vec(U,V),A,m)` #sym.arrow $mel(vec(U,V),A,m)$
   ],
   [matrix element],
 )