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DIFFERENTIATION TECHNIQUES Maybe the easiest and most useful formulas are the ones that say that the derivative is linear: Combined with the formula (xn)' = n xn-1, we see that every polynomial function has a derivative at any point. Example. For P(x) = 1-2x + 3x4 -5 x6, we have The next two formulas are the most powerful ones. They deal with the derivative of a product and a quotient. They are commonly called the product rule and the quotient rule. We have In particular, we h
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submitted by dilip (62 m) on 15 May 2007 13:23:40 IST (0 comments 88 views)
STIRLING'S FORMULA An important formula in applied mathematics as well as in probability is the Stirling's formula known as where is used to indicate that the ratio of the two sides goes to 1 as n goes to . In other words, we have or Proof of the Stirling's Formula First take the log of n! to get Since the log function is increasing on the interval , we get for . Add the above inequalities, with , we get Though the first integral is
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submitted by dilip (62 m) on 15 May 2007 13:20:31 IST (0 comments 61 views)
FAMOUS QUOTES !) Mark Twain Twenty years from now you will be more disappointed by the things that you didn't do than by the ones you did do. So throw off the bowlines. Sail away from the safe harbor. Catch the trade winds in your sails. Explore. Dream. Discover. 2) Luigi Pirandello In bed my real love has always been the sleep that rescued me by allowing me to dream. 3) Dr. Martin Luther King Jr. Take the first step in faith. You don't have to see the whole staircas
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submitted by dilip (62 m) on 15 May 2007 13:12:49 IST (0 comments 58 views)
EQUATION OF PARABOLA When you define a parabola by its equation (x ? h)2 = 4 p (y?k) you are using coordinate geometry, invented by Descartes in the 1600s. Today we prefer such a definition, because it allows geometrical properties to be handled by means of numbers, and our age is very, very good in handling numbers. The ancient Greeks, the first to study parabolas, were not so good with numbers (maybe because they lacked the decimal system), but they were v
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submitted by dilip (62 m) on 15 May 2007 12:48:17 IST (0 comments 93 views)
Chanakya's Quotes - Worth Learning ************ ********* ********* ********* ********* *** "A person should not be too honest. Straight trees are cut first and Honest people are screwed first." Chanakya quotes (Indian politician, strategist and writer, 350 BC 75 BC) ************ ********* ********* ********* ********* *** "Even if a snake is not poisonous, it should pretend to be venomous." Chanakya quotes (Indian politician, strategist and writer, 350 BC-275 BC) ************ ********* ********* ********* ********* *** "The biggest guru-mantra is: Never share
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submitted by rssaj (12 m) on 15 May 2007 11:15:27 IST (1 comments 85 views)
INVERSE DOPPLE EFFECT While the usual Doppler effect means that the frequency increases if the observer approaches the source - and decreases as they move away from each other - the theorists have speculated, since 1943, about the possibility that these rules may be interchanged. That would create an "Inverse Doppler effect". In 2003, this situation was realized experimentally for the first time. Nigel Seddon and Trevor Bearpark in Bristol, United Kingdom, made a transmission line that
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submitted by striker (256 m) on 15 May 2007 02:08:13 IST (3 comments 101 views)
Life began with waking up and loving my mother's face.George EliotA mother is the truest friend we have, when trials, heavy and sudden, fall upon us; when adversity takes the place of prosperity; when friends who rejoice with us in our sunshine, desert us when troubles thicken around us, still will she cling to us, and endeavor by her kind precepts and counsels to dissipate the clouds of darkness, and cause peace to return to our hearts. Washington IrvingLord Illingworth: All women become like their mothers. That is their tragedy.An ounce of mother is worth a pound of clergy.Spanish ProverbAs is the mother, so is her daughterEzekiel 16:44 (The Bible)Old women even f
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submitted by amitsingh (273 m) on 12 May 2007 16:21:25 IST (3 comments 177 views)
CENTRIFUGAL FORCE -THE FALSE FORCE An evil word has worked its way into our daily vocabulary, and with it, an incorrect understanding of the way physics works. "Centrifugal force ( Latin for "center fleeing") is often used to describe why mud gets spun off a spinning tire, or water gets pushed out of the clothes during the spin dry cycle of your washer. It is also used to describe why we tend to slide to the outer side of a car going around a curve. It is a common explanation...the only problem is all of it is absolutely wrong!!! Centrifugal force does not exist...there is no such thing...it is a
