Tuesday, August 31, 2010

Side-Way Trading

Follow Me on Facebook Follow Me on Tweeter Digg this Delicious

As I mentioned in the "S&P 500 Financial" post on August 20, 2010: "At this moment the majority of technical indicators remain to be bearish by suggesting the higher odds of further decline." - the indexes (S&P 500, Nasdaq 100 and DJI) are lower, yet if you take at the hourly chart (1 bar = 1 hour) you will see that most of the time the indexes were in side-way action.

Side-way characteristics of the current down-trend could be noticed from the beginning (August 9, 2010) of this down-trend. It is difficult to compare the current down-trend to the previous down-trends we had over the last couple of years. Te previous down moves where more consistent and had much less side-way trading sessions. It is already almost a month since the indexes in the bearish move and, so far, during t! he recent decline, we have not seen two strongly negative session in a row. Yet, mainly because of the side-way trading, we still have not seen panic trading which would be characterized by the strong bearish volume to the price down-side and strongly oversold advance/decline issues and volume readings.

The other characteristic of the current down move is the high level of volatility. The volatility is not extremely high, yet it remains steady on the high level.

The same a s a week ago, I would say that the majority of technical indicators remain to be bearish by suggesting the better odds of the further decline. Yes, the Friday's advance has pushed some technical indicators into bullish sentiment and if you take a look at shorter-term technical analysis you may see some bullish signals. However, in order to have a strong up-move, in addition to the bullish signal, the stock market should! be predisposed to the up-move. So far, we may see bullish sig! nals on shorter-term frames, yet, personally, I have not seen any strongly oversold indications. Therefore, I would not place a long bet.


time table chart up to 100

Supermassive black holes and the entropy of the universe

New Scientist has an article about a recent paper by two Australian researchers (http://www.arxiv.org/abs/0909.3983), which contains detailed estimates of the entropy of various components of the universe (black holes, neutrinos, photons, etc.). This paper is related to some work I did with with Frampton, Kephart and Reeb: What is the entropy of the universe?. (Discussion on Cosmic Variance.)

Our work did not focus on the numerical values of various contributions to the entropy (we made some simple estimates), but rather what the physical meaning is of this entropy -- in particular, that of black holes; see excerpt below.

New Scientist: Mammoth black holes push universe to its doom

30 September 2009 by Rachel Courtland

THE mammoth black holes at the centre of most galaxies may be pushing the universe closer to its final fade-out. And it is all down to the raging disorder within those dark powerhouses.

Disorder is measured by a quantity called entropy, something which has been on the rise ever since the big bang. Chas Egan and Charles Lineweaver of the Australian National University in Canberra used the latest astrophysical data to calculate the total entropy of everything in the universe, from gas to gravitons. It turns out that supermassive black holes are by far the biggest contributors to the universe's entropy. Entropy reflects the number of possible arrangements of matter and energy in an object. The number of different configurations of matter a black hole could contain is staggering because its internal state is completely mysterious.

Egan and Linewe! aver found that everything within the observable universe cont! ains abo ut 10^104 units of entropy (joules per Kelvin), a factor of 10 to 1000 times higher than previous estimates that did not include some of the biggest known black holes (www.arxiv.org/abs/0909.3983, submitted to The Astrophysical Journal).

If entropy were ever to reach a maximum level, that would mean the heat death of the universe. In this scenario no energy can flow, because everything is the same temperature and so life and other processes become impossible. "Our results suggest we're a little further along that road than previously thought," Egan says.

But although black holes do boost the universe's total entropy, it is not clear whether they will hasten its heat death. Supermassive black holes don't contribute much to the flows of heat that even out temperature throughout the universe, says physicist Stephen Hsu at the University of Oregon in Eugene.

It's true that these black holes will slowly evaporate by releasing Hawking radiat! ion, particles created near the boundary of the black hole. And this radiation could move the universe towards heat death.

Black holes may evaporate via Hawking radiation, tipping the universe towards its heat death. However, it will take some 10^102 years for a supermassive black hole to evaporate. "The entropy inside those black holes is effectively locked up in there forever," Hsu says. So we may have reached a state approaching heat death long before, as stars burn out and their matter decays.

