Typo fixes by @navlalli (#188)

* Fix typos

* Fix typos in chapter 1

* Change u * exact to u_exact

* Add complex back to display_name

* Add message about jupytext in README

* Fix typos in chapter 2

* Fix typos in chapter 3

* Fix typos in subdomains tutorial

* Fix typos in chapter 4

* Revert import order

---------

Co-authored-by: Navraj Lalli <navrajsinghlalli@gmail.com>

Author: jorgensd

README.md

@@ -16,16 +16,16 @@ If you want to contribute to this tutorial, please make a fork of the repository
 act -j test-nightly
 ```
 
-Any code added to the tutorial should work in parallel.
-
 Alternatively, if you want to add a separate chapter, a Jupyter notebook can be added to a pull request, without integrating it into the tutorial. If so, the notebook will be reviewed and modified to be included in the tutorial.
 
-Also ensure that both Python file and notebook files are updated by using jupytext, i.e.
+Any code added to the tutorial should work in parallel. If any changes are made to `ipynb` files, please ensure that these changes are reflected in the corresponding `py` files by using [`jupytext`](https://jupytext.readthedocs.io/en/latest/faq.html#can-i-use-jupytext-with-jupyterhub-binder-nteract-colab-saturn-or-azure):
 
 ```bash
 python3 -m jupytext --sync  */*.ipynb
 ```
 
+Any code added to the tutorial should work in parallel.
+
 ## Dependencies
 
 It is adviced to use a pre-installed version of DOLFINx, for instance through conda or docker. Remaining dependencies can be installed with

chapter1/complex_mode.ipynb

@@ -73,7 +73,7 @@
    "source": [
     "However, as we would like to solve linear algebra problems of the form $Ax=b$, we need to be able to use matrices and vectors that support real and complex numbers. As [PETSc](https://petsc.org/release/) is one of the most popular interfaces to linear algebra packages, we need to be able to work with their matrix and vector structures.\n",
     "\n",
-    "Unfortunately, PETSc only supports one floating type in their matrices, thus we need to install two versions of PETSc, one that supports `float64` and one that supports `complex128`. In the [docker images](https://hub.docker.com/r/dolfinx/dolfinx) for DOLFINx, both versions are installed, and one can switch between them by calling `source dolfinx-real-mode` or `source dolfinx-complex-mode`. For the `dolfinx/lab` images, one can change the Python kernel to be either the real or complex mode, by going to `Kernel->Change Kernel...` and choose `Python3 (ipykernel)` (for real mode) or `Python3 (DOLFINx complex)` (for complex mode).\n",
+    "Unfortunately, PETSc only supports one floating type in their matrices, thus we need to install two versions of PETSc, one that supports `float64` and one that supports `complex128`. In the [docker images](https://hub.docker.com/r/dolfinx/dolfinx) for DOLFINx, both versions are installed, and one can switch between them by calling `source dolfinx-real-mode` or `source dolfinx-complex-mode`. For the `dolfinx/lab` images, one can change the Python kernel to be either the real or complex mode, by going to `Kernel->Change Kernel...` and choosing `Python3 (ipykernel)` (for real mode) or `Python3 (DOLFINx complex)` (for complex mode).\n",
     "\n",
     "We check that we are using the correct installation of PETSc by inspecting the scalar type.\n"
    ]
@@ -162,7 +162,7 @@
    "id": "9efe0968-bf32-4184-85f7-4e8cc3401cfb",
    "metadata": {},
    "source": [
-    "Similarly, if we want to use the function `ufl.derivative` to take derivatives of functionals, we need to take some special care. As `derivative` inserts a `ufl.TestFunction` to represent the variation, we need to take the conjugate of this to in order to assemble vectors.\n"
+    "Similarly, if we want to use the function `ufl.derivative` to take derivatives of functionals, we need to take some special care. As `ufl.derivative` inserts a `ufl.TestFunction` to represent the variation, we need to take the conjugate of this to be able to use it to assemble vectors.\n"
    ]
   },
   {

chapter1/complex_mode.py

@@ -59,7 +59,7 @@
 
