Expand knowledge base

1 files changed, 13 insertions, 2 deletions

diff --git a/content/know/concept/impulse-response/index.pdc b/content/know/concept/impulse-response/index.pdc
index fa921fa..f4c40a8 100644
--- a/content/know/concept/impulse-response/index.pdc
+++ b/content/know/concept/impulse-response/index.pdc
@@ -28,9 +28,9 @@ This can be used to find the response $u(t)$ of $\hat{L}$ to
 by simply taking the convolution with $u_p(t)$:
 
 $$\begin{aligned}
+    \hat{L} \{ u(t) \} = f(t)
+    \quad \implies \quad
     \boxed{
-        \hat{L} \{ u(t) \} = f(t)
-        \quad \implies \quad
         u(t) = (f * u_p)(t)
     }
 \end{aligned}$$
@@ -68,6 +68,17 @@ $$\begin{aligned}
 </div>
 </div>
 
+This is useful for solving initial value problems,
+because any initial condition can be satisfied
+due to the linearity of $\hat{L}$,
+by choosing the initial values of the homogeneous solution $\hat{L}\{ u_h(t) \} = 0$
+such that the total solution $(f * u_p)(t) + u_h(t)$
+has the desired values.
+
+Meanwhile, for boundary value problems,
+the related [fundamental solution](/know/concept/fundamental-solution/)
+is preferable.
+
 
 
 ## References