fix minor typos in session 7

Session 7 - Coordinate Transformation/Session 7 - Coordinate Transformation.ipynb

@@ -4,7 +4,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# 7. Tranformation functions\n",
+    "# 7. Transformation functions\n",
     "\n",
     "Coordinate transformations can be performed by matrix operations. Some common ones are:\n",
     "\n",
@@ -74,7 +74,7 @@
     "* In the **scaling matrix** $C_x$ and $C_y$ denote the scaling in the $x$- and $y$-direction, respectively. \n",
     "\n",
     "\n",
-    "* The **mirroring matrix** has no inputs and can bee seen as a boolean operation. It can be done in exactly one way or not done at all. \n",
+    "* The **mirroring matrix** has no inputs and simply flips the sign for the directions to be mirrored. \n",
     "\n",
     "See more here: https://upload.wikimedia.org/wikipedia/commons/2/2c/2D_affine_transformation_matrix.svg"
    ]
@@ -86,13 +86,13 @@
     "## Vectorization in `numpy`\n",
     "`numpy` can perform calculation in a vectorized manner meaning that vector and matrix operations can be done on entire arrays at a time as opposed to value by value. \n",
     "\n",
-    ">**Vectorization can eliminate the use of for loops in many scenarios**\n",
+    ">**Vectorization can eliminate the use of for-loops in many scenarios**\n",
     "> \n",
     ">This makes the code easier to read and write. And as an added bonus, vectorized calculations are also much faster than their looping counterparts.\n",
     "\n",
-    "For the equations above, we can utilize vectorization by using a arrays (or lists) of values for $x$ and $y$ instead of single values. That implies that $1$ also must be an array of ones with the same size.\n",
+    "For the equations above, we can utilize vectorization by using an arrays of values for $x$ and $y$ instead of single values. That implies that $1$ also must be an array of ones with the same size.\n",
     "\n",
-    "Thus, each vector $[x, y, 1]^T$ on the right hand side of the equations is actually an **array of arrays.**\n",
+    "Thus, each vector $[x, y, 1]^T$ on the right hand side of the equations are actually an **array of arrays.**\n",
     "\n",
     "The resulting vector $[x_{\\text{transformed}}, y_{\\text{transformed}}, 1]^T$ is of course also an **array or arrays.**\n",
     "\n",
@@ -274,7 +274,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### Unpacking values for the tranformation examples\n",
+    "### Unpacking values for the transformation examples\n",
     "The resulting array of arrays will have the following code structure\n",
     "\n",
     "~~~python \n",
@@ -364,7 +364,7 @@
     }
    ],
    "source": [
-    "# Create 1x5 vector of ones (1D array)\n",
+    "# Create 5x1 vector of ones (1D array)\n",
     "np.ones(5)"
    ]
   },
@@ -398,7 +398,7 @@
    "metadata": {},
    "source": [
     "# Exercise 1\n",
-    "Write a function that implements rotation of a array of coordinates `x` and `y`. The angle of rotation in clockwise direction should be an input parameter with default value of 90 degrees. The function should return the rotated coordinates `xr` and `yr`.\n",
+    "Write a function that implements rotation of an array of coordinates `x` and `y`. The angle of rotation in clockwise direction should be an input parameter with default value of 90 degrees. The function should return the rotated coordinates `xr` and `yr`.\n",
     "\n",
     "Test the function with these arrays.\n",
     "\n",
@@ -448,7 +448,7 @@
     "\n",
     "Since the given coordinates in Exercise 1 are symmetric about the $y$-axis, the mirrored coordinates will lie on top of the original ones. Try to test it by plotting.\n",
     "\n",
-    "You can quickly make a more visible test by moving all the $x$-coordinates, say 20 units to the right. Since we are using `numpy` this can be done by simply adding 20 to the array itself `x + 20`. This is a simple example of vectorization."
+    "You can quickly make a more visible test by moving all the $x$-coordinates, say 20 units to the right. Since we are using `numpy` this can be done by simply adding 20 to the array itself `x + 20`. This is refered to as Broadcasting."
    ]
   },
   {
@@ -463,7 +463,7 @@
     "```python\n",
     "def transform(x, y, rotation=0, scaling=(1, 1), translation=(0, 0), mirroring=False):\n",
     "    '''\n",
-    "    Perform a combined coordinate transformation according to given inputs. If no inputs are given, returns the unchanged coordinates.\n",
+    "    Perform a combined coordinate transformation according to given inputs. If no inputs are given, return the unchanged coordinates.\n",
     "\n",
     "    Args:\n",
     "        x (array)                   : x-values to transform.\n",
@@ -488,7 +488,7 @@
    "metadata": {},
    "source": [
     "# Additional Exercise\n",
-    "Write a alternative function for translation where the translation input can be given as a distance that the points should move and the corresponding angle from the $x$-axis. This can often be useful instead of the one defined earlier where the distances are given parallel to the $x$- and $y$-axes."
+    "Write an alternative function for translation where the translation input can be given as a distance that the points should move and the corresponding angle from the $x$-axis. This can often be useful instead of the one defined earlier where the distances are given parallel to the $x$- and $y$-axes."
    ]
   },
   {
@@ -803,7 +803,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.7.4"
+   "version": "3.7.3"
   },
   "latex_envs": {
    "LaTeX_envs_menu_present": true,