Tuesday, August 31, 2010

Note on simplifying expressions calculator

Entry simplifying exponential expressions planning:
In this article let me help you on simplifying expressions calculator. Algebra is the subdivision of science which deals with the learning of rules of operations and relations, and the concepts and constructions arising from them, including polynomials. Scheming simplifying exponential expressions is also a air of algebra.Exponents are represented by a force on a size or varied. Expressions are chainlike with exponential damage.

Index is a maths computation in algebra represented by two drawing 'a' & 'n', where a is the stand and n is the power. This could also help us on factors of 39. The index denotes the limit of nowadays the form is closed into, it is endeavour of algebra an! d they person positive properties, which enables us in simplifying the affine to them are surrendered in the following sections.
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Random Bullets of Grading Hell

Because it's all about the grading this week.

PhD qualifying exams were scored this week, and all but one passed. Of the passing grades, though, only one really impressed me. One wonders what the qualifying exam will measure that coursework will not, though perhaps it's the speed with which it is measured...The student who failed gets to try again in the spring. Lucky student. Lucky me, too, who gets to read the next 25-page attempt.

I am at this moment wading through undergrad exams. I wish I knew of a way to really measure what I want to measure without wading through pages and pages of handwritten text. That said, some students are actually exercising their capacity for original thinking in this exam, not just regurgitating my own words. Although the regurgitation abounds.

I am in the middle of grading seminar papers, and here, I must say, I am stuck. What, at the 700-level, distinguishes a B+ paper ! from an A-? This to me, is an unanswerable, but absolutely crucial question. What about a paper that applies the obvious (but complex) theory to an already overdone text? It adds nothing to the current discussion, but it is sound, well-written and thoughtful. What about the structural and stylistic mess that is based on a fundamentally brilliant premise, but is two or three really good revisions (expand, unpack, rephraser) away from a life beyond this iteration? What about the clever, stylish, smart paper that needs beefing up with theoretical rigor? What about the metholodological experiment that is executed well, but seems to turn out to have been not worth the energy because it yielded results largely predictable without the methodological brouhaha? Fortunately, there are two flat-out brilliant papers in the batch. At least I know what an A looks like.

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The Klein-Nishina Formula

In Chapter 15 of the 4^th Edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I present the Klein-Nishina formula (Eq. 15.17).

“The inclusion of dynamics, which allows us to determine the relative number of photons scattered at each angle, is fairly complicated. The quantum-mechanical result is known as the Klein-Nishina formula.”

At first glance, Eq. 15.17 doesn’t look quantum-mechanical, because it does not appear to contain Planck’s constant, h. However, closer inspection reveals that the variable x in the equation, defined on the previous page (Eq. 15.15), does indeed contain h. Russ and I don’t derive the Klein-Nishina formula, nor do we give much background about it. Yet, this equation played an important role in the development of quantum mechanics, and specifically of quantum electrodynamics.

In the book Nishina Memorial Lectures: Creators of Modern Physics, the Nobel Prize winning physicist Chen Ning Yang wrote a chapter about The Klein-Nishina Formula & Quantum Electrodynamics.

“One of the greatest scientific rev! olutions in the history of mankind was the development of Quan! tum Mech anics. Its birth was a very difficult process, extending from Planck’s paper of 1900 to the papers of Einstein, Bohr, Heisenberg, Schrodinger, Dirac, and many others. After 1925-1927, a successful theory was in place, explaining many complicated phenomena in atomic spectra. Then attention moved to higher energy phenomena. It was in this period, 1928-1932, full of great ideas and equally great confusions, that the Klein-Nishina formula played a crucial role. The formula was published in 1929, in the journals Nature and Z. Physik. It dealt with the famous classical problem of the scattering of light rays by a charged particle….”

Oskar Klein and Yoshio Nishina derived their formula starting from the Dirac equation, which is a relativistic version of Schrodinger’s equation for an electron, including the effect of spin . During the summer of 1928, Klein and Nishina performed the lengthy calculations necessary to derive their formula. They would work independently during the day, and then compare results each evening (as Russ and I say, the calculation is “fairly complicated”). The final result was published in the German journal Zeit. f. Phys. ("Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac," Volume 52, Pages 853-868, 1929). I don’t read German, so I can’t enjoy the original.

