A collection of calculus math quotes and even calculus songs.

"Calculus has its limits."

"The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers." -- Keith Devlin

"The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance." -- E. Purcell and D. Varberg

"God does not care about our mathematical difficulties - he integrates empirically" -- Albert Einstein

"But just as much as it is easy to find the differential [derivative] of a given quantity, so it is difficult to find the integral of a given differential. Moreover, sometimes we cannot say with certainty whether the integral of a given quantity can be found or not." -- Johann Bernoulli

"Among all of the mathematical disciplines the theory of differential equations is the most important... It furnishes the explanation of all those elementary manifestations of nature which involve time." -- Sophus Lie

"In the fall of 1972 President Nixon announced that the rate of increase of inflation was decreasing. This was the first time a sitting president used the third derivative to advance his case for reelection. -- Hugo Rossi"

"Calculus required continuity, and continuity was supposed to require the infinitely little; but nobody could discover what the infinitely little might be." -- Bertrand Russell

"Who has not been amazed to learn that the function y = e^{x}, like a phoenix rising from its own ashes, is its own derivative?" -- Francois le Lionnais

"I recoil with dismay and horror at this lamentable plague of functions which do not have derivatives. -- Charles Hermite

(written by: Denis Gannon(1940-1991) sung to the tune of "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 can't 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 can't master. **

** Oh, Calculus; Oh, Calculus,
My limit I am reaching.
Oh, Calculus; Oh, Calculus,
For mercy I'm beseeching.
My grades do not approach a B,
They're just an epsilon from D.
Oh, Calculus; Oh, Calculus,
My limit I am reaching. **

**Calculus Rhapsody **(to the tune of Bohemian Rhapsody by Queen)

By Phil Kirk & Mike Gospel

Lyrics:

Is this x defined?

Is f continuous?

How do you find out?

You can use the limit process.

Approach from both sides,

The left and the right and meet.

Im a just a limit, defined analytically

Functions continuous,

Theres no holes,

No sharp points,

Or asymptotes.

Any way this graph goes

It is differentiable for me for me.

All year, in Calculus

We've learned so many things

About which we are going to sing

We can find derivatives

And integrals

And the area enclosed between two curves.

Y prime oooh

Is the derivative of y

Y equals x to the n, dy/dx

Equals n times x

To the n-1.

Other applications

Of derivatives apply

If y is divided or multiplied

You use the quotient

And product rules

And don't you forget

To do the dance

Also oooh (don't forget the chain rule)

Before you are done,

You gotta remember to multiply by the chain

(Instrumental solo)

I need to find the area under a curve

Integrate! Integrate! You can use the integration

Raise exponent by one multiply the reciprocal

Plus a constant

Plus a constant

Add a constant

Add a constant

Add a constant labeled C

(Labeled C-ee-ee-ee-ee)

Im just a constant

Nobody loves me.

Hes just a constant

Might as well just call it C

Never forget to add the constant C

Can you find the area between f and g

In-te-grate f and then integrate g

(then subtract)

To revolve around the y-axis

(integrate)

outer radius squared minus inner radius squared

(multiplied)

multiplied by pi

(multiply)

Multiply the integral by pi!

Pi tastes real good with whipped cream!

Mama-Mia, Mama-Mia

Mama-Mia let me go.

Pre-calculus did not help me to prepare for Calculus, for Calculus, help me!

So you think you can find out the limit of y?

So you think you'll find zero and have it defined

Oh baby cant define that point baby

Its undefined

Goes to positive and negative infinity

Oooh. Oooh yeah, oooh yeah.

Differentiation

Anyone can see

Any mere equation

It is differentiable for me.

(Any way this graph goes)

Lyrics:

At first I was afraid, what could the answer be?

It said given this position find velocity.

So I tried to work it out, but I knew that I was wrong.

I struggled; I cried, "A problem shouldn't take this long!"

I tried to think, control my nerve.

It's evident that speed's tangential to that time-position curve.

This problem would be mine if I just knew that tangent line.

But what to do? Show me a sign!

So I thought back to Calculus.

Way back to Newton and to Leibniz,

And to problems just like this.

And just like that when I had given up all hope,

I said nope, there's just one way to find that slope.

And so now I, I will derive.

Find the derivative of x position with respect to time.

It's as easy as can be, just have to take dx/dt.

I will derive, I will derive. Hey, hey!

And then I went ahead to the second part.

But as I looked at it I wasn't sure quite how to start.

It was asking for the time at which velocity

Was at a maximum, and I was thinking "Woe is me."

But then I thought, this much I know.

I've gotta find acceleration, set it equal to zero.

Now if I only knew what the function was for a.

I guess I'm gonna have to solve for it someway.

So I thought back to Calculus.

Way back to Newton and to Leibniz,

And to problems just like this.

And just like that when I had given up all hope,

I said nope, there's just one way to find that slope.

And so now I, I will derive.

Find the derivative of velocity with respect to time.

It's as easy as can be, just have to take dv/dt.

I will derive, I will derive.

So I thought back to Calculus.

Way back to Newton and to Leibniz,

And to problems just like this.

And just like that when I had given up all hope,

I said nope, there's just one way to find that slope.

And so now I, I will derive.

Find the derivative of x position with respect to time.

It's as easy as can be, just have to take dx/dt.

I will derive, I will derive, I will derive!

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