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Then, copy that formula down for the rest of your stocks. But, as I said, dividends can make a huge contribution to the returns received for a particular stock. Also, you can insert charts and diagrams to understand the distribution of your investment portfolio, and what makes up your overall returns. If you have data on one sheet in Excel that you would like to copy to a different sheet, you can select, copy, and paste the data into a new location. A good place to start would be the Nasdaq Dividend History page. You should keep in mind that certain categories of bonds offer high returns similar to stocks, but these bonds, known as high-yield or junk bonds, also carry higher risk.

# Difference between distance and displacement calculus jokes

With a great deal of effort, several books of mathematical tables and techniques, and a few hours, the physicist gave the solved problem to the mathematician, who was duly impressed. Here's the problem: you have a pot of water on the stove, at 60 F. You want to heat it up to 70 F. What do you do? You turn the stove on. Fourier's equations govern how heat transfers from the stove to the pot, and you can solve them numerically to find out how long it takes for the water to reach 70 F.

You take the pot of water, stick it in the refrigerator until it cools down to 60 F, and then it simplifies to the previous problem! A: One. He gives it to seven Lithuanians, and reduces it to the previous joke. Mathematicians You can find aleph-one bottles of beer on the wall elsewhere. But here are a few jokes just about mathematicians and their antics. A famous mathematical puzzle problem involves the following: two trains on the same track begin a mile apart and head towards each other at 60 miles an hour.

A fly on one train flies at mph to the other train, and when it lands there, it flies back to the other train, and so on, flying back and forth between the two trains until it gets squashed in the middle. How far does the fly travel? A student once asked the great mathematician John von Neumann the above problem.

They think they have to add up the infinite series to find out how far the fly travels! Extra credit question: which way does the fly face at the end? Here's another one that highlights the bane of the mathematics student: the phrase "it is obvious that Though others did it before him, Laplace was notorious for leaving length demonstrations to the reader, usually preceded with "C'est visible que.. Bowditch meticulously filled in all the gaps, but before long he grew to dread those words, for he knew that when he saw them, he was in for a lengthy bit of derivation before what Laplace claimed was obvious was, in fact, obvious.

I had to suffer through not a few of Laplace's and other's "it is obvious that.. A professor was notorious for leaving complicated demonstrations to the students, with no more than a remark that "It is obvious that Another professor was notorious for writing very little on the board, verbally describing how to go from derivation to derivation, saying it was as obvious as "Two plus two equals four".

One day a group of students approached him, and begged him to write more on the board, so they could follow along. The professor, who didn't realize what he was doing, vowed to do so. The next day, however, he continued to lecture in his ordinary style, leaping from derivation to derivation with nary a mark on the board.

As you'll see in the physics section, there are lots of stories told about specific physicists. However, there aren't many stories told about specific mathematicians; the von Neumann story is the only one I can think of offhand. To remedy this, I shall use the time-honored comic tradition of taking an old joke, filing off a few serial numbers, and calling it new Karl Friedrich Gauss was a child prodigy who later blossomed into the greatest mathematician of the age.

When he was in his prime, a young man approached him, asking what he should do to become a great mathematician. You were publishing important mathematical treatises when you were even younger than I am now. Incidentally, Gauss decided to become a mathematician only after long debate; at the age of 19, he was undecided, and leaning towards a career in philology which today we might call linguitics.

Then he made the discovery of the millenium: how to construct a regular 17 sided polygon using only compass and straightedge; it was the first new construction technique to be discovered in almost two thousand years. With a lead like that, Gauss abandoned the study of words for the study of mathematics. Here's another joke about Gauss: Laplace was once asked by Alexander von Humboldt a German scientist who, in addition to writing an immensely popular work on science called Kosmos, was also responsible for making mountain climbing a popular sport who the great mathematician in Germany was.

Without hesitation, Laplace said, "Pfaff". Physicists I used to be a physics major, until I discovered I had absolutely no laboratory skills. I still enjoy theoretical physics, and try and usually fail miserably to keep up with the fast-growing subject. My favorite joke about physicists or about a particular physicist, at any rate is the following Wolfgang Pauli, the great Austrian physicist who died much too young, went to heaven.

At the gate he was greeted by St. Peter who said "Herr Doktor Pauli! As a reward for your contributions to human understanding of physics, God Himself has consented to let you ask him one question. Peter took Pauli to an anteroom, where God awaited Pauli's question.

