A WEDDING PROPOSAL BY Mr. ALGEBRA TO Mr. CALCULUS

Dear Mr Calculus
I am asking your opinion about the marriage of my sons " Mr Zero" and "Mr Infinity" with your daughters Miss Differentiation and Miss Integration. I have consulted 'Mr Vector' who told me that this Marriage is strictly according to 3rd law of marriage " To every husband, there is equal and opposite wife" He further continued that the two pairs will lead a happy life. I have also come to know that your daughters are in love with my sons.

Of My sons, Zero is very popular among the students and possess a high name and fame. As regard to 2nd son infinity any thing added or subtracted from him he remains unchanged. After consulting the formula and Pundit of Logarithm, you may fix up the date for marriage. I am confident that you will accept the proposal. You can also consult Aunt dynamics, Alpha, Beta, Gamma, Delta and Statistics. Sigma will accompany us in marriage party. Please convey my best wishes to sister Geometry and her daughter "Co ordinate geometry"

Your sincerely
Mr ALGEBRA
MATHEMATICS LANE
MATHS HOUSE
MATHS CITY

SALARY THEOREM

MATHEMATICS-LANGUAGE OF THE UNIVERSE

Do you know which langauge shared by all human beings regardless of the culture, religion, or gender?
It is Mathematics , the only language shared by all human beings and language of symbols.
Pi is still 3.14159, regardless of what country you are in . Adding up the cost of a basket full of groceries involves the same math process regardless of whether the total is expressed in dollars, yen or rupees. With this universal language, all of us, no matter what our unit of exchange, are likely to arrive at math results the same way.
All of us possess the ability to be " literate" in the shared language of math. The math literacy is called numeracy, and it is this shared language of numbers that connects us with people across continents and through time. It is what links ancient scholars and medieval merchants, astronauts and artists peasants and presidents
With this language we can explain
the mysteries of the universe or secrets of DNA.
We can understand the forces of planetary motion
Discover cures for catastrophic diseases
calculate the distance from any city of America to any city of India
We can build computers and transfer information across the globe.
We can save money for retirement
So math is not just for calculus majors. It is for all of us.
It is not just calculating difficult equations. It is about making better decisions and , hopefully leading richer, fuller lives.
Mathematics is Universal by the following quotes

"I bow to that glorious Lord of the Jainas, who as the shining lamp of the know-ledge of numbers made to shine whole of the universe", said Mahaviracharya in Ganita Sara Sangraha.

The laws of nature are but the mathematical thoughts of God. ~Euclid

I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because like Spinoza's God, it won't love us in return. ~Bertrand Russell, 1912

The man ignorant of mathematics will be increasingly limited in his grasp of the main forces of civilization. ~John Kemeny

Mathematics is the gateway and the key to other sciences- Roger Bacon

INTERSTING NUMBER 37

NUMBER 37 IS AN INTERESTING NUMBER:
SEE THE PATTERN:
111/(1+1+1)=37
222/(2+2+2)=37
333/(3+3+3)=37
444/(4+4+4)=37
555/5+5+5=37
666/(6+6+6)=37
777/(7+7+7)=37
888/(8+8+8)=37
999/(9+9+9)=37

YOUR AGE BY CHOCOLATE MATHS

Hi Everybody,

Have a sweet morning.. or .afternoon.. or .evening !!!





YOUR AGE BY CHOCOLATE MATHS


Don't tell me your age , the Hershey Man will know!

YOUR AGE BY CHOCOLATE MATHS This is pretty neat.

DON'T CHEAT BY SCROLLING DOWN FIRST!
It takes less than a minute .
Work this out as you read .

Don't read the bottom until you've worked it out!

1. Pick the number of times a week you'd like to have chocolate
(more than once but less than 10)


2. Multiply this number by 2 (just to be bold)

3.. Add 5

4. Multiply it by 50 -- I'll wait while you get the calculator
(or use the one listed under 'accessories' on your computer)

5. If you already had your birthday this year add 1759 ...
If you haven't, add 1758.

6. Now subtract the four digit year that you were born


You should have a three digit number

The first digit of this was your original number
(i.e., how many times you want to have chocolate each week)

The next two numbers are


YOUR AGE! (Oh YES, it is!!)


2009 IS THE ONLY YEAR IT WILL WORK, SO SPREAD IT AROUND WHILE IT LASTS.
Chocolate
Calculator

MATH FUN

Let me take only a minute

Just do the following multiplication :

13837 x Your Age x 73 = ? ? ?

You get very interesting resut, let me know.


You get the same result if you multiply 10001 * your age * 101

How is that?

FIND OUT MISTAKE

Find out the mistake in this :

Division by Zero

Everyone knows that0/2=0 , the problem is that far too many people also say that

or 2 = 2 ! Remember that division by zero is undefined! You simply cannot divide by

0

zero so don’t do it!

Here is a very good example of the kinds of havoc that can arise when you divide by zero. See if you can find the mistake that I made in the work below.

1. a = b We’ll start assuming this to be true.

2. ab = a ^2 Multiply both sides by a.

3. ab - b^2 = a^ 2 - b^2 Subtract b^2 from both sides.

