Calculus
In Introduction To Differentiation
The Gradient Of A Curve At A Point
Absolute Maximum And Minimum On A Restricted Domain
Gil Strang's Introduction to Calculus for Highlights for High School
Gil Strang gives an overview of his video series
Calculus for MIT's Highlights for High School program.
Designed to give an easier introduction to calculus.
Big Picture of Calculus
Calculus is about change.
One function tells how quickly another function is changing.
Professor Strang shows how calculus applies to ordinary life situations,
such as:
* driving a car
* climbing a mountain
* growing to full adult height
Big Picture: Derivatives
Calculus finds the relationship between
the distance traveled and the speed
- easy for constant speed, not so easy for changing speed.
Professor Strang is finding the "rate of change"
and the "slope of a curve" and the "derivative of a function."
Max and Min and Second Derivative
At the top and bottom of a curve (Max and Min), the slope is zero.
The "second derivative" shows whether the curve is bending down or up.
Here is a real-world example of a minimum problem:
What route from home to work takes the shortest time?
Big Picture: Integrals
The second half of calculus looks for the distance traveled
even when the speed is changing.
Finding this "integral" is the opposite of finding the derivative.
Professor Strang explains how
the integral adds up little pieces to recover the total distance.
I know the speed at each moment of my trip, so how far did I go?
The Exponential Function
Professor Strang explains how the "magic number e"
connects to ordinary things like the interest on a bank account.
The graph of y = ex has the special property
that its slope equals its height (it goes up "exponentially fast"!).
This is the great function of calculus.