Why to 1? Halfway through, Pauli sputtered in exasperation, "Das ist ganz falsch! Unfortunately, if I used it in a joke, I would be morally bound to cite its actual value, and furthermore to explain what it was. This I would have done Anyway, a similar story is told about Einstein Einstein's General Theory of Relativity predicts a certain displacement of starlight, caused by a large mass; a solar eclipse in provided the first opportunity to test the theory.

A reporter asked Einstein how he would feel if the observations did not support relativity. One of the expeditions to measure the Einsteinian displacement of starlight was headed up by the English physicist Arthur Stanley Eddington. Recently, some doubts have been raised about the validity of Eddington's experiment though General Relativity itself has been tested under a number of other conditions and has passed with flying colors. Talking about Eddington, though A reporter once asked Arthur Stanley Eddington who was one of the teams who used the eclipse of to verify general relativity whether it was true that the theory of relativity was so complicated that, except for Einstein, only two other people in the world could understand it.

Eddington sat silently for a moment, his brow furrowed. The reporter, fearful that he had offended Eddington, asked what was wrong. I was just trying to figure out who the other person was. For those who aren't Jewish, a "brouchah" I hope I spelled it right is some sort of a benediction given an inanimate object, to make it permissible for a Jew to use it.

Leon Lederman, having just acquired a brand new particle accelerator, and, to make absolutely sure nothing would go wrong, wanted to get a brouchah for it. First, he approached an Orthodox Rabbi. Lederman explained, and after some thought, a consultation of the Torah, a few conversations with the other rabbis, the rabbi finally answered, "My son, I am afraid I cannot give a brouchah for such an object.

Imagine that Usain Bolt was wearing a speedometer. At what precise moment was he running the fastest? And exactly how fast was that? The concept seems almost paradoxical. At any instant, Usain Bolt was at precisely one place. He was frozen, as in a snapshot. So what would it mean to speak of his speed at that instant? Speed can only occur over a time interval, not in a single instant. The enigma of instantaneous speed goes far back in the history of mathematics and philosophy, to around B.

Recall that in his paradox of Achilles and the tortoise, Zeno claimed that a faster runner could never overtake a slower runner, despite what Usain Bolt proved that night in Beijing. And in his arrow paradox, Zeno argued that an arrow in flight could never move. Mathematicians are still unsure what point he was trying to make with his paradoxes, but my guess is that the subtleties inherent in the notion of speed at an instant troubled Zeno, Aristotle and other Greek philosophers.

Their uneasiness may explain why Greek mathematics always had so little to say about motion and change. Like infinity, those unsavory topics seem to have been banished from polite conversation. Two thousand years after Zeno, the founders of differential calculus solved the riddle of instantaneous speed.

Their intuitive solution was to define instantaneous speed as a limit — specifically, the limit of average speeds taken over shorter and shorter time intervals. For this strategy to succeed, we have to assume his distance down the track varied smoothly. But did his distance actually vary smoothly as a function of time? To estimate his instantaneous speed, we need to go beyond the data and make an educated guess about where he was at times in between those points.

A systematic way to make such a guess is known as interpolation. The idea is to draw a smooth curve between the data available. There are many different curves that meet these criteria. Statisticians have devised a host of techniques for fitting smooth curves to data. Since the curve is smooth by design, we can calculate its slope at every point.

It indicates that Bolt reached a top speed of around After that he decelerated, so much so that his speed dropped to The graph confirms what everyone saw; Bolt slowed down dramatically near the end, especially in the last 20 meters, when he relaxed and celebrated. The next year, at the World Championships in Berlin, Bolt put an end to the speculation about how fast he could go.

He ran hard to the finish and shattered his Beijing world record of 9. Because of the great anticipation surrounding this event, biomechanical researchers were on hand with laser guns, similar to the radar guns used by police to catch speeders. Running, after all, is a series of leapings and landings. Intriguing as they are, these little wiggles are annoying and bothersome to a data analyst. What we really wanted to see was the trend, not the wiggles, and for that purpose, the earlier approach of fitting a smooth curve to the data was just as good and arguably better.

After collecting all that high-resolution data and observing the wiggles, the researchers had to clean them off anyway. They filtered them out to unmask the more meaningful trend. To me, these wiggles hold a larger lesson. I see them as a metaphor, a kind of instructional fable about the nature of modeling real phenomena with calculus. If we try to push the resolution of our measurements too far, if we look at any phenomenon in excruciatingly fine detail in time or space, we will start to see a breakdown of smoothness.

The same thing would happen with any form of motion if we could measure it at the molecular scale.

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