From 075683cdf4588fe16f41d9f7b46b9720b42b2553 Mon Sep 17 00:00:00 2001
From: Prefetch
Date: Wed, 17 Jul 2024 10:01:43 +0200
Subject: Improve knowledge base

---
 source/know/concept/material-derivative/index.md | 10 +++-------
 1 file changed, 3 insertions(+), 7 deletions(-)

(limited to 'source/know/concept/material-derivative')

diff --git a/source/know/concept/material-derivative/index.md b/source/know/concept/material-derivative/index.md
index 6bb83c5..4eb43e9 100644
--- a/source/know/concept/material-derivative/index.md
+++ b/source/know/concept/material-derivative/index.md
@@ -36,7 +36,7 @@ $$\begin{aligned}
 
 In effect, we have simply made the coordinate $$\va{r}$$ dependent on time,
 and have specifically chosen the time-dependence to track the parcel.
-The net evolution of $$f$$ is then its "true" (i.e. non-partial) derivative with respect to $$t$$,
+The evolution of $$f$$ is then its derivative with respect to $$t$$,
 allowing us to apply the chain rule:
 
 $$\begin{aligned}
@@ -58,11 +58,7 @@ $$\begin{aligned}
 Note that $$\va{v} = \va{v}(\va{r}, t)$$,
 that is, the velocity can change with time ($$t$$-dependence),
 and depends on which parcel we track ($$\va{r}$$-dependence).
-
-Of course, the parcel is in our imagination:
-$$\va{r}$$ does not really depend on $$t$$;
-after all, we are dealing with a continuum.
-Nevertheless, the right-hand side of the equation is very useful,
+This result is very useful for fluid dynamics,
 and is known as the **material derivative** or **comoving derivative**:
 
 $$\begin{aligned}
@@ -76,7 +72,7 @@ The first term is called the **local rate of change**,
 and the second is the **advective rate of change**.
 In effect, the latter moves the frame of reference along with the material,
 so that we can find the evolution of $$f$$
-without needing to worry about the continuum's motion.
+without needing to explicitly account for the continuum's motion.
 
 That was for a scalar field $$f(\va{r}, t)$$,
 but in fact the definition also works for vector fields $$\va{U}(\va{r}, t)$$:
-- 
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