Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus, and join calculus.
The war is over
The last battles are gone
Swords laying broken
My bloodwork is all done
I sit down for calming
My breath is lessening
I�m starting to tremble
My sight is clearing
My head is weary
A dreadful awakening
What has driven me
Into insanity
Awaking from this dreadful tragedy
I return to myself
Beginning to dwell in this elegy
Put my anger on the shelf
Awaking from this dreadful tragedy
I return to myself
Beginning to dwell in this elegy
Put my anger back on the shelf
I look around
As I raise from my rest
Discover what I�ve done
No life I have left
My heart is in pieces
My soul is laying bare
Awaking from this dreadful tragedy
I return to myself
Beginning to dwell in this elegy
Put my anger on the shelf
Awaking from this dreadful tragedy
I return to myself
Beginning to dwell in this elegy
They raise their glasses, as he surveys unseen
Wrath is increasing, anger makes his eyes gleam
Seeing his foes, celebrating their victory
He gives a promise, that he will destroy his enemy
Godforsaken fools..... I will return
Raise, raise, my dark fiends of light
Up from your graves, into the night
Raise, raise, my dark fiends of light
Up from your graves, into the night
As he stands nearby, he speaks the incantation
Tearing the dead, back from their damnation
Ground starts to quake, as they return from their graves
Thousands of corpses, rushing ahead like waves
Godforsaken fools..... I will return
Raise, raise, my dark fiends of light
Up from your graves, into the night
Raise, raise, my dark fiends of light
Up from your graves, into the night
Follow him blind, they have heard his call
Incessantly marching, heading for the fall
Clattering blades, made to strike and kill
Thirsting for blood, their task they will fulfill
Raise, raise, the dark fiends of light
Up from your graves, into the night
Raise, raise, the dark fiends of light
The demon has risen again
Calling his forces to arms
In these hours of fear
We come together as well
Oooh..... together we rise
We shall unite, to overcome his domain
The dark demons force, to end his reign
We shall unite, to overcome his domain
If you join us, we will be strong again
With armor and sword at our side
We'll (hold out) against obscurity
Chasing back the clouds at the sky
We will bring back the light
Oooh..... together we rise
We shall unite, to overcome his domain
The dark demons force, to end his reign
We shall unite, to overcome his domain
If you join us, we will be strong again
Sharpen your axes and swords
And be prepared for the fight
Let's bring back freedom for all
Destroy the demon for all time
Oooh..... together we rise
We shall unite, to overcome his domain
The dark demons force, to end his reign
We shall unite, to overcome his domain
I've planned a deal with unknown mights
And hope to win no compromise
The mighty beast in front of me
That can fulfill my dreams
But I defraud the guarding beast
The keeper of this mystic tale
It banished me into my dreams
Now I've to suffer in hell
I've seen a thousands worlds before
But this one is the strangest
In front of me a gleaming stone
That once was filled with magic
In it's inscription stands
That I'll have just one chance
When the demon is gone
I can return
Now, when the demon is gone
I can return back to reality
I have just one chance to leave this legend
From now and from nevermore
My time here is running out
The beholder's getting weaker
Behind his throne the open gate
That leads to my salvation
But suddenly the demon opens his eyes
And a dreadful flash is blowing me away
My whole body is surrounded by fire
And something is dragging me deeper into this dream
Now, when the demon is gone
I can return back to reality
I have just one chance to leave this legend
The dragon flies, on his mighty wings
Towards the walls, of the dark fortress
Bursting out in rage, cleansing fire rains
When the towers fall, nothing will remain
We will meet, eye to eye
He will pay, eye for an eye
I'll enjoy, his last cry
We will meet, eye to eye
So bittersweet, the taste of revenge
Legions of hate, decamp in fear
No chance to flee, he hounds them to death
Where is the one, he?s seeking for
We will meet, eye to eye
He will pay, eye for an eye
I'll enjoy, his last cry
We will meet, eye to eye
Close to the end, nearly all slain
Still haven't found, the king of the dark
Is he alive, or already gone
All lies in debris, he must be dead
Where is he?, eye to eye
No revenge?, eye for an eye
Have I heard?, his last cry
I'm on my way to look out for someone
I promise treasures and wonders to be done
To those who will follow me on my way
To kill the demon, to demand him to pay
On my way I will go - crusade of the damned
To return I will kill - crusade of the damned
On my crusade to break the demon's spell
Who will follow me to hell
No-one will follow but I have to go
They fear the demon and his deadly blow
I leave alone and I feel like I'm damned
To fight on my own, to make my last stand
On my way I will go - crusade of the damned
To return I will kill - crusade of the damned
On my crusade to break the demon's spell
Who will follow me to hell
Against the walls of the dark fortress I ride
Storming the gates of damnation
Against the walls of the dark fortress I ride
