From 0b1a36992755caa7016b280941266306707e9817 Mon Sep 17 00:00:00 2001 From: Lance Larsen Date: Wed, 2 Dec 2020 13:52:06 -0700 Subject: [PATCH] Update ._main_nonlin001.html The mathematical proof of linearity was was missing the derivative prime symbols that are needed. --- doc/pub/nonlin/sphinx/._main_nonlin001.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/pub/nonlin/sphinx/._main_nonlin001.html b/doc/pub/nonlin/sphinx/._main_nonlin001.html index 4d455c04..9aedbfd2 100644 --- a/doc/pub/nonlin/sphinx/._main_nonlin001.html +++ b/doc/pub/nonlin/sphinx/._main_nonlin001.html @@ -131,8 +131,8 @@

Differential equations

For example, the term \(T(u) = (\sin^2 t)u'(t)\) is linear because

-\[\begin{split}T(au_1 + bu_2) &= (\sin^2 t)(au_1(t) + b u_2(t))\\ -& = a(\sin^2 t)u_1(t) + b(\sin^2 t)u_2(t)\\ +\[\begin{split}T(au_1 + bu_2) &= (\sin^2 t)(au_1(t) + b u_2(t))'\\ +& = a(\sin^2 t)u_1'(t) + b(\sin^2 t)u_2'(t)\\ & =aT(u_1) + bT(u_2){\thinspace .}\end{split}\]

However, \(T(u)=\sin u\) is nonlinear because

@@ -996,4 +996,4 @@

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