diff --git a/lectures/autodiff.md b/lectures/autodiff.md
index 37bef07..aa88920 100644
--- a/lectures/autodiff.md
+++ b/lectures/autodiff.md
@@ -13,6 +13,12 @@ kernelspec:
 
 # Adventures with Autodiff
 
+
+```{include} _admonition/gpu.md
+```
+
+## Overview
+
 This lecture gives a brief introduction to automatic differentiation using
 Google JAX.
 
@@ -25,14 +31,15 @@ powerful implementations available.
 One of the best of these is the automatic differentiation routines contained
 in JAX.
 
+While other software packages also offer this feature, the JAX version is
+particularly powerful because it integrates so well with other core
+components of JAX (e.g., JIT compilation and parallelization).
+
 As we will see in later lectures, automatic differentiation can be used not only
 for AI but also for many problems faced in mathematical modeling, such as
 multi-dimensional nonlinear optimization and root-finding problems.
 
 
-```{include} _admonition/gpu.md
-```
-
 We need the following imports
 
 ```{code-cell} ipython3
diff --git a/lectures/job_search.md b/lectures/job_search.md
index d80c1db..33a05df 100644
--- a/lectures/job_search.md
+++ b/lectures/job_search.md
@@ -20,8 +20,12 @@ kernelspec:
 In this lecture we study a basic infinite-horizon job search problem with Markov wage
 draws 
 
-The exercise at the end asks you to add recursive preferences and compare
-the result.
+```{note}
+For background on infinite horizon job search see, e.g., [DP1](https://dp.quantecon.org/).
+```
+
+The exercise at the end asks you to add risk-sensitive preferences and see how
+the main results change.
 
 In addition to what’s in Anaconda, this lecture will need the following libraries:
 
@@ -238,6 +242,8 @@ res_wage_index = min(stop_indices[0])
 res_wage = w_vals[res_wage_index]
 ```
 
+Here's a joint plot of the value function and the reservation wage.
+
 ```{code-cell} ipython3
 fig, ax = plt.subplots()
 ax.plot(w_vals, v_star, alpha=0.8, label="value function")
diff --git a/lectures/newtons_method.md b/lectures/newtons_method.md
index 0c0d5f0..4da4fe5 100644
--- a/lectures/newtons_method.md
+++ b/lectures/newtons_method.md
@@ -20,18 +20,14 @@ kernelspec:
 
 One of the key features of JAX is automatic differentiation.
 
-While other software packages also offer this feature, the JAX version is
-particularly powerful because it integrates so closely with other core
-components of JAX, such as accelerated linear algebra, JIT compilation and
-parallelization.
+We introduced this feature in {doc}`autodiff`.
 
-The application of automatic differentiation we consider is computing economic equilibria via Newton's method.
+In this lecture we apply automatic differentiation to the problem of computing economic equilibria via Newton's method.
 
 Newton's method is a relatively simple root and fixed point solution algorithm, which we discussed 
 in [a more elementary QuantEcon lecture](https://python.quantecon.org/newton_method.html).
 
-JAX is almost ideally suited to implementing Newton's method efficiently, even
-in high dimensions.
+JAX is ideally suited to implementing Newton's method efficiently, even in high dimensions.
 
 We use the following imports in this lecture