Lyrics

All lyrics by Marc Gutman except where otherwise credited.

Download the newest version of the lyrics in .doc form.

THE ROCKULUS
5 Sizes of Numbers
The Limit’s Alright
Differentiabul
Jumps Pinches Gaps and Holes
Power Rule
Critical Points
Chain Rule
IM-P-L-I-C-I-T
Triggy Rules
Product Rule
Quotient Rule
Mean Angst
MAXIMA and minima
Without Riemann
Under The Curve
Integration By Parts
Physics Extravaganza
L’Hôpital (I have Calculus in the Heart)
Darcside
The Ballad of Taylor and Maclurin

5 Sizes of Numbers
(In the style of : The Beatles - In My Life)

There are 5 sizes of numbers,
Big Infinity and small Zero,
And the Finite in the middle,
They’re the ones, I’m sure you know.

But now we look between Finite and Zero.
To numbers so small, they’re nothing at all,
But still a little larger than a Zero.
Their name is Infinitesimal.

On the other side of Finite,
There are numbers too large to say,
Infinites are what we call them,
They are big, in every way.

But they will never quite be Infinity,
They’re not quite as big, not even close.
We’ll use all of these numbers in Cal-cu-lus,
The numbers, I love the most.


The Limit’s Alright
(In the style of : The Who - The Kids Are Alright)

I don’t mind if there’s no value at this point,
It’s fine, I’ll find the value anyway.

‘Cause I know, if I come, from the left and the right,
If they meet I will find that the limit’s alright.

Sometimes, I see that x approaches a,
So x, gets infinitely close to a.

And I know, if I come, from the left and the right,
Close enough, I will find that the limit’s alright.

Each small Epsilon’s gonna have a small Delta for sure!
They’ll get so small, they can’t get any smaller!

Sometimes, I see that x approaches a,
So x, gets infinitely close to a.

And I know, if I come, from the left and the right,
If they meet I will find that the limit’s alright.

Differentiabul
(In the style of : They Might Be Giants - Istanbul(Not Constantinople))

f of x plus h minus f of x all over h as h drops to zero
is the formula to find the derivative
in other words state the instantaneous rate.
f of x plus h minus f of x all over h as h drops to zero
is the formula to find the derivative
to find the slope at one point.

Infinitesimals dy over dx,
Why he wrote it I can’t say,
Leibniz just liked it better that way,

So,
f of x plus h minus f of x all over h as h drops to zero
is the formula to find the derivative,
Now Hooke will be coming with a rope…
Newton found the limit of the slope.

Infinitesimals dy over dx.
Why he wrote it I can’t say…
Leibniz just liked it better that way!

f of x plus h minus f of x all over h as h drops to zero
is the formula to find the derivative,
Now Hooke will be coming with a rope…
Newton found the limit of the slope.

Jumps Pinches Gaps and Holes
(In the style of : Graham Pike - Head Shoulders Knees and Toes)

Jumps, Pinches, Gaps and Holes,
Gaps and Holes!

Jumps, Pinches, Gaps and Holes,
Gaps and Holes!

Vertical Tangents and Asymptotes!

Jumps, Pinches, Gaps and Holes,
Gaps and Holes!

Power Rule
(In the style of : Petula Clark - Downtown)

When you have A times an X to the B,
you know you always use:

Power Rule.

Look A B X to the B minus one,
is the derivative.

Power Rule.

Derivatives of constants are always a slope of Zero.
Square Root is the one half power,
You have nothing to fear, Oh! how can you lose?
For all polynomials you can forget all your troubles,
cause everyone knows you use:

Power Rule!

1 over X is Just,

Power Rule!

X to the minus 1.

Power Rule!

Fo Polynomials, Foo!

There is no Dana, just Zool.

Critical Points
(In the style of : Madonna - Material Girl)

The first derivative will show you increase or decrease.
It’s positive or negative y’know respectively.

If the d’rivative is zero or it’s undefined,
Then that point is critical and always on your mind!

You know a saddle is a critical point,
that also is an inflection point.
You know, you know a saddle is an inflection point,
that also is a critical point.

The second d’rivative will tell you concave up or down.
Concave up, positive smile and down negative frown.

The second d’rivative is zero in between the sections,
Of concave up or down and they are called points of inflection.

You know a saddle is a critical point,
that also is an inflection point.
You know, you know a saddle is an inflection point,
that also is a critical point.
It’s a critical, it’s a critical, it’s a critical point.

Chain Rule
(In the style of : Aretha Franklin - Chain of Fools)

For compositions,
I thought u substitution.
So change x out now, save it for the solution.

Oh, you got d - y - d - x is
I know It’s just d - y - d - u,
times d - u - d - x,
Oh respect this Chain Rule

Chain chain chain…
Chain Rule.
Chain chain chain…
Chain Rule.