The large result obtained by the Egan and Lineweaver for the entropy of the universe is primarily due to supermassive black holes. How do we interpret that entropy? Here is an excerpt from our paper (excuse the latex).

Note the entropy used in this paper describes the uncertainty in the precise quantum state of a system. If the system is macroscopic the full quantum state is only accessible to a kind of ``super-obser! ver'' who is unaffected by decoherence \cite{decoherence}. Ind! ividual observers within the system who have limited experimental capabilities can only detect particular decoherent outcomes. These outcomes arise, e.g., from an effective density matrix that results from tracing over degrees of freedom which are out of the experimenter's control (i.e., which form the ``environment''). In \cite{BID} the experimental capabilities necessary to distinguish decoherent branches of the wavefunction, or, equivalently, the precise quantum state of Hawking radiation from a black hole, are discussed. It is shown that a super-observer would either need (at minimum) the capability of making very precise measurements of accuracy $\exp(- M^2 )$ (see also the proposal of Maldacena \cite{eternal} for a specific measurement to determine whether black hole evaporation is unitary), or alternatively the capability of engineering very precise non-local operators, which measure a large fraction of the Hawking radiation at once, including correlations (i.e., as opposed t! o ordinary particle detectors, which only measure Fock state occupation numbers and are not sensitive to phase information).

An observer who lacks the capabilities described in the previous paragraph would be unable to distinguish the states in the $S = M^{3/2}$ subspace in Fig.~\ref{figure1} from those in the larger $S = M^2$ subspace, assuming the unitary evaporation resembles, in gross terms, Hawking evaporation, with the information hidden in correlations among the emitted quanta. In that case, the future uncertainty for ordinary (non-super) observers might be better characterized by the larger $S = M^2$ entropy. Putting it another way, an ordinary (non-super) observer is forced (due to experimental limitations) into a coarse grained description of the radiation; they cannot distinguish between most of the radiation states, and for them the $S = M^2$ entropy is appropriate. For a super-observer, however, due to unitary evolution, the uncertainty in the quantu! m state does not increase. For them, black holes do not have g! reater e ntropy than the precursor states from which they formed.

For the super-observers described above, the large black hole entropies in Table I do not reflect the actual uncertainties in the (current and future) state of the universe and are in that sense misleading. A black hole of mass $M$ whose formation history is typical for our universe (e.g., it originated from gravitational collapse of a star or galactic core) satisfies the bound S [less than] M^{3/2} \cite{MI}. Thus, re-evaluating the numbers in Table I, the total entropy of all black holes in our universe is not bigger than the total matter entropy: the dominant uncertainty in the precise state of the universe, at least as far as arises from known physics, is, in fact, due to CMB photons or neutrinos.





Figure 3 caption: Ordinary matter (star, galactic core, etc.) collapses to form an astrophysical black hole. Under unitary evolution, the number of final Hawking radiation states that are actually accessible from this collapse is $\sim \exp M^{3/2}$, i.e.~precisely the number of ordinary astrophysical precursors (\ref{th1}). It is therefore much smaller than the the number of $\sim \exp M^2$ states a black hole, and its eventual Hawking radiation, could possibly occupy if nothing about its formation process were known.


Final mysterious comment, maximally compressed for the cognoscenti: assuming unitarity, black holes do not push us closer to heat death (equilibrium) in the multiverse! , but can contribute (albeit very slowly) to the (coarse g! rained) heat death experienced by a non-super observer (i.e., an observer subject to decoherence). See here for more on equilibrium in the multiverse.

standard entropy table

Have questions about math problems

Have questions about math problems, get help on this website. You will learn the toughest questions with the easiest way to solve it!!

solving math equations

Krugman: Greece Could "Solve" Its Problems if it Could Print More Money

In his best-seller, The Return of Depression Economics (which I am having my MBA students read this spring), Paul Krugman declared that most economic problems can be "solved" rather easily: the government prints more money. I am not making up that declaration, nor am I embellishing it or putting it out of context. That is what he said, and, like Sgt. Friday, just the facts, ma'am.

