From ac6e7b7ac0ae6b3044dfa189d9bc927b82600184 Mon Sep 17 00:00:00 2001
From: Peder Larson <peder.larson@ucsf.edu>
Date: Fri, 11 Sep 2026 15:49:13 -0700
Subject: [PATCH] Fix aligned equations in PDF build

Co-authored-by: Copilot App <223556219+Copilot@users.noreply.github.com>
---
 Notebooks/In Vivo Contrast Mechanisms.ipynb | 8 ++++----
 Notebooks/K-space.ipynb                     | 4 ++--
 2 files changed, 6 insertions(+), 6 deletions(-)

diff --git a/Notebooks/In Vivo Contrast Mechanisms.ipynb b/Notebooks/In Vivo Contrast Mechanisms.ipynb
index e19bf3d..61b015e 100644
--- a/Notebooks/In Vivo Contrast Mechanisms.ipynb	
+++ b/Notebooks/In Vivo Contrast Mechanisms.ipynb	
@@ -66,16 +66,16 @@
     "\n",
     "The smallest size we can measure with MRI is an imaging voxel, so our image measurements are a sum of the transverse magnetizations across the voxel, including both $T_2$ and off-resonance: \n",
     "\n",
-    "$$\\begin{align}\n",
+    "$$\\begin{aligned}\n",
     "s_{\\mathrm{voxel}}(t) & = \\int_{\\mathrm{voxel}} M_{XY}(\\vec{r},0) \\exp(-t/T_2(\\vec{r})) \\exp(-i 2 \\pi \\Delta f_r(\\vec{r}))  \\  d\\vec{r} \\\\\n",
     "& \\approx M_{XY}(\\vec{r},0) \\exp(-t/T_2^*(\\vec{r}))\n",
-    "\\end{align}$$\n",
+    "\\end{aligned}$$\n",
     "\n",
     "<!-- \n",
-    "$$\\begin{align}\n",
+    "$$\\begin{aligned}\n",
     "s(t) & = \\int m(\\vec{r}) \\exp(-t/T_2(\\vec{r})) \\exp(-i 2 \\pi \\Delta f_r(\\vec{r}))  \\  d\\vec{r} \\\\\n",
     "& \\approx \\int m(\\vec{r}) \\exp(-t/T_2^*(\\vec{r})) \\ d\\vec{r}\n",
-    "\\end{align}$$\n",
+    "\\end{aligned}$$\n",
     "-->\n",
     "\n",
     "(Note that any effects of applied gradients are removed during the image reconstruction process.)\n",
diff --git a/Notebooks/K-space.ipynb b/Notebooks/K-space.ipynb
index c9e66a3..bcf1e0a 100644
--- a/Notebooks/K-space.ipynb
+++ b/Notebooks/K-space.ipynb
@@ -48,10 +48,10 @@
     "\n",
     "The MRI signal comes from the precession of the transverse magnetization, and thus is proportional to the transverse magnetization.  The MRI signal also comes from any precessing magnetization within the sensitive volume of the RF receive coils.  In other words, it is also not localized to a single location, but rather is summed over a volume:\n",
     "\n",
-    "$$\\begin{align}\n",
+    "$$\\begin{aligned}\n",
     "s(t) & = \\int M_{XY}(\\vec{r},t) \\ d\\vec{r} \\\\\n",
     " & =  \\int m(\\vec{r}) \\exp(-i2\\pi \\vec{k}(t) \\cdot \\vec{r}) \\ d\\vec{r}\n",
-    " \\end{align}$$ \n",
+    " \\end{aligned}$$ \n",
     "\n",
     "The amazing result here is that this describes our MRI signal in the form of a Fourier Transform:\n",
     "\n",