diff --git a/Manifest.toml b/Manifest.toml
index 5e34b02..56a8795 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -168,7 +168,7 @@ deps = ["Libdl", "LinearAlgebra", "Random", "Serialization", "SuiteSparse_jll"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[deps.SpatialHashing]]
-git-tree-sha1 = "d832097e5c801030045d7e8223b93bd337620cb0"
+git-tree-sha1 = "633b7699c3d67433bb6139aa57fe5360fb469f0b"
 repo-rev = "main"
 repo-url = "https://github.com/Alexander-Barth/SpatialHashing.jl"
 uuid = "e2e8a281-5b48-4fd6-b542-65e07fde0794"
@@ -188,9 +188,9 @@ version = "2.2.0"
 
 [[deps.StaticArrays]]
 deps = ["LinearAlgebra", "Random", "StaticArraysCore", "Statistics"]
-git-tree-sha1 = "8982b3607a212b070a5e46eea83eb62b4744ae12"
+git-tree-sha1 = "832afbae2a45b4ae7e831f86965469a24d1d8a83"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "1.5.25"
+version = "1.5.26"
 
 [[deps.StaticArraysCore]]
 git-tree-sha1 = "6b7ba252635a5eff6a0b0664a41ee140a1c9e72a"
diff --git a/docs/src/index.md b/docs/src/index.md
index 8c92fc6..c486430 100644
--- a/docs/src/index.md
+++ b/docs/src/index.md
@@ -14,7 +14,7 @@ The fluid is represented by a set of discrete particles. Each particle is center
 ```
 
 where $\mathbf v_i$ is the velocity of the i-th particle.
-Each particle can have a property $A$
+Each particle can have a property $A$:
 
 ```math
 A(\mathbf r) = \int A(\mathbf r') W(|\mathbf r - \mathbf r'|,h) d^n r'
@@ -27,13 +27,13 @@ and it normalized:
 \int W(|\mathbf r - \mathbf r'|,h) d^n r' = 1
 ```
 
-and converges to a Dirac function if $h$ tends to zero.
+and converges to the Dirac function $\delta(\mathbf r - \mathbf r')$ if $h$ tends to zero.
 
 ```math
 \lim_{h \rightarrow 0} \int W(|\mathbf r - \mathbf r'|,h) d^n r' = \delta(\mathbf r - \mathbf r')
 ```
 
-For small $h$, we can therefore approximate the integral using the discrete sum:
+For small $h$ enought and sufficiently many particles, we can therefore approximate the integral using the discrete sum:
 
 ```math
 A(\mathbf r) = \sum_i V_i A_i W(|\mathbf r - \mathbf r_i|,h)
@@ -65,7 +65,7 @@ which can be seen as a discretized form of:
 \frac{d\rho}{dt} = -\rho \nabla \cdot v
 ```
 
-The pressure gradient is computed using the symmetric form:
+The pressure gradient is computed using the symmetric form by analogy of the evolution equation of density:
 
 ```math
 \nabla p(r_i) = \rho_i \sum_j m_j