Today, he looks once again at the crisis in Greece, which has spread to Spain and where Austrians see fiscal folly and wages and work policies that are totally out of line with the structures of production in those country, a situation that must be put back into balance to end the crisis, Krugman sees the lack of inflation being at fault. Don't take my word for it. Read on:
The fact is that three years ago none of the countries now in or near crisis seemed to be in deep fiscal trouble. Even Greece’s 2007 budget deficit was no higher, as a share of G.D.P., than the deficits the United States ran in the mid-1980s (morning in America!), while Spain actually ran a surplus. And all of the countries were attracting large inflows of foreign capital, largely because markets believed that membership in the euro zone made Greek, Portuguese and Spanish bonds safe investments.

Then came the global financial crisis. Those inflows of capital dried up; revenues plunged and deficits soared; and membership in the euro, which had encouraged markets to love the crisis countries not wisely but too well, turned into a trap.

What’s the nature of the trap? During the years of easy money, wages and prices in the crisis countries rose much faster than in the rest of Europe. Now that the money is no longer rolling in, those countries need to get costs back in line.

But that’s a much harder thing to do now than it was when each European nation had its own currency. Back then, costs could be brought in line by adjusting exchange rates — e.g., Greece could cut its wages relative to German wages simply by reducing the value of the drachma in terms of Deutsche marks. Now that Greece and Germany share the same currency, however, the only way to reduce Greek relative costs is through some combination of German inflation and Greek deflation. And since Germany won’t accept inflation, deflation it is.
Krugman, of course, supports Germany having a round of inflation. We have been down this road before, people, and it ends in disaster. In the late 1920s, Great Britain did not want to devalue the Pound, which at that time should have been trading at about $3.50 instead of the $4.86 "official" rate.

To keep the $4.86 rate intact, Benjamin Strong, who then was the chairman of the New York Federal Reserve Bank, cut a deal with Montagu Norman, Britain's equivalent of the Secretary of the Treasury, to inflate the U.S. Dollar. This led to the infamous stock market bubble that burst in October, 1929, and President Hoover's response to that crash (to try to prop up failing firms, as well as prop up high prices and wages) led to the Great Depression.

The Germans have their own history with inflation (1923 anyone?) and are not about to go the Benjamin Strong route, as to do so would create a series of troubles down the road. Unfortunately, inflation ultimately distorts an economy's structure of production, leads to unsustainable booms, and then to disaster. However, Keynesians like Krugman hold that the Very Worst Thing that can happen to an economy is deflation, and that prosperity is possible only through inflation.

Here is the problem with Krugman's prescription (Germany inflate, Greece continue as is): It does nothing to get the Greek fundamentals back into order and it distorts the economic fundamentals in Germany. In other words, it does nothing to solve the real, underlying problems in Greece, but it lays the foundation for a future crisis in Germany, as inflation will create its own problems.

If you wish to see an important difference between Austrians and Keynesians, here it is. Keynesians really don't see economic fundamentals, nor do they see any issues with factors of production. Instead, in their view, the economy is a homogeneous mix that works when government throws lots of money into the recipe. If there are imbalances (and the theory does not allow for that to happen, although Krugman himself recognizes that imbalances could be an issue), then inflation can solve everything. Unfortunately, what happens when governments engage in policies of inflation is that the seeming good effects come first, but then when the factor prices get out of balance with what is being produced, the economy moves toward an inevitable bust, and any attempts to "fix" things through another round of inflation only make things worse.

Austrians, on the other hand, look first at the factors of production for the distortions in the entire structure of the economy. Deflation, far from being the enemy of the economy, allows those factors to get back into balance with the overall structure of production, and direct production to consumer desires. It is the opposite of inflation: the bad effects come first (unemployment and initial dislocation), but the "good" effects come later (a recovery).

There is no way to bridge the gap between Keynesians and Austrians. Today, it is the Keynesians that rule, and it is economy that ultimately will suffer because their "theories" ultimately lead to disaster.

