Data science makes math concepts easier to understand.
I’m going to teach you the fundamental theorem of calculus and it’s going to sound so simple that you could explain it to kid in grade school. 👇
I’m going to teach you the fundamental theorem of calculus and it’s going to sound so simple that you could explain it to kid in grade school. 👇
I’ll be using some covid data to illustrate my point.
For the purposes of this explanation assume we’re talking about covid cases both past and present (not just the active infections).
For the purposes of this explanation assume we’re talking about covid cases both past and present (not just the active infections).
Fundamental Theorem of Calculus, Part 1:
“The daily change in the total number of cases so far is equal to the new cases.”
(The red area in both plots represents the same number of cases)
“The daily change in the total number of cases so far is equal to the new cases.”
(The red area in both plots represents the same number of cases)
Fundamental Theorem of Calculus, Part 2:
“Adding up all the new cases during a certain time period is equivalent to subtracting the total number of cases at the start of the period from the total number of cases at the end.”
(The black areas represent the same number eof cases)
“Adding up all the new cases during a certain time period is equivalent to subtracting the total number of cases at the start of the period from the total number of cases at the end.”
(The black areas represent the same number eof cases)
That’s it. This is the basic intuition behind the fundamental theorem of calculus.
For fun, let’s take a peek at what it looks like in mathematical notation.
For fun, let’s take a peek at what it looks like in mathematical notation.
Fundamental Theorem of Calculus, Part 1:
Fundamental Theorem of Calculus, Part 2:
In general, the fundamental theorem of calculus establishes a link between the process of adding up a series of values and the change in the total sum of those values.
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I messed up the image for Fundamental Theorem of Calculus Part 2. Sorry for the confusion. It should be this:
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