At last I am banished in time
On my way I will go
To return I will kill
On my crusade to break the demon's spell
Moon is riding high in the sky, it's light cannot deceive
That I'm lost here in this time, one point still far to go
To overcome eternal distance, time is running away
On my long and scary journey, to break the spell
Banished into ancient times
My destiny will never die
Follow the guiding light
Lost in a strange and foreign time
On the path I have to go, alone but not lonely
I listen to my inner voice, I trace my senses
I'm in need of company, someone to help me
To get back to my own world, to leave this land
Banished into ancient times
My destiny will never die
Follow the guiding light
Lost in a strange and foreign time
Think about the ancient times
Of a time passed by
How long will my quest last
My world?s so far away
Millions of ages in between
Will I ever get back
I'm left here on my own
Will I ever reach
The place that I call home
Banished into ancient times
My destiny will never die
Follow the guiding light
I look straight into the light
That blinds me in the dark
That haunts my sleep at night
The fear that grips my heart
Don't kneel to the master
I hold my head upright
To kneel is to suffer and to die
Be aware of your might
Eyes of red keep gleaming
Looking filled with hate,
Until I wake up screaming.
I don't accept this fate
Don't kneel to a master
Hold my head upright
To kneel is to suffer and to die
Be aware of your might
When I lay me down
In madness I�ll dwell
Falling into the deep
The grounds of hell
The Pain that hurts me
Are the piercing claws of hate
The evil inside of me
Can�t hide me from my fate
Shadows dancing on the wall
I have heard my suffering call
I can�t hide or run away
Suffering till the end of days
I can feel the burning heat
Singeing my twisted mind
My torn and restless sleep
Salvation I can�t find
Don't kneel to a master
Hold my head upright.
To kneel is to suffer and to die
There's a secret hidden for you
Try to solve it and find out the clue
If you find out what we say
You get the story in the right way
Take your chance
Look at the stone
It's hiding the truth
Guess what the inscription is telling you
Look at the stone
It's hiding the truth
Guess what the inscription is telling you
Read the fragments in the line
And the secret you will divine
Hidden in numbers, there lies the truth
Put them in order, you have nothing to lose
Take your chance
Look at the stone
It's hiding the truth
Guess what the inscription is telling you
Look at the stone
It's hiding the truth
At the dawn of day, two armies arise
In the morning fog, from shades of the night
Out there on the hills, they darken the sun
The last stand is here, one chance to be won
Into this raging war, out of the sun
The dragon strikes down, killing the one
Into this raging war, out of the sun
The dragon strikes down, killing the one
Burst his chest and burn his heart to ashes
At last he pays for his reign with agony
The spell breaks and the undead fall again
At the end of the day, forever victory
The undead knights, storming against the lines
The darkest hour strikes the clock of life
Thousands of men were killed, by the walking dead
At the battles end, the earth turns red
Into this raging war, out of the sun
The dragon strikes down, killing the one
Into this raging war, out of the sun
The dragon strikes down, killing the one
Burst his chest and burn his heart to ashes
At last he pays for his reign with agony
The spell breaks and the undead fall again
At the end of the day, forever victory
Into this raging war, out of the sun
The dragon strikes down, killing the one
Into this raging war, out of the sun
The dragon strikes down, killing the one
Burst his chest and burn his heart to ashes
At last he pays for his reign with agony
The spell breaks and the undead fall again
They are carved in stone
By nature's hands
Sculptures made for eternity
To witness aeons of fate
Faces and limbs
Build by random force
But so real staring
Like the eyes of the world
Secret signs from the other world
Forever for all to see
Secret signs from the other world
Telling tales of the history
A land from beyond
Of spirit filled stones
Can tell so much more
Than libraries reveal
But there are signs
Rising up from the past
To show us another world
Sometimes we remember
Secret signs from the other world
Forever for all to see
Secret signs of the other world
Telling tales of the history
Secret signs from the other world
Forever for all to see
Secret signs of the other world
After the smoke has left
And the fire has burned down
He leaves his hideaway
And through ashes he goes
There are just ruins left
What once was his realm
He falls on his knees
And raises his hands up high
I will remember the fire
Day of the dragon's feast
I will remember the fire
I seek to kill the beast
His burden he will bear
Oh dragon, beware of him
He will hunt you down
And for the search he leaves
For his hordes you've killed
He demands you to pay
And for the blood you've spilled
He'll strike your life away
I will remember the fire
Day of the dragons feast
I will remember the fire
I seek to kill the beast
Walking a thousand miles
Through forests, fens and thorns
Hate is gnawing at his soul
As he inquires on
How far he has to go
Will his search never end?
