Move to TODO boxes

Author: Technici4n

src/05_Direct_methods.jl

@@ -38,8 +38,6 @@ TableOfContents()
 md"""
 # Direct methods for linear systems
 
-TODO polynomial interpolation now comes later
-
 In the previous chapter on polynomial interpolation we were already
 confronted with the need to solve linear systems, that is a system
 of equations of the form
@@ -52,6 +50,9 @@ as well as a right-hand side $\mathbf{b} \in \mathbb{R}^n$.
 As the solution we seek the unknown $\mathbf{x} \in \mathbb{R}^n$.
 """
 
+# ╔═╡ adb09dc3-a074-4b5f-9757-85c05d22ee83
+TODO("polynomial interpolation now comes later")
+
 # ╔═╡ 419d11bf-2561-49ca-a6e7-40c8d8b88b24
 md"""
 - `nmax = ` $(@bind nmax Slider([5, 10, 12, 15]; default=10, show_value=true))
@@ -2330,6 +2331,7 @@ version = "17.4.0+2"
 # ╠═3295f30c-c1f4-11ee-3901-4fb291e0e4cb
 # ╟─21c9a859-f976-4a93-bae4-616122712a24
 # ╟─b3cb31aa-c982-4454-8882-5b840c68df9b
+# ╠═adb09dc3-a074-4b5f-9757-85c05d22ee83
 # ╟─be5d3f98-4c96-4e69-af91-fa2ae5f74af5
 # ╟─419d11bf-2561-49ca-a6e7-40c8d8b88b24
 # ╠═011c25d5-0d60-4729-b200-cdaf3dc89faf

src/07_Interpolation.jl

@@ -689,11 +689,12 @@ Notably Chebyshev nodes enjoy the following convergence result:
 
 This is an example of **exponential convergence**: The error of the approximation scheme reduces by a *constant factor* whenever the polynomial degree $n$ is increased by a constant increment. 
 
-TODO: "previous chapter" remark likely outdated after pushing interpolation back
-
 The **graphical characterisation** is similar to the iterative schemes we discussed in the previous chapter: We employ a **semilog plot** (using a linear scale for $n$ and a logarithmic scale for the error), where exponential convergence is characterised by a straight line:
 """
 
+# ╔═╡ 21c98bd4-b3eb-4406-bcd2-0abfbeb9bb93
+TODO("'previous chapter' remark likely outdated after pushing interpolation back")
+
 # ╔═╡ d4cf71ef-576d-4900-9608-475dbd4d933a
 let
 	fine = range(-1.0, 1.0; length=3000)
@@ -727,14 +728,15 @@ is one of the **desired properties**.
     When discussing convergences rates of iterative numerical algorithms and
     the accuracy of numerical approximation schemes (interpolation, differentiation, integration, discretisation) unfortunately a different terminology is employed. In the following let $α > 0$ and $0 < C < 1$ denote appropriate constants.
 
-	TODO "Last chapter" reference is likely outdated after pushing interpolation back
-
 	- **Iterative schemes:** Linear convergence
 	  * If the error scales as $α C^{n}$ where $n$ is the iteration number, we say the scheme has **linear convergence**. (Compare to the last chapter.)
     - **Approximation schemes:** Exponential convergence
 	  * If the error scales as $α C^{n}$ where $n$ is some accuracy parameter (with larger $n$ giving more accurate results), then we say the scheme has **exponential convergence**.
 """
 
+# ╔═╡ 647f96ee-c0ad-4bd8-9de1-f24a7dcf6b24
+TODO("'Last chapter' reference is likely outdated after pushing interpolation back")
+
 # ╔═╡ a15750a3-3507-4ee1-8b9a-b7d6a3dcea46
 md"""
 ### Stability of polynomial interpolation
@@ -3312,8 +3314,10 @@ version = "1.4.1+2"
 # ╟─25b82572-b27d-4f0b-9be9-323cd4e3ce7a
 # ╟─c38b9e48-98bb-4b9c-acc4-7375bbd39ade
 # ╟─479a234e-1ce6-456d-903a-048bbb3de65a
+# ╠═21c98bd4-b3eb-4406-bcd2-0abfbeb9bb93
 # ╟─d4cf71ef-576d-4900-9608-475dbd4d933a
 # ╟─56685887-7866-446c-acdb-2c20bd11d4cd
+# ╠═647f96ee-c0ad-4bd8-9de1-f24a7dcf6b24
 # ╟─a15750a3-3507-4ee1-8b9a-b7d6a3dcea46
 # ╟─7f855423-72ac-4e6f-92bc-73c12e5007eb
 # ╟─eaaf2227-1a19-4fbc-a5b4-45503e832280

src/10_Boundary_value_problems.jl

@@ -177,8 +177,6 @@ u(0) &= b_0, \quad u(L) = b_L,
 ```
 were $b_0, b_L \in \mathbb{R}$.
 
-TODO IVP is now after BCP, adjust reference accordingly
-
 Similar to our approach when [solving initial value problems (chapter 12)](https://teaching.matmat.org/numerical-analysis/12_Initial_value_problems.html)
 we **divide the full interval $[0, L]$ into $N+1$ subintervals** $[x_j, x_{j+1}]$
 of uniform size $h$, i.e. 
@@ -188,6 +186,9 @@ x_j = j\, h \quad j = 0, \ldots, N+1, \qquad h = \frac{L}{N+1}.
 Our goal is thus to find approximate points $u_j$ such that $u_j ≈ u(x_j)$ at the nodes $x_j$.
 """
 
+# ╔═╡ 782dff7d-76f5-4977-98cb-81881a05331a
+TODO("IVP is now after BCP, adjust reference accordingly")
+
 # ╔═╡ 82788dfd-3462-4f8e-b0c8-9e196dac23a9
 md"""
 Due to the Dirichlet boundary conditions $u(0) = b_0$ and $u(L) = b_L$.
@@ -2659,6 +2660,7 @@ version = "1.4.1+2"
 # ╟─3e10cf8e-d5aa-4b3e-a7be-12ccdc2f3cf7
 # ╟─7fd851e6-3180-4008-a4c0-0e08edae9954
 # ╟─52c7ce42-152d-40fd-a910-78f755fcae47
+# ╠═782dff7d-76f5-4977-98cb-81881a05331a
 # ╟─82788dfd-3462-4f8e-b0c8-9e196dac23a9
 # ╟─d43ecff3-89a3-4edd-95c2-7262e317ce29
 # ╟─1fb53091-89c8-4f70-ab4b-ca2371b830b2