CALCULUS CAROLS

1. (01) Fill the Boards with Differentials
("Deck the Halls")
Fill the boards with differentials.
FA LA LA LA LA LA LA LA LA
Note, the du's are essential.
FA LA LA LA LA LA LA LA LA
C's are constants, here before us.
FA LA LA LA LA LA LA LA LA
Integration cannot floor us
FA LA LA LA LA LA LA LA LA
Quizzes always make us queasy.
FA LA LA LA LA LA LA LA LA
Maxs and mins are never easy.
FA LA LA LA LA LA LA LA LA
Conic volumes we can measure.
FA LA LA LA LA LA LA LA LA
Nines and tens we'll always treasure.
FA LA LA LA LA LA LA LA LA

2. (02)
Mr G is Teaching BC!
("Santa's Coming to Town")
Oh! You better take out an 89,
Open your ears and open your eyes,
Mr G is teaching BC!
He's talking too fast and making 2s 4s,
Wondering why we're taking his course,
Mr G is teaching BC!
He's putting up a graph now,
And draws a single line,
And by the time my graph is drawn,
He's added a pi sign!
Huh? You better not miss a single class,
If you ever hope to pass,
Mr G is teaching BC!

3. (03) The 12 Days of Calculus
On the 12th day of Calculus, Mr. G gave to me:
12 digressions off topic,
11 AB1s for homework,
10 frustrating Hals*,
09 disks and shells,
08 MCQ Mondays,
07 integrable equations,
06 modes for graphing
*** 05 Disaster Curves!!! ***
04 max and mins,
03 reference angles,
02 complex roots,
and a fear of trigonometry!
*note that "Hal" is our nickname for the TI­89

4. (04) The 12 Days of Newton!
On the 12th day of Calculus, Newton gave to
me twelve homework problems,
11 differential equations,
10 feuds with Hooke,
9 orbiting planets,
8 tides of water,
7 spectrum colors,
6 reflecting telescopes,
5 optic rings,
4 flying comets,
3 Laws of Motion,
2 refracting prisms
and an apple falling from a tree.

5. (05)
Derivatives, Derivatives!
("Oh Christmas Tree")
Derivatives, derivatives,
They help us find the rate of change.
Derivatives, derivatives,
They're not that hard, they're in our range!
The product rule is so much fun,
It's one prime two plus two prime one.
Derivatives, derivatives,
They help us find the rate of change!
Derivatives, derivatives,
They help us find the rate of change.
Derivatives, derivatives,
They're not that hard, they're in our range!

6. (06)
Oh Calculus, Oh Calculus
("Oh Christmas Tree")
Oh Calculus, Oh Calculus,
How tough are both your branches!
Oh Calculus, Oh Calculus,
To pass, what are my chances?
Derivatives I cannot take,
At integrals, my fingers shake!
Oh Calculus, Oh Calculus,
How tough are both your branches!
Oh Calculus, Oh Calculus,
Your theorems I cannot master!
Oh Calculus, Oh Calculus,
My proofs are a disaster!
You pull a trick out of the air,
Or find a reason, God knows where.
Oh Calculus, Oh Calculus,
Your theorems I cannot master!
Oh Calculus, Oh Calculus,
Your problems do distress me!
Oh Calculus, Oh Calculus,
Related rates depress me!
I walk toward lampposts in my sleep,
And running water makes me weep!
Oh Calculus, Oh Calculus,
Your problems do distress me!
Oh Calculus, Oh Calculus,
My limit I am reaching!
Oh Calculus, Oh Calculus,
For mercy I am beseeching.
My grades do not approach a B,
They're just an epsilon from D!
Oh Calculus, Oh Calculus,
My limit I am reaching!

7. (07)
Oh Calculus, Oh Calculus!
("Oh Christmas Tree")
Oh Calculus, Oh Calculus.
How different seem thy branches!
Oh Calculus, Oh Calculus.
How different seem thy branches!
Derivatives tell us the rate of change,
For areas we integrate,
Oh Calculus, Oh Calculus,
How different seem thy branches!
Derivative, Derivative,
the limit your foundation.
Derivative, Derivative,
the limit your foundation.
A quotient, both parts growing nil,
Behold you reach a value still!
Derivative, Derivative,
the limit your foundation.
Oh Integral, Oh Integral,
Partitions getting finer.
Oh Integral, Oh Integral,
Partitions getting finer.
Add more and more of less and less
the errors disappear, we guess!
Oh Integral, Oh Integral,
Partitions getting finer.
Oh Calculus, Oh Calculus,
United are thy branches.
Oh Calculus, Oh Calculus,
United are thy branches.
Because of that eternal gem,
The Fundamental Theorem!
Oh Calculus, Oh Calculus,
United are thy branches.

8. (08)
Oh Calculus, Oh Calculus
("Oh Chanukah, Oh Chanukah")
Oh Calculus, Oh Calculus,
Come enter the mystery.
Let’s all learn theorems,
And find out its history.
Gather in Garcia’s class,
He’ll give us knowledge.
Calculus to learn,
And it’ll help us in college.
And while we are learning,
We are intrigued by its root.
One person per theorem,
Giving us wisdom.
To give their theorems tribute!
One person per theorem,
Giving us wisdom.
To give their theorems tribute!