Until his last breath's done
He's searching on and on
I will remember the fire
Day of the dragons feast
I will remember the fire
Countless legions of highhanded prophets
Spreading fear since humanity was born
End of all days
Perished in Flames
Souls damned for eternity
But it`s not now
Countless chasms of human fantasy
Creating Horrors and nothing divine
End of all days
Perished in Flames
Souls damned for eternity
But it`s not now
And I don`t think tomorrow
Or another day in a lifetime
The end of all days
It seems to be a game
To scream the final warning
End of all days
Perished in Flames
Souls damned for eternity
But it`s not now
If someone out there is really angry
He would have destroyed us a long time before
End of all days
Perished in Flames
Souls damned for eternity
But it`s not now
And I don`t think tomorrow
Or another day in a lifetime
The end of all days
Since the day we learned to kill each other
There was a reason to make it an end
End of all days
Perished in Flames
Souls damned for eternity
But it`s not now
And for the cause it takes a longtime preparing
We�ll take the time to blow ourselves away
End of all days
Perished in Flames
Souls damned for eternity
But it`s not now
And I don`t think tomorrow
Or another day in a lifetime
Selected for eternity
Where mighty names remain
Born to immortality
And overcome the sea of oblivion
With a crown on the head
They will lift the mourning veil
With a crown on the head
They will walk the gloomy dale
Admired and lifted to the sky
Their flame of live will die
Chosen to be kings
When they spread their wings
Kings who die
Although they live on forever
Souls drifting into the never
They�ll last on forever
The kings who die
Songs of wisdom and brave hearts
Of great legends sang by the bards
We�ll never forget when they are gone
Immortal for the work they have done
Kings who die
Although they live on forever
Souls drifting into the never
They�ll last on forever
Oh, kings who die
Kings who die
Although they live on forever
Souls drifting into the never
They�ll last on forever
In the desert of my life
I searched the wisdom well
Lugging the golden calf
Of my futile problems
The sense of human existence
The only thing in life
On a quest for salvation
Discontent was hunting me
Drowned in a sea of false prophecies
[Choir:] Tell me the way I have to go
In a world of faith I am a heavenseeker
[Choir:] Tell me the things I have to know
And I�m not alone
[Choir:] You are not alone
No one told me what to do
No one ruled my life for me
I was lost and found by myself
The path was rewarded divine
Too long I ignored the power
That flows from self-respect
The spirits I own will follow
Loyal companions on my way
Drowned in a sea of false prophecies
[Choir:] Tell me the way I have to go
In a world of faith I am a heavenseeker
[Choir:] Tell me the things I have to know
And I�m not alone
[Choir:] You are not alone
All my life I was searching
For something to adore
Power to solve my problems
A convenient ruler
I followed desolate ways
In freedom and silence
I begun to listen the winds
The voice of my inner self
Drowned in a sea of false prophecies
[Choir:] Tell me the way I have to go
In a world of faith I am a heavenseeker
[Choir:] Tell me the things I have to know
And I�m not alone
There he sits on his throne
With burning eyes and cloven hooves
The fallen one, now alone
So far away, where his spirit moves
�It�s such a long time ago
Since the day you created man
What a circus what a show
That was the day the horror began�
[Choir:] So many years have gone
Bring back the times
[Choir:] So many things have been done
Let me live in the good old days
[Choir:] Since the good old days
[Choir:] So many years have gone
Bring back the times
[Choir:] So many things have been done
Let me live in the golden years
[Choir:] Since the good old days
�Once I was the only bad guy
But now there are billions of them
I think it�s time to say goodbye
I�m just a loser compared to man�
[Choir:] So many years have gone
Bring back the times
[Choir:] So many things have been done
Let me live in the good old days
[Choir:] Since the good old days
[Choir:] So many years have gone
Bring back the times
[Choir:] So many things have been done
Let me live in the golden years
[Choir:] Since the good old days
[Choir:] So many years have gone
Bring back the times
[Choir:] So many things have been done
Let me live in the good old days
[Choir:] Since the good old days
[Choir:] So many years have gone
Bring back the times
[Choir:] So many things have been done
Let me live in the golden years
Im witnessing strange occurrences
In the labyrinth of my mind
Persons and places I know
Appearing in abstract relations
Between visions and reality
Unconsciousness frees memories
That I won�t remember awake
Hidden in unreal sceneries
Locked in the depths of my mind
Fragments of reality
That scene behind my eyes
If I only could remember
These pictures in my head
Fragments of reality
That scene behind my eyes
If I only could remember
The sensual world lies deep within
Burning in riot and in motion
The storm of pictures on the edge
Can`t seize it with my rapid eyes
Fragments of reality
That scene behind my eyes
If I only could remember
These pictures in my head
Fragments of reality
That scene behind my eyes
If I only could remember
Fragments of reality
That scene behind my eyes
If I only could remember
These pictures in my head
Fragments of reality
That scene behind my eyes
It's written in stone... my way... my path... it leads me home...
