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Diffstat (limited to 'build/website/mathematics/calculus/source/derivative.ms')
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diff --git a/build/website/mathematics/calculus/source/derivative.ms b/build/website/mathematics/calculus/source/derivative.ms new file mode 100644 index 0000000..00bff8f --- /dev/null +++ b/build/website/mathematics/calculus/source/derivative.ms @@ -0,0 +1,29 @@ +delim $$ +.TL +The Derivative +.AU +Preston Pan +.AI +Pacific School of Innovation and Inquiry + +.NH 1 +Introduction +.LP +The derivative operator is one of the most important +concepts in calculus, and one of the fundamental building blocks +for all advanced studies regarding STEM. Therefore, it is good +to know the basics behind the subject. I will be introducing them +from the perspective of infinitesimal number, or the hyperreal number +system as it is more formally known. + +.LP +Imagine that you are a physicist studying rate of change. You can measure +the position of a certain object through time, and you want to describe +the average velocity of the object. Since you know that: + +.EQ +delim $$ +v sub average = {\[*D] d(t)} over {\[*D] t} +.EN + +where \[*D]d(t) |