Youth Curriculum

1. COMPLEX/
IMAGINARY NUMBERS
JUS A LIL MORE DERIVATIVES

2. QUIZ TIME
•
•
• What are we finding when we do ?
Hint: The answer is one word:)
d
dt
(t2
) = ?
d
dt
(t4
) = ?
d
dt
(t2
)

3. Example 1:
x = t2
TAKING DERIVATIVES OF THE POSITION
1. Copy the 2 from the top and put it in front of the t.
2. Subtract 1 from the 2 up top
3. Sit back and realize that you are a calculus genius!
x = 2t
x = 2t2
1.
x = 2t1
2.
EINSTEIN GOT NOTHIN’
ON YOU!
3.

4. QUIZ TIME - SOLUTIONS
• Answer
• Answer
• What are we finding when we do ?
d
dt
(t2
) = 2t1
or 2t
d
dt
(t4
) = 4t3
d
dt
(t2
)
d
dt
(t2
) = Speed

5. MY FAVORITE PHYSICIST!
WOLFGANG PAULI
• Pauli was an Austrian theoretical
physicist and one of the pioneers
of quantum physics.
• Pauli received the Nobel Prize in Physics for
his "decisive contribution through his
discovery of a new law of Nature, the
exclusion principle or Pauli principle".
• Some of the greatest scientist moved
beyond physics to other realms of science.
• For Pauli, he became great friends with Carl
Jung and developed theories of
synchronicity

6. PAULI MATRICES
σ1 = σx =
[
0 1
1 0]
σ2 = σy =
[
0 −i
i 0 ]
σ2 = σz =
[
1 0
0 −1]
• These matrices help us to better understand the
“state” of an electron. Think about texting your
friend.
Friend: How did you like the chicken nuggets at lunch
today.
You: They were soooo great. I wish I had them all the
time!
• If your friend could see your face, she would know
you’re being sarcastic and you really thought the
chicken nuggets were bad.
This is what the Pauli matrices do for learning more
about electrons. They give us more information
about the electron.

7. • Me: My memes are the best!
• My cats:

8. TAKING A DERIVATIVE OF SPEED
• Now lets go down the rabbit hole a little
farther!
•
• - Remember, that v is the letter for
speed!
• What is we took the derivative of speed?
•
d
dt
(t4
) = 4t3
v = 4t3
dv
dt
=
d
dt
(4t3
)

9. TAKING A DERIVATIVE OF SPEED
• Remember, when we take the derivative of speed we get
• Acceleration!
• Well, there is only one extra step!

10. TAKING DERIVATIVES OF THE POSITION
THEN, TAKE DERIVATIVE OF SPEED
1. Copy the 2 from the top and put it in front of the t.
2. Subtract 1 from the 2 up top
3. Sit back and realize that you are a calculus genius!
• - The is the function for the position of
Josh as he walks around his house
•
• - The derivative of position is SPEED!
•
•
x = t4
dx
dt
=
d
dt
(t4
)
v = 4t3
dv
dt
=
d
dt
(4t3
)
a = 12t2
d
dt
(4t3
) = 3 × 4t2
= 12t2
You do the same steps.
Except that the 4 and 3
have to be multiplied
together! Thats it:)

11. LET’S LOOK AT SOME EXAMPLES
x = t3
dx
dt
=
d
dt
(t3
)
v = 3t2
dv
dt
=
d
dt
(3t2
)
a = 2 × 3t a = 6t
x = t5
dx
dt
=
d
dt
(t5
)
v = 5t4
dv
dt
=
d
dt
(5t4
)
a = 4 × 5t3
a = 20t3

12. LET’S LOOK AT SOME EXAMPLES
x = t7
dx
dt
=
d
dt
(t7
)
v = 7t6
dv
dt
=
d
dt
(7t6
)
a = 6 × 7t5
a = 42t5
x = t2
dx
dt
=
d
dt
(t2
)
v = 2t1
dv
dt
=
d
dt
(2t1
)
a = 1 × 2t0 a = 2
If a is just a number
there is no acceleration!

13. JUST A RECAP OF DERIVATIVES
• Remember that a derivative looks at how something is changing over time
• Speed is when we look at how position is changing over time
• Accelerations is when we look at how velocity is changing over time
• Well, we can look at how other things are changing as well!

14. MAGNETIC FIELDS CREATE
CURRENTS:
ANOTHER FORM OF DERIVATIVES

15. CHANGING MAGNETIC FIELDS
MAGNETIC FIELDS
• A
• Here we have a function for magnetic field.
• Taking the derivative of a magnetic field will give you VOLTAGE!
• Voltage comes from things like batteries. But, it can come from moving magnetics
as well!
V = −
dB
dt

16. • Let’s look at an example
•
•
•
• Let’s talk about how we did this!
•
B = t2
+ t3
dB
dt
=
d
dt
(t2
+ t3
)
d
dt
(t2
+ t3
) = 2t + 3t2
V = 2t + 3t2
MAGNETIC FIELDS
CHANGING MAGNETIC FIELDS

17. COMPLEX/IMAGINARY
NUMBERS

18. IMAGINARY NUMBERS
We are told that all the numbers, like ALL the numbers ever exist on the number line.
Think about whole number, numbers with decimals, fractions. (like I said ALL the numbers)

19. HISTORY OF NUMBERS
The number line used to begin at 0. This was cool and worked for
simple stuff. But subtraction threw a monkey wrench right into math.

20. HISTORY OF NUMBERS
So, because of subtraction, negative numbers were born. Bask in all its glory.
But, wait there is so much more!
The culprit was division and decimals. Like what happens in-between the numbers.
Then, we had fractions!!!!! Yay, I know you all love fractions!

21. NUMBER HISTORY
So, that’s the end of the story right?
Nope, not even close!

22. NUMBER HISTORY
• Then, math peeps went crazy and started to make numbers that could not be
expressed as decimals, fractions or whole numbers.
These are like . This number goes on for ever and ever and ever and ever
and….well, you get the point.
• And no the story continues.
π

23. MISFIT NUMBERS
THE NUMBER THAT WOULD NOT FIT
•
• This number is not allowed on the number line.
• Why you ask.
• Well,
−1
25 = 5, 4 = 2, −1 = Has no solution

24. THE NUMBER THAT WOULD NOT FIT
So math peeps invented a new number line

25. THE MISFIT NUMBERS
So, a number on the complex plane looks like:
Now, a number has a “real” part (a) & an
“imaginary” part (b)
i = −1
a + biReal Imaginary