From ced599db7e03612b31ed7764e5246a56369cd5a0 Mon Sep 17 00:00:00 2001
From: Michael Orlitzky <michael@orlitzky.com>
Date: Thu, 15 Nov 2012 12:11:20 -0500
Subject: [PATCH] Add the code for problem 5iii. Minor fixes to octave code.
 Update the makefile to execute octave scripts.

---
 legendre_p.m       | 8 ++++----
 legendre_p_tilde.m | 9 +++++----
 2 files changed, 9 insertions(+), 8 deletions(-)

diff --git a/legendre_p.m b/legendre_p.m
index 276e740..0481d47 100644
--- a/legendre_p.m
+++ b/legendre_p.m
@@ -1,11 +1,11 @@
 function P = legendre_p(n)
-  ## Return the nth legendre polynomial.
+  ## Return the `n`th Legendre polynomial.
   ##
-  ## INPUTS:
+  ## INPUT:
   ##
   ##   * ``n`` - The index of the polynomial that we want.
   ##
-  ## OUTPUTS:
+  ## OUTPUT:
   ##
   ##   * ``P`` - A polynomial function of one argument.
   ##
@@ -19,7 +19,7 @@ function P = legendre_p(n)
     ## The second base case.
     P = @(x) x;
   else
-    ## Compute recursively.
+    ## Not one of the base cases, so use the recursive formula.
     prev = legendre_p(n-1);
     prev_prev = legendre_p(n-2);
     P = @(x) (1/n).*( (2*n - 1).*x.*prev(x) - (n-1).*prev_prev(x) );
diff --git a/legendre_p_tilde.m b/legendre_p_tilde.m
index 0b3a87b..2c9d2ab 100644
--- a/legendre_p_tilde.m
+++ b/legendre_p_tilde.m
@@ -1,7 +1,7 @@
 function P_tilde = legendre_p_tilde(n, a, b)
-  ## Return the nth Legendre polynomial scaled to the interval [a,b].
+  ## Return the `n`th Legendre polynomial scaled to the interval [a,b].
   ##
-  ## INPUTS:
+  ## INPUT:
   ##
   ##   * ``n`` - The index of the polynomial that we want.
   ##
@@ -9,7 +9,7 @@ function P_tilde = legendre_p_tilde(n, a, b)
   ##
   ##   * ``b`` - The right endpoint of the interval.
   ##
-  ## OUTPUTS:
+  ## OUTPUT:
   ##
   ##   * ``P_tilde`` - A polynomial function of one argument.
   ##
@@ -17,7 +17,8 @@ function P_tilde = legendre_p_tilde(n, a, b)
     ## Can't do anything here. Return nothing.
     P = NA;
   else
-    ## Compute the Legendre polynomial over [-1,1] and mangle it.
+    ## Compute the Legendre polynomial over [-1,1] and mangle it to fit
+    ## the interval [a,b].
     P = legendre_p(n);
     P_tilde = @(x) P( (2/(b-a)).*x + 1 - (2*b)/(b-a) );
   end
-- 
2.44.2