Transcript Calculus

Calculus
What is it?
What good is it?
What is Calculus?
A
systematic method for solving
problems about systems that change.
A language for describing dynamic
systems.
A collection of ideas based on
infinite processes and limits.
Systems that change
Precalculus
Calculus
Limit
Process
With Calculus you can…
Calculate
the slope of line…
even when the shape of the line is
always changing!
Systems that change
Precalculus
A
B
200 Miles
4 Hours
Average speed =
50 mph
Limit Calculus
Process
Instantaneous
Speed = 55 mph
With Calculus you can…
Calculate
the speed of a car or a
particle in space…
even when the speed is always
changing!
Systems that change
Precalculus
Limit Calculus
Process
y  x 3  6x 2  9x 1
5
5

4
Area = 20
4
Area = 12
With Calculus you can…
Calculate
the area under a curve…
even when the height is always
changing!
A method for solving problems
about systems that change
Precalculus
formulas:
Slope of a line
Average speed
Area of a rectangle
Calculus
formulas:
Slope of a curve
Instantaneous speed
Area under a curve
A language for describing
dynamic systems.
Precalculus:
Calculus:
Slope of a line
Average speed
Area of a rectangle
Slope
Instantaneous speed
Area
Other things calculus can do:
Explain
why the angle between an
observer and a rainbow is 42 degrees.
Connect designs on a laser printer to
form letters of arbitrary size.
Find the best seat in the theater for
viewing a movie.
Etc.
What is Calculus?
A
systematic method for solving
problems about systems that change.
A language for describing dynamic
systems.
"Velocity is the derivative of
position"
ds
v
dt
The
relation between velocity and
position is given precisely in the
language of calculus.

"Force is the derivative of
momentum"
d(mv)
F
dt
Newton's
second law of motion is
accurately and precisely described in
the language of calculus.

ds
v
dt
The
d(mv)
F
dt
language of calculus shows that
the relationship between velocity and
position is the same as that between
 force and momentum.
What is Calculus?
A
systematic method for solving
problems about systems that change.
A language for describing dynamic
systems.
A collection of ideas based on
infinite processes and limits.
Big Ideas of Calculus
Limits
Differential
Integral
Calculus
Calculus
What good is calculus?
…there is an opposition in all things.
If not so … righteousness could not
be brought to pass; neither
wickedness; neither holiness nor
misery; neither good nor bad.
Wherefore, all things are a compound
in one.
II Nephi 1:81-83
Voyager II movie.
QuickTime™ and a
H.264 decompressor
are needed to see this picture.
Calculus was used to find:
Trajectory
of flight
Effect of gravity of Saturn &
Jupiter
Amount of fuel needed
After 12 years of flight, Voyager II
came within 41 miles of its target,
3000 miles from Neptune
The same calculus used to:
Determine trajectories of airborne
bombs and missiles
The same calculus can be used:
To help solve the problems of resource
and energy distribution that are
necessary for peace on earth.
Those who know the calculus
will be the ones who choose which
problems will be solved in this
generation, whether for good or for
evil.
Remember…
To be learned is good
if they hearken to the counsels of
God.
II Nephi 6:61