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submitted by dilip (62 m) on 14 May 2007 22:21:22 IST (2 comments 136 views)
*A letter of Husband to Wife:* Dear Sweetheart, I can't send my salary this month, so I am sending 100 kisses... You are my sweetheart. Your husband *His Wife replied back after some days to her Husband:* Dearest sweetheart, Thanks for your 100 kisses, I am sending the expenses details. 1. The Milk man agreed on 2 kisses for one month's milk. 2. The electricity man only agreed after 7 kisses. 3. Your house owner is coming every day and taking two or three kisses instead of the rent. 4. Supermarket owner did not accept kisses only, so I have given him some other items..... 5. Other expenses 40 kisses Please don'
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submitted by shitij_iitD (27 m) on 11 May 2007 08:56:08 IST (3 comments 157 views)
In the 1700s, Daniel Bernoulli investigated the forces present in a moving fluid. This slide shows one of many forms of Bernoulli's equation. The equation appears in many physics, fluid mechanics, and airplane textbooks. The equation states that the static pressure ps in the flow plus the dynamic pressure, one half of the density r times the velocity V squared, is equal to a constant throughout the flow. We call this constant the total pressure pt of the flow. As discussed on the gas properties page, there are two ways to look at a fluid; from the large, macro scale properties of the fluid that we can measure, and from the small, micro scale of the molecular mot
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submitted by Urva (187 m) on 14 May 2007 14:56:28 IST (2 comments 203 views)
WAVE MECHANICSPrince Louis de Broglie?????( 1892-1987 )????? In 1923, while still a graduate student at the University of Paris, Louis de Broglie published a brief note in the journal Comptes rendus containing an idea that was to revolutionize our understanding of the physical world at the most fundamental level. He had been troubled by a curious "contradiction" arising from Einstein's special theory of relativity. First, he assumed that there is always associated with a particle of mass m a periodic internal phenomenon of frequency ? [?, rather than the traditional Greek letter "nu", is used here for purposes of compati
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submitted by striker (256 m) on 14 May 2007 13:56:41 IST (1 comments 95 views)
When we began to study electric forces we introduced the concept of the electric field, . In particular, we had the fundamental relation between the force on a charge q in an electric field: = q. We will introduce a magnetic field in a similar manner. Before doing this, however, we define what is known as the cross product x between two vectors and . Consider two such vectors in the plane of this page with an angle between them, as in Fig. 1.1. Figure 1.1: Two vectors x , which itself is a vector, is defined as follows: the magnitude of x is given by | x | = ||| sin V1V2sin , (1)
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submitted by Urva (187 m) on 14 May 2007 15:10:29 IST (0 comments 151 views)
Most people think that IIT JEE is very difficult examination. However, JEE is only a different examination.One thing certain is IIT JEE requires a very systematic preparation. Earlier you start preparing for it the better.JEE defers from conventional board exams in one major way. JEE tests your fundamentals of the subject and your ability to think logically and analytically.To begin with, you must arrange for professional guidance, if you do not have one available at home. Secondly, practice of solving JEE level problems being of paramount importance, you must have access to enough recommended books / notes.(1) You can get join postal / classroom coaching.(2) You ca
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submitted by sravan (183 m) on 14 May 2007 12:06:47 IST (0 comments 141 views)
WAVE MECHANICSPrince Louis de Broglie?????( 1892-1987 )????? In 1923, while still a graduate student at the University of Paris, Louis de Broglie published a brief note in the journal Comptes rendus containing an idea that was to revolutionize our understanding of the physical world at the most fundamental level. He had been troubled by a curious "contradiction" arising from Einstein's special theory of relativity. First, he assumed that there is always associated with a particle of mass m a periodic internal phenomenon of frequency ? [?, rather than the traditional Greek letter "nu", is used here for purposes of compati
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submitted by striker (256 m) on 14 May 2007 11:42:01 IST (0 comments 75 views)
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