Later, the theory of Quantum Electrodynamics (QED) was developed to more completely describe the quantum mechanical interactions of electrons and photons. For an elementary introduction to this subject, see Richard Feynmann’s book ! QED. (I have to admit, although I took several semesters of quantum mechanics in graduate school, I never really mastered quantum electrodynamics.) When the problem of the scattering of light by electrons was reexamined using QED, the result was identical to the Klein-Nishina formula derived earlier. To learn more about how these results were obtained, see The Road to Stueckelberg's Covariant Perturbation Theory as Illustrated by Successive Treatments of Compton Scattering, by J. Lacki, H. Ruegg, and V. Telegdi (http://arxiv.org/abs/physics/9903023). But beware, the paper is quite mathematical and not for the faint of heart.

Who were the two men who derived this formula? Oskar Klein (1894-1977) was a Swedish theoretical physicist. He is known for the Kaluza-Klein theory, the Klein-Gordon equation, and the Klein paradox. Yoshio Nishina (1890–1951) was a Japanese physicist. He was a friend of Niels Bohr, and a close associate of Albert Einstein. The crater Nishina on the Moon is named in his honor. During World War II he was the head of the Japanese atomic program.

Let me share one last anecdote about Klein, Nishina, and Paul Dirac that I find amusing. Gosta Ekspong tells the story in his chapter The Klein-Nishina Formula, in the book The Oskar Klein Memorial Lectures.

“When Dirac paid a short visit to Copenhagen in 1928, he met Klein and Nishina. The three of them were once conferring in the library of the Bohr Institute. Dirac was a man of few words, so when the remark came from Nishina that he had found an error of sign in the new Dirac paper on the electron, Dirac drily answered: “But the result is correct.” Nishina, in an attempt to be helpful, said: “There must be two mistakes,” only to get Dirac’s reply that “there must be an even number of mistakes.”

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Pre-Calculus For Dummies

Great Price "Pre-Calculus For Dummies" for $11.20 Today

It seems the authors break their own rule in the first chapter on PEMDAS. This is a simple problem, but they wrote it out wrong in answers where they perform addition and subtraction first before multiplication. I think it should be the other way around. i.e. Ex 4 - Ch 1. abs(5 * 1 - 4 + 6) = 7 not 9. Every monkey knows multiplication is performed first. I'm not sure what the authors were thinking starting with subtraction first???I'm kinda blushing here...I punched this into my TI-89 Titanium and I get the same answer as I had come up with for the nominator. Calculators follow PEMDAS rule, so am I missing something here? Please, put an errata up people and have a forum, otherwise your books are useless. This is a refresher for me as I'm going in for calculus next fall. Mi! stakes as such would flunk a student in those courses...

Pre-Calculus For Dummies Features

ISBN13: 9780470169841
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Pre-Calculus For Dummies Overviews

Getting ready for calculus but still feel a bit confused? Have no fear. Pre-Calculus For Dummies is an unintimidating, hands-on guide that walks you through all the essential topics, from absolute value and quadratic equations to logarithm! s and exponential functions to trig identities and matrix oper! ations.

With the help of this clear, easy-to-use resource, you’ll soon get a handle on all of the concepts — not just the number crunching — and understand how to perform all pre-calc tasks, from graphing to tackling proofs. You’ll also get a new appreciation for how these concepts are used in the real world, and find out that getting a decent grade in precalc isn’t as impossible as you thought. Discover how to:

Apply the major theorems and formulas
Understand quadratic, square-root, absolute value, cubic, and cube-root functions
Graph trig functions like a pro
Flip-flop with inverse functions
Find trig values on the unit circle
Work with trig identities and advanced identities
Tackle analytic geometry
Solve oblique triangles with the laws of sines and cosines
Use polar coordinates to express points on a plane
Identify function limits and continuity !
Place vectors on a coordinate plane.
Rotate and shift conic section forms
Solve systems with mingling and matrices

If “the fun and easy way to learn pre-calc” seems like an oxymoron to you, order Pre-Calculus For Dummies today, and get ready to be surprised!

