Post-lecture fixes

Author: mfherbst

src/01_Introduction.jl

@@ -1,13 +1,13 @@
 ### A Pluto.jl notebook ###
-# v0.20.4
+# v0.20.6
 
 using Markdown
 using InteractiveUtils
 
 # This Pluto notebook uses @bind for interactivity. When running this notebook outside of Pluto, the following 'mock version' of @bind gives bound variables a default value (instead of an error).
 macro bind(def, element)
     #! format: off
-    quote
+    return quote
         local iv = try Base.loaded_modules[Base.PkgId(Base.UUID("6e696c72-6542-2067-7265-42206c756150"), "AbstractPlutoDingetjes")].Bonds.initial_value catch; b -> missing; end
         local el = $(esc(element))
         global $(esc(def)) = Core.applicable(Base.get, el) ? Base.get(el) : iv(el)

src/05_Interpolation.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.20.5
+# v0.20.6
 
 using Markdown
 using InteractiveUtils

src/09_Numerical_integration.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.20.5
+# v0.20.6
 
 using Markdown
 using InteractiveUtils
@@ -107,9 +107,9 @@ and **then integrate that** instead of $f$ itself.
 Since the integration of the polynomial is essentially exact,
 the error of such a scheme is **dominated by the error of the polynomial
 interpolation**.
-As we found out in [the chapter on Interpolation](https://teaching.matmat.org/numerical-analysis/05_Interpolation.html) polynomials
-through equispaced nodes become rather inaccurate for large $n$
-due to Runge's phaenomenon.
+Recall the [chapter on Interpolation](https://teaching.matmat.org/numerical-analysis/05_Interpolation.html), where we noted polynomials
+through equispaced nodes to become numerically unstable and
+possibly inaccurate for large $n$ due to Runge's phaenomenon.
 
 Therefore we will pursue **piecewise linear polynomial interpolation**
 instead of fitting an $n$-th degree polynomial.
@@ -140,9 +140,9 @@ let
 		plot!(p, [a + i * h, a + i * h], [0, f(a + i * h)];
 			  ls=:dash, c=:black, label="", lw=1.5)
 	end
-	annotate!(p, [(a,   -0.5, L"t_0"),
+	annotate!(p, [(a,   -0.5, L"a = t_0"),
 				  (a+h, -0.5, L"t_1"),
-				  (a+n*h, -0.5, L"t_n")])
+				  (a+n*h, -0.5, L"t_n = b")])
 
 	ylims!(p, (-0.9, 10.5))
 	p
@@ -1219,7 +1219,7 @@ QuadGK = "~2.11.2"
 PLUTO_MANIFEST_TOML_CONTENTS = """
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.11.4"
+julia_version = "1.11.5"
 manifest_format = "2.0"
 project_hash = "0b137bedfe8a154be757099565fbd14062a17cca"
 
@@ -1760,7 +1760,7 @@ version = "0.3.27+1"
 [[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
-version = "0.8.1+4"
+version = "0.8.5+0"
 
 [[deps.OpenSSL]]
 deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]

src/10_Numerical_differentiation.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.20.5
+# v0.20.6
 
 using Markdown
 using InteractiveUtils

src/11_Initial_value_problems.jl

@@ -1,5 +1,5 @@
 ### A Pluto.jl notebook ###
-# v0.20.5
+# v0.20.6
 
 using Markdown
 using InteractiveUtils
@@ -568,7 +568,7 @@ More precisely one can formulate:
 	where $C > 0$ and $L > 0$ are constants.
 
 We note:
-- If the local truncation error $τ^{(n)}_h$ converges with order $p$, then the one-step methods also converges globally with order $p$.
+- If the local truncation error $τ^{(n)}_h$ converges with order $p$, then the explicit methods also converges globally with order $p$.
 - However, the global error has an **additional prefactor** $(e^{L (t_n-a)} -1)$, which **grows exponentially in time**. This is an effect of the accumulation of error from one time step to the next. In particular if $b \gg a$ or results can get rather inaccurate **even for higher-order methods** beyond Forward Euler where $p > 1$. This point we will pick up in the section on *Stability and implicit methods* below.
 - For Theorem 2 to hold there are a few more details to consider (e.g. problem (1) should have  a unique solution). More information can be unfolded below.
 """
@@ -1518,7 +1518,7 @@ PlutoUI = "~0.7.62"
 PLUTO_MANIFEST_TOML_CONTENTS = """
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.11.4"
+julia_version = "1.11.5"
 manifest_format = "2.0"
 project_hash = "073d0fedb2bdd79c9801f78082bc44acadfdc9ec"
 
@@ -2914,7 +2914,7 @@ version = "0.3.27+1"
 [[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
-version = "0.8.1+4"
+version = "0.8.5+0"
 
 [[deps.OpenSSL]]
 deps = ["BitFlags", "Dates", "MozillaCACerts_jll", "OpenSSL_jll", "Sockets"]