No, Greece cannot "solve" anything by going back to the Drachma and printing out the wazoo. Instead, it is up to that country to get its house back in order by letting the factors, including labor, get back into balance. That means, in the initial stages, that Greeks will find their wages being cut and their standard of living will fall. Yet, that initial stage is absolutely necessary if, in the long run, Greeks want to enjoy a higher standard of living in the future with an economy that is sustainable.

[Note]: It is good to be posting here again. I have been following the Tonya Craft trial in Ringgold, Georgia, and it is a fiasco. The prosecutors are running the show, and they are acting like typical high school bullies. It is a tragedy and a train wreck in progress.

solve my word problem

Solve your Algebra Problem in Tutornext.com

There is only little student have fun while studying algebra. I’m one of student that is really hated with algebra. I know algebra is very important, and will very useful in our live. That’s why I try hard to learn algebra.

In this era, we have great weapon to get information, what is that? Yes, internet. I’m searching the internet to get help with my Algebra 1 problem. And bingo, I get what I need. Tutornext.com, this site is Online Tutoring specifically for K-12. They offer Algebra 1 Help, and this is what I’m looking for. With this site, I think I will get my Algebra 1 Answers. Their price for the online tutor is really reasonable, if I can say is cheap. We can connect with the tutor whenever we want, and this is really great for student.

If you already in Algebra 2, this site will very helpful. They also offer Algebra 2 help, and you will get your Algebra 2 Answers. You can connect with the tutor whenever you want, while you have question for your algebra problem. With this online tutoring site, you can save your time (without having to come to the lessons).

Jangan lupa baca yang ini juga




solve algebra

Help!

Here's the deal:  I'm working on curriculum for my school and Algebra 2 is making my eyes cross.  I think the major problem is the state of Virginia is in a transition year between "old" Standards of Learning (SOLs), and "new" ones.  This year is supposed to be the year that we're still teaching and assessing the old SOLs, but we're supposed to teach the new ones, too.  Those of you that teach Algebra 2 already know that there's an enormous amount of information to cover in a short period of time.  To give you context, our school teaches it as a semester-long block course.  There's only so much a brain can handle in one day, though! 

Here's the first draft of my skills list and structure...I'm not sure what to do about the old vs. new SOLs (my skills list is based on the old SOLs because that is what will be assessed).

Note:  Gray items are not included in old or new SOLs but might be necessary for student understanding
          Blue items are being taken out of the SOLs starting next year
          Red items are new to the SOLs starting this year

Unit 1 Algebra 1 Review/Solving Equations


1 Solve multi-step equations and inequalities
2 Matrix +/-
3 Solve compound inequalities
4 Solve absolute value equations
5 Solve absolute value inequalities

Unit 2 Polynomial Review/Add Depth

6 Factor trinomial a = 1
7 Factor trinomial a > 1
8 Factor special cases (sum/diff of cubes, diff of squares, perfect square trinomials)
9 Factor out GCF first (factor completely)
10 Exponent rules
11 +/- polynomials
12 Multiply polynomials
13 Divide polynomials

Unit 3 Rational Expressions

14 Identify undefined values
15 Simplify rational expressions by factoring and canceling out common factors
16 Multiply and divide fractions
17 Multiply and divide rational expressions
18 Add and subtract fractions
19 Add and subtract rational expressions
20 Simplify complex fractions
21 Solve rational equations

Unit 4 Radicals, Radical Equations and Complex Numbers

22 Simplify numbers under radical
23 Simplify monomials under radical
24 Multiply and divide radicals
25 Add and subtract radicals
26 Nth roots to rational exponents and vice versa
27 Simplify expressions with nth roots and rational exponents
28 Solve radical equations
29 Simplify square roots with negative terms inside radical using i
30 Add and subtract complex numbers
31 Powers of i
32 Multiply complex numbers

Unit 5 Functions (intro)

33 Domain and range of relations (from ordered pairs, mapping, graph, table)
34 Identify relations that are functions and one-to-one
35 Given graph and a value k, find f(k)
36 Given graph, find zeros
37 Given graph and a value k, find where f(x)=k