Every chain, has got one more link,
For each composition, but don’t lose your strength.

Oooh, babe (Woo, woo, woo, woo)
You gotta see the function alone! (Ooo, ooo, ooo, ooo)
Don’t matter what’s inside it at all! (Ooo, ooo, ooo, ooo)
Take the Derivative, take it easy!
Oh don’t change its insides just you clone and now apply the:
Chain, chain, chain…
Chain Rule.
Chain, chain, chain…
Chain Rule.
Oh, we are not finished,
we still gotta take,
derivative of inside,
and multiply all I can babe!

Chain, chain, chain…
Chain Rule.
Chain, chain, chain…
Chain Rule.

IM-P-L-I-C-I-T
(In the style of : Aretha Franklin - Respect)

Change in what? Change in time.
Change in z, or maybe y.

All I’m asking, is for a little Respect,
When you take derivatives
dz
When you take derivatives
When you take them,
When you take derivatives
dt
When you take derivatives

dy’s just a little change in height,
dx is a run, but o so slight,
ratios of differentials happen with respect
they’re just a little bit, just a little bit.

IM-P-L-I-C-I-T find out what it means to me,
IM-P-L-I-C-I-T take with respect to t.

Triggy Rules
(In the style of : Adam Ant - Goody Two Shoes)

D’riv-ative of Sine X, is Cosine X.
Derivative of Secant X is, Amazing! Secant X Tan X
Driv-ative Tangent X, Secant Squared X.
Remember the Chain rule, Chain Rule!
Don’t forget the dx, dx!

Triggy rules, triggy rules,
Triggy, triggy, trigg rules,

Triggy rules, triggy rules,
Triggy, triggy, trigg rules,

Y’know trig don’t choke,
Derivatives of co-functions are-
All Negative.

Ya substitute the functions for the co-functions as implied.

I said y’know trig don’t choke,
Derivatives of co-functions are-
All negative.

Ya substitute the functions for the co-functions as implied.


Product Rule
(In the style of : The Beatles - Till There Was You)

First d Last, Last d First,
You must add both terms together.
When your function’s made up of two.
The Product Rule.

Quotient Rule
A Classic Calculus Mnemonic, Unknown Author
(In the style of : Friedrich W. Möller - The Happy Wanderer)

Lo D Hi! - MINUS! - Hi D Lo! - OVER!
Over Lo! Over Lo-ho-ho-ho-ho-ho

Lo D Hi! - MINUS! - Hi D Lo! - OVER!
Lo squared: The Quotient Rule!

Mean Angst
(In the style of : Cracker - Teen Angst)

Take two points called A and B, and find the slope so easily,
Rise over Run, of the line through them.

In between, now there is a point, its name is C, and I surely don’t…
Wanna underestimate its importance.

‘Cause what the point proves now is the Mean Value Theorem,
Which holds for continuous curves.

‘Cause the slopes at point C and the line that I mention,
Are equal as can be observed.

*I don’t know what the world may need,
But another theorem’s a good start for me.
Take two points of the same height on a function.

C’s still the point that’s in between,
That Theorem of Value sure is Mean.
Think I mean that it’s time to extend it.

*Cause what the world needs now are some true words of wisdom
Like Horizontal Tangent at Point C, yeah.

Cause what the curve needs now is another slope of zero
Like I need a Rolle in my head.

*These lines are the same as the original.

MAXIMA and minima
(In the style of : Orffenbach - Can Can)

For Maxima and minima just take derivitinima!
Happiness, now just assess the zero, zero, zero, zero!
Don’t forget you must inspect the endpoints as they are suspect!
Find the values of our function, look for Highs and Lows!

Local Maxima are on an Interval,
Local Minima are on an Interval!
Global Maxima aren’t on an Interval,
Global Minima aren’t on an Interval!
-terval! -terval! -terval!

Saddle, Peak and Trough and
Saddle, Peak and Trough and
Saddle, Peak and Trough and
Peak and Trough and
Peak and Trough and
Saddle, Peak and Trough and
Saddle, Peak and Trough and
Saddle, Saddle,
Peak and Trough and
Peak and Trough.

and!
Saddle, Peak and Trough and
Saddle, Peak and Trough and
Saddle, Peak and Trough and
Peak and Trough and
Peak and Trough and
Saddle, Peak and Trough and
Saddle, Peak and Trough and
Saddle, Saddle,
Peak and Trough and
Peak and Trough.

Now Maxima and minima
are also called the extrema,
Sometimes they can be absolute
as long as there’s no greater, lesser,
Relative implies a region that the extremum is in.
DON’t confuse a saddle point!
With an Extremum!

Local Maxima are on an Interval,
Local Minima are on an Interval!
Global Maxima aren’t on an Interval,
Global Minima aren’t on an Interval!
-terval! -terval! -terval!

Saddle, Peak and Trough!