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This book is well-written. It explains the most complex lessons, from class, and "dumbs it down" for those of us who need that extra help. Pre-Cal for Dummies has helped me in many cases.

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This is one of the worst "dummies" books I've ever read. It was condescending, dull, and poorly written. If you're! looking for pre-calculus help, look elsewhere.

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Time and Distance Problem 12

This is a algebra time and distance problem asked by an anonymous user in the ask a question section which stated,

"A boat travels 10 km upstream and 10 km back. The time for the round trip is 10 hrs. The speed of the stream is 4 km/hr. What is the speed of the boat in still water? Can someone help? I need it as a decimal."

Answer Coming Soon!

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Instant Answers in Google Suggest

Google's search suggestions started to include instant answers for Math calculations, unit conversions, currency conversions, weather information, simple facts, local time, package tracking, word definitions and more. That means you no longer have to click the search button and open a new page to see the results: the answers are displayed instantly.

"This kind of information will appear in Suggest either above or below the suggested search terms for a variety of queries. For example, you can type "delta 140" to see the flight status. You can also quickly discover the current time, figure out how many Euros you'll get per dollar, or even brush up on metric conversions," explains Google.

My only issue is that Google's answers can't be copied. If you try to select the suggestion, you'll notice that the answer is not added to the search box, so the only way to copy the result is to open the search results page.

Some of the instant answers are available even if you don't use Google's homepage: check the search suggestions from Firefox, Chrome, IE 8 and Google Toolbar.

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SA Says 400 Million Connected Convergent Devices in 2014

The Connected Convergent Devices (CCDs) market will claim a global installed base of over 400 million units by 2014, according to research just released by analyst firm Strategy Analytics. The report, “Connected Convergent Devices: The New Battleground,” envisions CCDs filling the gap between smartphones and netbooks—a gap that is ripe for growth.

The firm estimates the value of the CCD market will exceed $50 billion in 2014. Some cannibalization is inevitable, according to the report, particularly among the tablets, netbooks, eBook readers and Mobile Internet devices (MIDs) categories.“ All categories have the potential to be very disruptive,” said Peter King, Director of the Connected Home Device service at Strategy Analytics. “However, all have their place in the market, and as casual computing develops, new products such as the tablet can be additive to the market as well as cannibalistic”.

CE, Mobile and PC companies are vying for the consumer wallet with a variety of Connected Convergent Devices, including tablets, netbooks, smartbooks, eBook readers and MIDs. “We have recently witnessed price erosion and product withdrawals! in the eBook reader market, and the netbook market growth has slowed down since the introduction of the Apple iPad,” added King. “As rival tablets hit the market by year-end, many driven by Google’s Android, we will see even more competition in this dynamic new market segment.”

This sounds reasonable as these devices have come down drastically in price. With the Kindle now at $139, I am tempted to buy one. If it was over $300 like the original devices, I might as well buy an iPad or netbook and get a device the does several functions.

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I Love Me Some ExamView

I spent the last two days on school business building a set of common formative assessments in ExamView that are aligned to my department's skills list for our algebra and pre-algebra classes. Many of the questions are dynamic which means that for any given question type, multiple versions of the question can be created by the click of a button. As I was looking through the question banks, I realized that there were some skills that didn't have questions that fit what we will be trying to assess. Solution? Build it yourself.

The process is a bit tedious at first, but I was able to use previously made questions to figure out how to build a simple question regarding slope.

Step 1: Define your algorithms.

Step 2 : Create a graph using pre-defined variables.

Step 3: Define the distractors.

Yeah, gotta say I love this feature. Finding questions with good distractors is tough at best. But if you decide on an algorithm based on common misconceptions, you're good to go. In this problem, I d! ecided the common misconceptions for students calculating slop! e based on a graph were: