A Tip for Older People: Differential Calculus

Say an equation is factored as y = (x+a)(x+b)(x+c) and so forth.

Then dy/dx = the sum of the various factor products, taken n-1 at a time.

This means that if the factored polynomial has n factors, each factor product has n-1 factors.

Example #1:
   y = x2 + 3x + 2 = (x+1)(x+2)
Then     dy/dx = (x+1) + (x+2)
Example #2:
   y = x4 + 10×3 + 35×2 + 50x + 24 = (x+1)(x+2)(x+3)(x+4) … factor the polynomial, if possible

   dy/dx = (x+2)(x+3)(x+4) + (x+1)(x+3)(x+4) + (x+1)(x+2)(x+4) + (x+1)(x+2)(x+3)
     
   d2y/dx2 = 2{(x+3)(x+4) +(x+2)(x+4) + (x+2)(x+3) + (x+1)(x+4) + (x+1)(x+3) + (x+1)(x+2)}

   d3y/dx3 = 6{(x+1) + (x+2) + (x+3) + (x+4)2}

Easily Add And Subtract Fractions

Tip #3:

Today’s Tutorial is how to easily add and subtract fractions.

First multiply the numerator of fraction 1 with the denominator of fraction 2. This is the first part of the new denominator. Then comes the operation. The second number in the new numerator is the numerator of the 2^nd fraction multiplied by the denominator of the first fraction. The denominator of the new fraction is just the product of the denominators. If you have more than 2 fractions, just do this in groups of 2. Perform the operation in the numerator, then reduce.

Btw, I’ll also be posting a practice worksheet that you can do. Check the answers on your calculators after you have done them. If you have any questions, email me at vedicmathforkids@gmail.com.

Tip #2 – Multiply numbers quick and easy

Today’s tip is an elegant way of multiplying numbers  using a simple pattern.

For example 21×23=483

So how do you  get this?

We first write 23 below 21. We multiply vertically, that is,first we multiply 2 by 2 to get 4. We do the same for the other end, and multiply 1 by 3 to get 3. The middle is a bit complicated. We do two cross products and add them. In this case, we add the product of 2 by 3 to the product of 2 times 1. This is the middle digit. If the middle is greater than 10, 1 is added to the left.

Another example is 33 x 44.

First do it the Vedic way, and get an answer. Then do it the traditional way. The answer is in the video.

I’ll also be posting a practice worksheet that you can do. Check the answers on your calculators after you have done them. If you have any questions, email me at vedicmathforkids@gmail.com.

Tip#1: Find the square of any number ending with 5.

Today’s tutorial involves finding the square of ANY number ending in “5”.

For example, 75² = 5625.

So how do you  getthis? (By the way, if you came here ready with a calculator, throw it out the window, because as far as Vedic math is concerned, a calculator = cheating! If you came with pencil and paper, keep it for the first few, and then throw them out the window too. These tips are supposed to make math easy, so easy that you can do it mentally and not break a sweat!)

Alright, since the last digit is 5, the answer always includes 25. If you haven’t noticed this, the square of 15 is 225. It has a 25 in it. The square of 25 is 625. It too has a 25 in it.

So write down 25 in your nice little blank. Now comes the first part.

Take the rest of the number that doesn’t include the 5 you handled with the 25 a few moments ago. Find the number one more than it. In other words, add 1 to it. Now take this new number and multiply it by the old number (the number you added 1 to to get the new number). In other words, you are squaring a number, then adding the number to the result. Try it with the square of 75.

An Introduction to Vedic Mathematics

Vedic Mathematics is:

• An ancient form of mathematics in the Vedas that was used by Indians centuries before Newton invented calculus.
• A form of math based on 16 sutras, or formulas.
• These formulas cover subtraction, multiplication, and many other operations
• These formulas are also very cohesive in that operations can be reversed and the same techniques can be used for opposite operations.

Why Sutras?

According to Sri Bharati Krishna Tirtha Maharaj, the Vedas were written in Sutras because it was easy for students to memorize (and it definitely works to kids’ advantage to remember these formulas or “rules of thumb.”)Vedic Mathematics covers all areas of mathematics, even those that were thought not to exist in those times, like calculus (both differential and integral). The Pythagorean theorem was not discovered by Pythagoras: It was rediscovered by Pythagoras in Baudhayana’s Sutra: The chord which is stretched across the diagonal of a square produces an area of double the size. A similar observation pertaining to oblongs is also noted. Our Western decimal system of counting 1,2,3,4,5 etc, was not invented by Europeans. It was invented by Indians, and via the Arabs and their trade routes to Europe, it slowly spread and has now been accepted worldwide.
Indians discovered the Newton-Gauss interpolation formula, the formula for the sum of an infinite series, and many others. Though the world credits the Europeans, the Europeans, like Charles Whish of the Royal Asiatic Society of Great Britain and Ireland, recognize the contribution of Indian mathematicians. Charles Whish  was one of the first Europeans to recognize that Indian mathematicians had anticipated by almost 300 years many European developments in the field of mathematics.

So what’s the use of Vedic Mathematics for me?

Vedic mathematics will tremendously enhance your speed in doing all kinds of math problems. You can calculate the square of any number that ends in 5 without going to a calculator, or pencil and paper. You’ll only need your head and mental math. That’s the beauty of Vedic math. It makes regular math a lot simpler! Stay tuned for more!