 # However, as we would like to solve linear algebra problems of the form $Ax=b$, we need to be able to use matrices and vectors that support real and complex numbers. As [PETSc](https://petsc.org/release/) is one of the most popular interfaces to linear algebra packages, we need to be able to work with their matrix and vector structures.
 #
-# Unfortunately, PETSc only supports one floating type in their matrices, thus we need to install two versions of PETSc, one that supports `float64` and one that supports `complex128`. In the [docker images](https://hub.docker.com/r/dolfinx/dolfinx) for DOLFINx, both versions are installed, and one can switch between them by calling `source dolfinx-real-mode` or `source dolfinx-complex-mode`. For the `dolfinx/lab` images, one can change the Python kernel to be either the real or complex mode, by going to `Kernel->Change Kernel...` and choose `Python3 (ipykernel)` (for real mode) or `Python3 (DOLFINx complex)` (for complex mode).
+# Unfortunately, PETSc only supports one floating type in their matrices, thus we need to install two versions of PETSc, one that supports `float64` and one that supports `complex128`. In the [docker images](https://hub.docker.com/r/dolfinx/dolfinx) for DOLFINx, both versions are installed, and one can switch between them by calling `source dolfinx-real-mode` or `source dolfinx-complex-mode`. For the `dolfinx/lab` images, one can change the Python kernel to be either the real or complex mode, by going to `Kernel->Change Kernel...` and choosing `Python3 (ipykernel)` (for real mode) or `Python3 (DOLFINx complex)` (for complex mode).
 #
 # We check that we are using the correct installation of PETSc by inspecting the scalar type.
 #
@@ -92,7 +92,7 @@
 print(L)
 print(L2)
 
-# Similarly, if we want to use the function `ufl.derivative` to take derivatives of functionals, we need to take some special care. As `derivative` inserts a `ufl.TestFunction` to represent the variation, we need to take the conjugate of this to in order to assemble vectors.
+# Similarly, if we want to use the function `ufl.derivative` to take derivatives of functionals, we need to take some special care. As `ufl.derivative` inserts a `ufl.TestFunction` to represent the variation, we need to take the conjugate of this to be able to use it to assemble vectors.
 #
 
 J = u_c**2 * ufl.dx

chapter1/fundamentals_code.ipynb

@@ -35,7 +35,7 @@
     "\n",
     "Inserting $u_e$ in the original boundary problem, we find that  \n",
     "\\begin{align}\n",
-    "    f(x,y)= -6,\\qquad u_d(x,y)=u_e(x,y)=1+x^2+2y^2,\n",
+    "    f(x,y)= -6,\\qquad u_D(x,y)=u_e(x,y)=1+x^2+2y^2,\n",
     "\\end{align}\n",
     "regardless of the shape of the domain as long as we prescribe \n",
     "$u_e$ on the boundary.\n",
@@ -1541,7 +1541,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.6"
+   "version": "3.10.12"
   },
   "vscode": {
    "interpreter": {

chapter1/fundamentals_code.py

@@ -43,7 +43,7 @@
 #
 # Inserting $u_e$ in the original boundary problem, we find that  
 # \begin{align}
-#     f(x,y)= -6,\qquad u_d(x,y)=u_e(x,y)=1+x^2+2y^2,
+#     f(x,y)= -6,\qquad u_D(x,y)=u_e(x,y)=1+x^2+2y^2,
 # \end{align}
 # regardless of the shape of the domain as long as we prescribe 
 # $u_e$ on the boundary.

chapter1/membrane.md

@@ -8,7 +8,7 @@ In this section, we will turn our attentition to a physically more relevant prob
 
 We would like to compute the deflection $D(x,y)$ of a two-dimensional, circular membrane of radius $R$, subject to a load $p$ over the membrane. The appropriate PDE model is 
 \begin{align}
-     -T \nabla^2D&=p \quad\text{in }\quad \Omega=\{(x,y)\vert x^2+y^2\leq R \}.
+     -T \nabla^2D&=p \quad\text{in }\quad \Omega=\{(x,y)\vert x^2+y^2\leq R^2 \}.
 \end{align}
 Here, $T$ is the tension in the membrane (constant), and  $p$ is the external pressure load. The boundary of the membrane has no deflection. This implies that $D=0$ is the boundary condition. We model a localized load as a Gaussian function:
 \begin{align}
@@ -36,7 +36,7 @@ With $D_e=\frac{AR^2}{8\pi\sigma T}$ and dropping the bars we obtain the scaled
 \begin{align}
     -\nabla^2 w = 4e^{-\beta^2(x^2+(y-R_0)^2)}
 \end{align}
-to be solved over the unit disc with $w=0$ on the boundary. Now there are only two parameters which vary the dimensionless extent of the pressure, $\beta$, and the location of the pressure peak, $R_0\in[0,1]$. As $\beta\to 0$, the solution will approach the special case $w=1-x^2-y^2$. Given a computed scaed solution $w$, the physical deflection can be computed by
+to be solved over the unit disc with $w=0$ on the boundary. Now there are only two parameters which vary the dimensionless extent of the pressure, $\beta$, and the location of the pressure peak, $R_0\in[0,1]$. As $\beta\to 0$, the solution will approach the special case $w=1-x^2-y^2$. Given a computed scaled solution $w$, the physical deflection can be computed by
 \begin{align}
     D=\frac{AR^2}{8\pi\sigma T}w.
 \end{align}