The mathematics of continuous change Instead of looking at average or overall results calculus looks at how things change from second to second Calculus The mathematics of continuous change Instead of looking at average or overall results calculus looks at how things change from second to se ID: 622476
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Calculus
The mathematics of continuous change
Instead of looking at average or overall results, calculus looks at how things change from second to second.Slide3
Calculus
The mathematics of continuous change
Instead of looking at average or overall results, calculus looks at how things change from second to second.Slide4
For example, you remember problems like this:
Grandma drives 40mph for 6 hours. How far does she drive?Slide5
For example, you remember problems like this:
Grandma drives 40mph for 6 hours. How far does she drive?
40 X 6
240 milesSlide6
In the real world, though, nobody drives 40mph constantly for 6 hours.
Speed limits vary.
You speed up going downhill
and slow down going uphill.
You accelerate and hit the
brakes.
You might even stop and start
again.Slide7
Calculus looks at what happens at any given second while you’re driving—not just the overall average.Slide8
Calculus was developed around the year 1700, separately but simultaneously, by Isaac Newton in England and Gottfried von Leibniz in Germany.Slide9
3 main topics of calculus
Limits
Derivatives
AntiderivativesSlide10
Limits
What is infinity
?Slide11
Limits
What
happens when you divide by zero?Slide12
Derivatives
What is the slope of a curve?Slide13
Derivatives
How
are things changing
?Slide14
Derivatives
How
can you make the maximum profit or achieve the least cost in business?Slide15
Antiderivatives
(Integrals)
What is the area or volume of an irregular region
?Slide16
Antiderivatives
(Integrals)
What
function has a given graph (or will create desired standards)?