Storming, the gate, the dragons
Storming, the gate, the dragons, gate
High above the sky, where golden dragons fly
In this mystic land, that lies beyond all time
A holy place so free, for all eternity
But in the distant fields, they see a shadow arise
Woe to the dragons - they're about to die
Storming the dragons' gate, the battle rages hard
Storming the dragons' gate, they're ripped apart
Storming the dragons' gate, the battle rages hard
Storming the dragons' gate, they're ripped apart
One by one they fall, hear the demons' call
He sends his legions of hate, against the dragons' light
In order to erase, eternal enemies
The land is turning red, drinking the blood of the dead
Woe to the dragons - they're about to die
Storming the dragons' gate, the battle rages hard
Storming the dragons' gate, they're ripped apart
Storming the dragons' gate, the battle rages hard
Storming the dragons' gate, they?re ripped apart
After the battle is gone, there is left just one
This one was hiding while he saw the others die
When he swears revenge, hate burns in his heart
He shall never rest, until this fire is gone
Last of the dragons - seeking for revenge
Stormed was the dragons' gate, their destiny is hard
Stormed was the dragons' gate, they were ripped apart
Stormed was the dragons' gate, their destiny is hard
Falling into emptiness
Where nothing else will last
Embraced by loneliness
Forgotten is the past
Be welcome my friend
At the dawn of a new age
With a wave of a hand
Create a land and be a sage
A world to invent
At the dawn of a new age
With a wave of a hand
Diviner of the next page of dreams
A land created only by thoughts
Damned or chosen by the gods
A heavy burden that's to bear
Be the storyteller's heir
The mind is caught inside a web
Oblivion claws into the head
Remembrance fades with every wish
Be welcome my friend
At the dawn of a new age
With a wave of a hand
Create a land and be a sage
A world to invent
At the dawn of a new age
With a wave of a hand
Diviner of the next page of dreams
An endless story that is told
Where the feather creates the world
The storybook will show the way
But there�s a dreadful price to pay
Where is the long forgotten path
Redeem the world from its wrath
No answer in reality
Save the world of fantasy
Be welcome my friend
At the dawn of a new age
With a wave of a hand
Create a land and be a sage
A world to invent
At the dawn of a new age
With a wave of a hand
Voices from the other side
Behind stained glass
They�re waiting for a guest
Reflections, distortions of yourself
Wrathful shadows
Are living in this maze
Eyes in a mirror world
Reveal your truth of your inner views
Time is lost without a trace
Deep inside this mirror mace
Shadows in a haze
Like demons with your face
Darkness imprisoning the mind
Dead close to madness
The verge of despair
Soulless grimaces so unreal
Indicating traits
That are lying deep within
Eyes in a mirror world
Reveal your truth of your inner views
Time is lost without a trace
Deep inside this mirror mace
Shadows in a haze
Like demons with your face
Time is lost without a trace
Deep inside this mirror mace
Shadows in a haze
Like demons with your face
Phantoms of hate and death appear
Inverting every mind
Daring to go inside
Illusions or reality
The day of reckoning
Uncovering our souls
Eyes in a mirror world
Reveal your truth of your inner views
Time is lost without a trace
Deep inside this mirror mace
Shadows in a haze
Drifting away into the guiding light
Into the realm of my inquiry
Good and evil are by my side
The two beings are awaiting me
They will judge your life
They will see your sins
Here on the other side
Here were your kismet grins
It�s my time for a decision
Will I belong to heaven or hell
We are sitting in a theatre
A movie plays, it shows my way
A gloomy voice sounds from afar
"Welcome to your judgement day"
It�s my time for a decision
Will I belong to heaven or hell
Weighing out what I have done
My deeds are balanced out perfectly
So I�ve to choose my way alone
To find my place for eternity
It�s my time for a decision
I make my choice between heaven or hell
[WEIRD MODERATOR (KAI):]
Congratulations ... you�ve won the jackpot !!!