Without Riemann
(In the style of : Eminem - Without Me)

“G. F. B. Riemann: no gimmicks”

To find the whole area under the curve, under the curve, under the curve
To find the whole area under the curve, under the curve, under the curve
Interval: A to B. f of x, stay with me:
f of x, f of x, f of x, f of x, f of x, f of x, f of x….

I’ve a curve that’s all angles, I’m using rectangles,
To find the area so?I use slices, 1 to n.
Well if you want slices this is what I’ll tell ya,
Each little width is B minus A over n-ah,
‘Cause width is changing-on-the x its delta -
X, And height: f of x sub i from the middle,
or the right or left cause you’re evaluating,
from the i of the slice that you are calculating.

A! The Area’s from mul-ti-plication,
of the width an the height gimme some adulation.
I know that you got Sigma Notation,
When your slices add in a big summation!

So the BCE, won’t disagree,
And let me decree Archimedes.
He had the same idea in ancient Greece.
But it feels exhausting without Rie-

mann, Hanover kid summing the bits,
And more cunning and witz, than Brechtian skitz.

And get on it, it’s all working out, you don’t shun it,
I just set up my summation, time to sum it!

And this looks like a job for Rie-
mann, add it up from A to B and
The more slices that you see
Can increase your accuracy.

And this looks like a job for Rie-
mann, INTEGRAL from A to B and
Sliced to infinity,
for your per-fect accuracy.

Under The Curve
(In the style of : Red Hot Chilli Peppers - Under the Bridge)

Area un-der
the curve f of x is
equal to the an-
ti-driv-a-tive of
f of x dx.
It is fundamental
Geometry and
Analysis tied.

Integral from A to B;
Anti-derivatae.
Take the val-ue at B sub
-tract the val-ue at A.


Integration By Parts
(In the style of : The Platters - Only You)

Inte - grooool of u d v by parts,
Inte - grooool of u d v my hearts,
Inte - grooool of u d v
will always equal u
times v minus integral v d u

Physics Extravaganza
(In the style of : Gilbert & Sullivan - Modern Major General)

Position is the place you are at any given time you see,
The instantaneous rate of change of that is the velocity,
Which is direction and the speed two parts of information,
Its instantaneous rate of change is called acceleration.

The total distance traveled is by no means an atrocity,
the integral of absolute value of the velocity!
Another point of interest know the integral of force is work.
Accelerations rate of change is surge or lurch or jolt or jerk!

Displacement is how far you are from your initial starting spot,
Remembering the average value of a function is a lot,
One over B minus A times the value of the integral
from A to B of f of x dx if on an interval.

L’Hôpital (I have Calculus in the Heart)
(In the style of : Bonnie Tyler - Total Eclipse of the Heart)

L’Hôpital
Every now and then I get a little bit of trouble when I’m taking a limit.
L’Hôpital
Every now and then I get a zero for the numerator and the denominator.
L’Hôpital
Every now and then I get a limit that’s confusing in some kind of indeterminate form.
L’Hôpital
Every now and then I get a little bit terrified but then I think of all your advice.
L’Hôpital
Guillaume François Antoine Marquis de
L’Hôpital
Guillaume François Antoine Marquis de L’Hôp!

So we take the rate of change,
Of the top and of the bottom,
We don’t need to rearrange,
We’re just go-ing to compare them,
And I know that we’re making this strange,
Cause we take the limit again,
If we find out that we cannot define
Our limit, we will have to go repeat one more time.
This almost always works, but if you’re in the dark,
An Oscillating Function may be leaving its mark!

And then this song doesn’t work!

But most of the time, well it does,
For most of the time our song works.

Once upon a time I had trouble with math,
But now they all think that I am smart,
There’s nothing I can’t do,
I have Calculus in the heart.

Once upon a time I was crying all night,
But now I do my math in the dark.
Nothing I can say,
I have Calculus in the heart.

DARCSIDE

I got a dark side that comes
With a cold stare,
I got a Darcsine that knows
How to prepare:
One over Square root of
one minus ex squared.

Sounds and bounds won’t play fair.

I got a dark side like
A-tilla the Hun,
My Darcsecant takes a
Back seat to no one,
One over ex Square-root
Ex-squared mi-nus one.

Inverse makes exclusion.

I got a dark side which
Makes people so scared,
Darctangent one over
one plus an ex squared.
Cofunction drivatives are
Always neg-tived.

Darc Side for a Trig Dread.

The Ballad of Taylor and Maclurin

A function can become a sweet series,
Said Taylor as he stepped into the breeze,
From term zero to term infinity,
You’ll find out every term so easily:

Evaluate the nth derivative at ‘a’,
times ‘x’ minus ‘a’ to the nth power,
over n factorial,

Then Maclurin said, “Hello,
I’d prefer it if the ‘a’ was just Zero.”

© 2006 Marc Gutman