4. b ( a - b) = ( a + b ) ( a - b )Factor both sides.

5. b = a + b Divide both sides by a - b .

6. b = 2b Recall we started off assuming a = b .

7. 1 = 2 Divide both sides by b.

So, we’ve managed to prove that 1 = 2! Now, we know that’s not true so clearly we

made a mistake somewhere. Can you see where the mistake was made?

The mistake was in step 5. Recall that we started out with the assumption a = b .

However, if this is true then we have a - b = 0 ! So, in step 5 we are really dividing by zero!

That simple mistake led us to something that we knew wasn’t true, however, in most

cases your answer will not obviously be wrong. It will not always be clear that you are dividing by zero, as was the case in this example. You need to be on the lookout for this kind of thing.

Remember that you CAN’T divide by zero!

APPLICATION OF DIFFERENTIATION

Uses of Differentiation

Increasing and Decreasing Functions

An increasing function is a function where: if x₁ > x₂, then f(x₁) > f(x₂) , so as x increases, f(x) increases. A decreasing function is a function which decreases as x increases. Of course, a function may be increasing in some places and decreasing in others. A point where a function changes from an increasing to a decreasing function or visa-versa is known as a turning point. A turning point is a type of stationary point (see below).

We can use differentiation to determine if a function is increasing or decreasing:

A function is increasing if its derivative is always positive. A function is decreasing if its derivative is always negative.

Examples

y = -x has derivative -1 which is always negative and so -x is decreasing.

y = x² has derivative 2x, which is negative when x is less than zero and positive when x is greater than zero. Hence x² is decreasing for x<0>0 .

Stationary Points

Stationary points are points on a graph where the gradient is zero. There are three types of stationary points: maximums, minimums and points of inflection (/inflexion). The three are illustrated here:

Example

Find the coordinates of the stationary points on the graph y = x² .
We know that at stationary points, dy/dx = 0 (since the gradient is zero at stationary points).

By differentiating, we get: dy/dx = 2x. Therefore the stationary points on this graph occur when 2x = 0, which is when x = 0.

When x = 0, y = 0, therefore the coordinates of the stationary point are (0,0). In this case, this is the only stationary point. If you think about the graph of y = x², you should know that it is "U" shaped, with its lowest point at the origin. This is what we have just found.

Maximum, Minimum or Point of Inflection?

At all the stationary points, the gradient is the same (= zero) but it is often necessary to know whether you have found a maximum point, a minimum point or a point of inflection. Therefore the gradient at either side of the stationary point needs to be looked at (alternatively, we can use the second derivative).
At maximum points, the gradient is positive just before the maximum, it is zero at the maximum and it is negative just after the maximum. At minimum points, the gradient is negative, zero then positive. Finally at points of inflexion, the gradient can be positive, zero, positive or negative, zero, negative. This is illustrated here:

Example

Find the stationary points on the graph of y = 2x² + 4x³ and state their nature (i.e. whether they are maxima, minima or points of inflexion).
dy/dx = 4x + 12x²
At stationary points, dy/dx = 0
Therefore 4x + 12x² = 0 at stationary points
Therefore 4x( 1 + 3x ) = 0
Therefore either 4x = 0 or 3x = -1
Therefore x = 0 or -1/3

When x = 0, y = 0
When x = -1/3, y = 2x² + 4x³ = 2(-1/3)² + 4(-1/3)³ = 2/9 - 4/27 = 2/27

Looking at the gradient either side of x = 0:
When x = -0.0001, dy/dx = negative
When x = 0, dy/dx = zero
When x = 0.0001, dy/dx = positive
So the gradient goes -ve, zero, +ve, which shows a minimum point.

Looking at the gradient either side of x = -1/3 .
When x = -0.3334, dy/dx = +ve
When x = -0.3333..., dy/dx = zero
When x = -0.3332, dy/dx = -ve
So the gradient goes +ve, zero, -ve, which shows a maximum point.

Therefore there is a maximum point at (-1/3 , 2/27) and a minimum point at (0,0).

Solving Practical Problems

This method of finding maxima and minima is very useful and can be used to find the maximum and minimum values of all sorts of things.

Example

Find the least area of metal required to make a closed cylindrical container from thin sheet metal in order that it might have a capacity of 2000p cm³.

The total surface area of the cylinder, S, is 2pr² + 2prh
The volume = pr²h = 2000p
Therefore pr²h = 2000p.
Therefore h = 2000/r²

Therefore S = 2pr² + 2pr( 2000/r² )
= 2pr² + 4000p
r

So we have an expression for the surface area. To find when the surface area is a minimum, we need to find dS/dr .
dS = 4pr - 4000p
dr r²
When dS/dr = 0:
4pr - (4000p)/r² = 0
Therefore 4pr = 4000p
r²
So 4pr³ = 4000p
So r³ = 1000
So r = 10

You should then check that this is indeed a minimum using the technique above.
So the minimum area occurs when r = 10. This minimum area is found by substituting into the equation for the area the value of r = 10.

S = 2pr² + 4000p
r
= 2p(10)² + 4000p
10
= 200p + 400p
= 600p

Therefore the minimum amount of metal required is 600p cm²