Add a new chapter to describe window functions

Chapters/05-transforming.qmd

@@ -149,7 +149,7 @@ Partition shuffles are a very popular topic in Apache Spark, because they can be
 A classic example of wide operation is a grouped aggregation. For example, lets suppose we had a DataFrame with the daily sales of multiple stores spread across the country, and, we wanted to calculate the total sales per city/region. To calculate the total sales of a specific city, like "São Paulo", Spark would need to find all the rows that corresponds to this city, before adding the values, and these rows can be spread across multiple partitions of the cluster.
 
 
-## The `transf` DataFrame
+## The `transf` DataFrame {#sec-transf-dataframe}
 
 To demonstrate some of the next examples in this chapter, we will use a different DataFrame called `transf`. The data that represents this DataFrame is freely available as a CSV file. You can download this CSV at the repository of this book[^transforming-1].
 

Chapters/10-datetime.qmd

@@ -1,6 +1,6 @@
 # Tools for dates and datetimes manipulation {#sec-datetime-tools}
 
-Units of measurement that represents time are very commom types of data in our modern world. Nowadays, dates and datetimes (or timestamps) are the most commom units used to represent a specific point in time. In this chapter, you will learn how to import, manipulate and use this kind of data with `pyspark`.
+Units of measurement that represent time are very commom types of data in our modern world. Nowadays, dates and datetimes (or timestamps) are the most commom units used to represent a specific point in time. In this chapter, you will learn how to import, manipulate and use this kind of data with `pyspark`.
 
 In Spark, dates and datetimes are represented by the `DateType` and `TimestampType` data types, respectively, which are available in the `pyspark.sql.types` module. Spark also offers two other data types to represent "intervals of time", which are `YearMonthIntervalType` and `DayTimeIntervalType`. However, you usually don't use these types directly to create new objects. In other words, they are intermediate types. They are a passage, or a path you use to get to another data type.
 
@@ -24,7 +24,7 @@ Dates are normally interpreted in `pyspark` using the `DateType` data type. Ther
 
 ### From strings
 
-When you have a `StringType` column in your DataFrame that contains dates that currently being stored inside strings, and you want to convert this column into a `DateType` column, you basically have two choices: 1) use the automatic column conversion with `cast()` or `astype()`; 2) use the `to_date()` Spark SQL function to convert the strings using a specified date format.
+When you have a `StringType` column in your DataFrame that contains dates that are currently being stored inside strings, and you want to convert this column into a `DateType` column, you basically have two choices: 1) use the automatic column conversion with `cast()` or `astype()`; 2) use the `to_date()` Spark SQL function to convert the strings using a specific date format.
 
 When you use the `cast()` (or `astype()`) column method that we introduced at @sec-cast-column-type, Spark will perform a quick and automatic conversion to `DateType` by casting the strings you have into the `DateType`. But when you use this method, Spark will always assume that the dates you have are in the ISO-8601 format, which is the international standard for dates. This format is presented at @fig-iso-8601-dates:
 
@@ -196,7 +196,7 @@ df2.show()
 
 ### From integers
 
-You can also convert integers directly to datetime values by using the `cast()` method. In this situation, the integers are interpreted as being the number of seconds since the UNIX time epoch, which is mid-night of 1 January of 1970 (`"1970-01-01 00:00:00"`). In other words, the integer `60` will be converted the point of time which is 60 seconds after `"1970-01-01 00:00:00"`, which would be `"1970-01-01 00:01:00"`.
+You can also convert integers directly to datetime values by using the `cast()` method. In this situation, the integers are interpreted as being the number of seconds since the UNIX time epoch, which is mid-night of 1 January of 1970 (`"1970-01-01 00:00:00"`). In other words, the integer `60` will be converted the point in time that is 60 seconds after `"1970-01-01 00:00:00"`, which would be `"1970-01-01 00:01:00"`.
 
 In the example below, the number 1,000,421,325 is converted into 19:48:45 of 13 September of 2001. Because this exact point in time is 1.000421 billion of seconds ahead of the UNIX epoch.
 
@@ -219,9 +219,9 @@ df3.show()
 
 
 
-However, you probably notice in the example above, that something is odd. Because the number 500 was converted into `"1969-12-31 21:08:20"`, which is in teory, behind the UNIX epoch, which is 1 January of 1970. Why did that happen? The answer is that **your time zone is always taken into account** during a conversion from integers to datetime values!
+However, you probably notice in the example above, that something is odd. Because the number 500 was converted into `"1969-12-31 21:08:20"`, which is in theory, behind the UNIX epoch, which is 1 January of 1970. Why did that happen? The answer is that **your time zone is always taken into account** during a conversion from integers to datetime values!
 
-In the example above, Spark is running on an operating system that is using the Brasília time zone (which is 3 hours late from international time zone - UTC-3) as the "default time zone" of the system. As a result, integers will be interpreted as being the number of seconds since the UNIX time epoch **minus 3 hours**, which is `"1969-12-31 21:00:00"`. So, in this context, the integer `60` would be converted into `"1969-12-31 21:01:00"` (instead of the usual `"1970-01-01 00:01:00"` that you would expect).
+In the example above, Spark is running on an operating system that is using the America/Sao_Paulo time zone (which is 3 hours late from international time zone - UTC-3) as the "default time zone" of the system. As a result, integers will be interpreted as being the number of seconds since the UNIX time epoch **minus 3 hours**, which is `"1969-12-31 21:00:00"`. So, in this context, the integer `60` would be converted into `"1969-12-31 21:01:00"` (instead of the usual `"1970-01-01 00:01:00"` that you would expect).
 
 That is why the number 500 was converted into `"1969-12-31 21:08:20"`. Because it is 500 seconds ahead of `"1969-12-31 21:00:00"`, which is 3 hours behind the UNIX time epoch.