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docs: consistency of variable names #103

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8 changes: 4 additions & 4 deletions docs/src/tutorials/integral_operators.md
Original file line number Diff line number Diff line change
Expand Up @@ -59,19 +59,19 @@ nothing # hide
Much goes on under the hood in the function above, and the sections on
[correction](@ref "Correction methods") and [compression](@ref "Compression
methods") methods will provide more details on the options available. The
important thing to keep in mind is that `S`, `D`, `K`, and `H` are discrete
important thing to keep in mind is that `S`, `D`, `K`, and `N` are discrete
approximations of the following (linear) operators:

```math
\begin{aligned}
S[\sigma](\boldsymbol{x}) &:= \int_{\Gamma} G(\boldsymbol{x}, \boldsymbol{y}) \sigma(\boldsymbol{y}) \mathrm{d} s_{\boldsymbol{y}}, \quad
&&D[\sigma](\boldsymbol{x}) := \mathrm{p.v.} \int_{\Gamma} \frac{\partial G}{\partial \nu_{\boldsymbol{y}}}(\boldsymbol{x}, \boldsymbol{y}) \sigma(\boldsymbol{y}) \mathrm{d} s_{\boldsymbol{y}} \\
D'[\sigma](\boldsymbol{x}) &:= \mathrm{p.v.} \int_{\Gamma} \frac{\partial G}{\partial \nu_{\boldsymbol{x}}}(\boldsymbol{x}, \boldsymbol{y}) \sigma(\boldsymbol{y}) \mathrm{d} s_{\boldsymbol{y}}, \quad
K[\sigma](\boldsymbol{x}) &:= \mathrm{p.v.} \int_{\Gamma} \frac{\partial G}{\partial \nu_{\boldsymbol{x}}}(\boldsymbol{x}, \boldsymbol{y}) \sigma(\boldsymbol{y}) \mathrm{d} s_{\boldsymbol{y}}, \quad
&&N[\sigma](\boldsymbol{x}) := \mathrm{f.p.} \int_{\Gamma} \frac{\partial^2 G}{\partial \nu_{\boldsymbol{x}} \partial \nu_{\boldsymbol{y}}}(\boldsymbol{x}, \boldsymbol{y}) \sigma(\boldsymbol{y}) \mathrm{d} s_{\boldsymbol{y}}
\end{aligned}
```

The actual type of `S`, `D`, `K`, and `H` depends on the `compression` and
The actual type of `S`, `D`, `K`, and `N` depends on the `compression` and
`correction` methods. In the simple case above, these are simply matrices:

```@example integral_operators
Expand Down Expand Up @@ -133,7 +133,7 @@ Calderón projectors:
\begin{aligned}
H = \begin{bmatrix}
-D & S \\
-N & D'
-N & K
\end{bmatrix}
\end{aligned}
```
Expand Down