You can choose between
Gate one...
A low prize apartment with a high-end radiator system
Or gate two...
A cool attic flat with a fantastic view
Flattering words from the evil guide
The good appealing to my belief
Each "one" is trying to pull me on his side
Making offerings for me to seize
It�s my time for a decision
I make my choice between heaven or hell
[DEVIL (ARNIE):]
Join the dark side
The only place to be
You surely won�t regret
Prophets you will receive
Become a lord of death
Let hate flow in your veins
Tormentor of the lost souls
Master of eternal pain
Now let me tell you the truth
I am not interested in both
Maybe it's fun to exist as a ghost
Evil dreams of fire
Eating through your soul
Entering the woods
Where the fear and darkness grow
Your heart starts to pound
Misty eyes that glow
Resolutions fading
Spirit�s running low
What lurks inside the deepest dark
In the forest where the shadows cross
The flaming evil that stalks the night
Meet your fears at the shadowcross
Shrieks of hellish laughter
Dance between the trees
As you grope in the dark
And nothing you can see
Your skin is pale and wet
Hope has gone from thee
Deafened by the silence
Feel what never should be
What lurks inside the deepest dark
In the forest where the shadows cross
The flaming evil that stalks the night
Meet your fears at the shadowcross
Frightened to the core
Through the fens you crawl
Confused by odd emotions
Hear the reaper call
Insane voices whisper
And the demons brawl
Closer to a breakdown
Into the black you fall
What lurks inside the deepest dark
In the forest where the shadows cross
The flaming evil that stalks the night
Meet your fears at the shadowcross
Oh, meet your fears
Between trees
Crossing the center of nothingness
In a flowing cloak of light
The gap between alone and loneliness
Is breaking up open wide
The age is a powerful enemy
In the endless desert of time
And after even death had died
A sea of tears will give new life
On the other side
Have you found what you�ve been searching for
Lay down your head and welcome to the dead
You cannot return when you�ve opened the door
This is your end
The gate to the other side
Wherever the journey ends
After one million tomorrows
In vast and distant horizons
At the end of all sorrows
What once was long forgotten
Will maybe come back someday
And when the light is born again
We will return in a better way
On the other side
Have you found what you�ve been searching for
Lay down your head and welcome to the dead
You cannot return when you�ve opened the door
This is your end
The gate to the other side
Crossing the center of nothingness
In a flowing cloak of light
The gap between alone and loneliness
Is breaking up open wide
The age is a powerful enemy
In the endless desert of time
And after even death had died
A sea of tears will give new live
Death is everyone's destiny
In your thoughts you�re creating the beyond
Death is everyone's destiny
But what you�ll really see will stay unknown
Beyond all pain and sufferings
Come on and lay down your head
And say hello to the dead
On the other side
On the other side
Have you found what you�ve been searching for
Lay down your head and welcome to the dead
You cannot return when you�ve opened the door
This is your end
In dark and endless nights
Fire's giving gloomy light
In the great hall we sit together
While outside the stormclouds gather
An oaken table,mighty walls
The glory circle in these halls
Listen to songs of forgotten aeons
The story of the nightmare demon
When we are gathered in the hall
They tell a wintertale
Of a time that is gone
They are singing their song
From a distance, some faint light
Coming closer, like ghosts in the night
It's a courier, and what he brings
From the darkness, are bad tidings
The evil demon, back from the dead
Darker than ever, again he spreads
Gaining force to, retaliate
Was our fight, to no avail
When we are gathered in the hall
They tell a wintertale
Of a time that is gone
They are singing their song
Hope is weakened, (our) pride is gone
It's all in vain, and nothing?s won
Fear is rising, the tide has turned
The golden future, is all burned
Feeling bitter, and crestfallen
My way home now, is stolen
Without mercy, and all our might
No surrender, we?ll take the fight
When we are gathered in the hall
They tell a wintertale
We will fight till it's won