9. (09) Jingle Bells for Newton!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, hey!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, y prime!
A little tiny kid,
Was born on Christmas Day.
They thought he was a wimp,
And laughed at him all day! HA HA HA!
But little did they know,
He'd really had enough!
That "short giant" showed them one day,
He'd beat a bully up!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, hey!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, y prime!
In school he was a dunce,
He didn't get good grades!
They thought that he would fail,
And not be a thing! HA HA HA!
But little did they know,
What he was to show them!
He became one of the greatest men
In the mathematics world!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, hey!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, y prime!
He went to Trinity,
Where Isaac Barrow taught.
And in 1669,
He took over his spot! HA HA HA!
During all this time,
He began to think a lot!
Then in '87 he went
And wrote Principia!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, hey!
Jingle Bells, Jingle Bells, Newton's day today,
Oh, what fun it is to derive in Newton's open sleigh, y prime!

10. (10) Riemann Sums Carol! ("Jingle Bells")
Riemann Sums, Riemann Sums,
Counting Areas
Of Rectangles whose widths get small
We need to count them all!
Riemann Sums, Riemann Sums,
Counting Areas
Of Rectangles whose widths get small
We need to count them all!
We Learn to integrate,
It's really lots of fun.
It's easier to find
Than those old Riemann Sums!
We learn to sub a u,
Then things get sort of hard.
But most of all we tabulate
When we get sick of parts!
Riemann Sums, Riemann Sums,
Counting Areas
Of Rectangles whose widths get small
We need to count them all!
Riemann Sums, Riemann Sums,
Counting Areas
Of Rectangles whose widths get small
We need to count them all!

11. (11) Calculus Rock ("Jingle Bell Rock")
Calculus, Calculus, Calculus Class
It's such a great pain in the ass (ymptote)!
Inte­gratin'
And using u­sub,
Deriving the quadratic formula!
All BC kids are really smart,
All AB kids are dumb.
But we still fail all the tests,
The disaster curve's fun!
I'm not a bright guy,
It's the wrong time
To use an integral.
The derivative of a function
Is the slope of the tangent line!
Calculus, Calculus, Calculus Class
You are an x triple prime (of time)!
If we're lucky, we just might pass
Here in Calculus, Here in Calculus, Here in Calculus class!

12. (12) An Engineer’s Xmas!
There are approximately two billion children (persons under 18) in the world. However, since
Santa does not visit children of Muslim, Hindu, Jewish or Buddhist (except maybe in Japan)
religions, this reduces the workload for Christmas night to 15% of the total, or 378 million
(according to the population reference bureau). At an average (census) rate of 3.5 children per
household, that comes to 108 million homes, presuming there is at least one good child in
each.
Santa has about 31 hours of Christmas to work with, thanks to the different time zones and
the rotation of the earth, assuming east to west (which seems logical). This works out to 967.7
visits per second. This is to say that for each Christian household with a good child, Santa
has around 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the
stocking, distribute the remaining presents under the tree, eat whatever snacks have been left
for him, get back up the chimney, jump into the sleigh and get onto the next house.
Assuming that each of these 108 million stops is evenly distributed around the earth (which,
of course, we know to be false, but will accept for the purposes of our calculations), we are now
talking about 0.78 miles per household; a total trip of 75.5 million miles, not counting
bathroom stops or breaks.
This means Santa’s sleigh is moving at 650 miles per second­­3,000 times the speed of sound.
For purposes of comparison, the fastest man made vehicle, the Ulysses space probe, moves at a
poky 27.4 miles per second, and a conventional reindeer can run (at best) 15 miles per hour.
The payload of the sleigh adds another interesting element. Assuming that each child gets
nothing more than a medium sized LEGO set (two pounds), the sleigh is carrying over 500
thousands tons, not counting Santa himself. On land, a conventional reindeer can pull no
more than 300 pounds. Even granting that the "flying" reindeer can pull 10 times the normal
amount, the job can’t be done with eight or even nine of them­­­Santa would need 360,000 of
them. This increases the payload, not counting the weight of the sleigh, another 54,000 tons,
or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch).
600,000 tons traveling at 650 miles per second creates enormous air resistance—this would
heat up the reindeer in the same fashion as a spacecraft re­entering the earth’s atmosphere.
The lead pair of reindeer would adsorb 14.3 quintillion joules of energy per second each. In
short, they would burst into flames almost instantaneously, exposing the reindeer behind
them and creating deafening sonic booms in their wake. The entire reindeer team would be
vaporized within 4.26 thousandths of a second, or right about the time Santa reached the fifth
house on his trip.
Not that it matters, however, since Santa, as a result of accelerating from a dead stop to 650
m.p.s. in .001 seconds, would be subjected to acceleration forces of 17,000 g’s. A 250 pound
Santa (which seems ludicrously slim) would be pinned to the back of the sleigh by 4,315,015
pounds of force, instantly crushing his bones and organs and reducing him to a quivering
blob of pink goo. Therefore, if Santa did exist, he doesn’t anymore!