Calculus demystified

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What a headache created Newton and his German Fellow Leibniz back in the 1660's. All they needed was to follow the regular math from Ptolemy, but We guess, it was due for the sake of the advancement of humankind.

Newton called it the Method of fluxions and fluents, and Der Herr Leibniz just did his own discovery around 1693. He said and the other one said, that there was not even the slightest idea of each others work. The quarrel went for centuries, until our grandparents decided to give them both the credit.

FUNCTIONS

Ever seen a kid react to an ice cream? How his/her mouth get watery and can't wait to have it?

Ever heard that saying, from any action there is a reaction? Sure you did!

In the case of Functions; for every X there is a Y....or F(x)=y

From the SET A of infinitesimal x's called DOMAIN of F

There is a SET B of correlated y's called the RANGE of F

Why this wise minds thought of this? They wanted a mathematical tool for their research in a new Scientific way.

If a car speeds up..then gas will be consumed quickly

If we practice our math skills more often..then the grades will raise up...you follow us?

If we write more hubs..then AdSense will pay accordingly!

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Y=-2X+4

The graphic is pretty clear. If we give the value of 2 to X..then Y will be zero

Y=-2(2)+4 Y=-4+4=0

mnemonics: Desperate housewives SET A will be called the DOMAIN of F (not passive!)

Survivor's SET B where all the Y's are held hostage will be called the deranged RANGE of F

LIMITS

Limits are very important to Calculus and was devised in order to study events in nature that cannot be predicted or are limited to a near expected range. For instance, if we fill a bucket with water and we hold it for one hour..there will be a limit for our strength to keep against our muscles. Let's go to our mathematical example.

If you feed 100 people and double the ration, but we take just one meal away

2x-1

but divide those 199 between the same amount of people... no matter how big the crowd will be:

2x-1/x

You will always reach this answer: 1.9999

Then the limit of that function for x= infinite, will be 2. Do we make sense?

Delta-Epsilon limit

This can be silly but we try to make examples with reality, away from abstraction:

Anna 'a' is being enticed by Derek DELTA who is wooing her away from her boyfriend'

Larry 'L', who in turn falls for Ericka EPSILON....now you know from real life, depending how hard Derek works on his last conquest he can win Anna away (-delta,+delta)

Same thing for Larry, depending on Ericka's body language and secret 'turn on' (-epsilon,+epsilon) She can have Larry any minute, if she wants to.

Now according to functions, Jealousy, rebounds and pay back will shape up the graph shown:

F(a)=L

Now we can get a little rigorous and apply our example to what mathematicians define in their own words:

  • choosing e > 0, indicating that we want the distance between f(x) and L to be less than e
  • we can find d > 0
  • so that if the distance from x to a is less than d but not equal to 0
  • then the distance from f(x) to L will be less than e.

DERIVATIVES

We have paved the way to give the easiest explanation about derivatives and its use. So far we want you to know that we have limited a ratio y/x to their infinitesimal approach. It can be noticed that this ratio is a slope and also a relationship between two physical quantities. Most Scientists around Newton's time studied and gathered information for further study; let's be more practical and compare speed VS time. All we can do is go to the basic equation:

V=D/T

V=Velocity D=distance T=time of course we use it every day..."I was going over 85miles/hour"

Newton and Leibniz wanted to work with instantaneous speeds for practical reasons. Say, you are going around a curve on a Highway, you know you are not going to keep an steady speed, either you slow down so the centrifugal force won't cause your car to flip or you regulate the gas accordingly. Now, that curve can match or represent our classical Cartesian coordinates F(t)=D; for every second there will be a distance traveled.

Let's continue on a second Hub..since we are running out of space...see you!

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Comments 11 comments

JT Walters profile image

JT Walters 4 years ago from Florida

Christmas has come early for me!! I have been waiting for this and you have finlly provided. Thnk you Lord there is hope for this country's educational system when it comes to advance mathematics!!

I voted Interesting, awesome and useful and UP Up And Away!!

Thanks D.

JT


Lord De Cross profile image

Lord De Cross 4 years ago Author

Hi JT Walters!

We tried to make it interesting, combining history and the passion from our own hearts. We need to help our young generations with tools at hand. We, as a power ,need to regain that status...and here, we are leaving something useful for them. Basically we did it at your request...we thought it was too much for the average reader, but will help some hopeful young 16 year old, who is afraid of this monster... Thanks again for your comments!

LORD


JT Walters profile image

JT Walters 4 years ago from Florida

D,

If you make one engineer with your hub or help one person achieve their dream then it is all worth it. It also exposes young people who would not ordinarily be exposed to higher Mathematics to the subject matter in a simple staright forward understable manner. It is brilliant. I have spent my life teaching these skills to young people who would like their skills and intellect to reach their ambtions and aspirations. You have done this for them. So thank you!!

JT


Lord De Cross profile image

Lord De Cross 4 years ago Author

Well then be it!

Alas! Lol!!

Was mocking my buddy Rousseau! We are jokers and can't help it! Thanks JT one more time!

LORD


JT Walters profile image

JT Walters 4 years ago from Florida

I bet in time these hubs make money because they are so deseparetly needed in society.

JT


Lord De Cross profile image

Lord De Cross 4 years ago Author

Did you know that we didn't think about the money? We just focused ourselves in writing about this monster. But, well, it will get somewhere..maybe right to the steps of Pennsylvania Avenue... who knows! Have a great day!

LORD


JT Walters profile image

JT Walters 4 years ago from Florida

You too my friend.

JT


AshtonFirefly profile image

AshtonFirefly 4 years ago

Interesting hub...I'm not great with math and calculus but this made sense to me :) voted up


Lord De Cross profile image

Lord De Cross 4 years ago Author

Thanks! Asthon! We were about to wait until january...but we took the plunge... and here we are. You can follow up with the next one...nothing hard at all.

LORD


Gypsy Rose Lee profile image

Gypsy Rose Lee 4 years ago from Riga, Latvia

Thanks so much for refresing my old brain. Great job.


Lord De Cross profile image

Lord De Cross 4 years ago Author

Hi there Gypsy Rose,

You took your time to torture yourself? No, just kidding! We just did this for our young kids, but it looks that it can appeal to everybody. Thanks for the words of appreciation!

LORD

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