Unit 6 Linear Functions


38 Slope from graph, equation, points
39 Graph from equation
40 Equation from graph
41 x- and y- intercepts
42 Determine whether lines are parallel, perpendicular, or neither from equation or graph
43 Write equations for parallel and perpendicular lines given line and point off the line
44 Graph linear inequalities

Unit 7 Systems


45 Solve systems of equations by graphing
46 Multiply Matrices using a graphing calculator
47 Inverse matrix method of systems
48 Systems of equations word problems
49 Graph systems of linear inequalities
50 Linear programming max/min problems

Unit 8 Functions (reprise)

51 Function math (addition, subtraction, multiplication, division)
52 Function composition, find a value i.e. f(g(3))
53 Function composition, find the function i.e. f(g(x))
54 Find an inverse function by switching variables

Unit 9 Quadratics

55 Graph from vertex form, identify max/min and zeros
56 Solve by factoring
57 Solve by Quadratic Formula (including complex solutions)
58 Determine roots using the discriminant
59 Write equation for quadratic given roots
60 Quadratic systems
61 Polynomials: relating x-intercept, zeroes and factors
62 End behavior for polynomials

Unit 10 Exponential/Logarithmic functions

63 Exponential growth or decay from function
64 Sketch base graph of exponential/log functions
65 Exponential to log and vice versa
66 Data analysis/curve of best fit for linear, quadratic, exponential and log

Unit 11 Transformations and Parent Functions

67 Graph absolute value functions
68 Horizontal and vertical translations of linear, quadratic, cubic, abs value, exponential and log
69 Reflections and stretching of linear, quadratic, cubic, abs value, exponential and log
70 Combinations of transformations on parent functions
71 Identify parent graphs of parent functions
72 Identify equations of parent functions

Unit 12 Conics

73 Identify a conic from graph
74 Identify a conic from equation

Unit 13 Variations

75 Write equation for direct, inverse and joint variation problems
76 Find the constant of variation

Unit 14 Sequences/Series

77 Write n terms of an arithmetic sequence
78 Find the sum of a finite arithmetic series
79 Write n terms of geometric sequence
80 Find sum of geometric series
81 Use formulas to find nth term
82 Identify sequence/series as arithmetic, geometric or neither

Unit 15  Statistics

83 Determine probabilities associated with areas under the normal crve
84  Compute permutations and combinations

 
If you made it this far, here's my call for help:  Anyone have advice/suggestions for how to make this work and/or a better way to organize the information into cohesive units that seem to occur in a somewhat logical order?  There is and will continue to be an emphasis on function families and transformations (as there should be).  I find it difficult to express on paper how each function category needs to be a resting place, but they are all connected in the ways that transformations apply.  Any ideas?
 
...oh...and I'm going to be teaching one section of deaf students and one section of blind students...in case that makes a difference

**edit:  I've added links to the old and new Virgina SOLs for Algebra 2 if anyone's interested**

simplify complex fractions calculator

properties of quadrilaterals

properties of quadrilaterals

Trapezoids:A pair of opposite sides is equal in trapezoid.If non-parallel pairs of opposite sides are equal then it is called as isosceles trapezium.The angles on the both sides of the base are equalThe sum of the adjacent angles are equal to 180oA trapezoid is nota parallelogramKite:The adjacent sides are equal, so it kites two pairs of equal sides. The diagonal angles is equal to 90oOne pair of opposite angle is equalThe diagonal is bisected by a longer diagonal

quadrilaterals pictures

New data!!!! Haircut costs

As we learn to represent and interpret our data, we collected the following data:
boys' haircut prices
12, 18, 22, 0, 0 ,0, 15, 0, 17, 16, 17.95, 10, 12
girls' haircut prices
35, 55, 50, 30, 18, 25, 0, 50, 40, 45, 45, 140, 40, 8, 25, 30, 22, 28

Represent each of these as a boxplot on the same axes AND
using the information starting on page 42 in the text, represent it also as a back to back stemplot.

We will interpret your results on Tuesday.

Be safe.
_________________________

8/20
We've used histograms, boxplots, and stemplots to represent univariate (one-dimensional) data. We've worked many problems from previous AP exams.

You're probably ready to close out this chapter (1). Let's focus on the parts we haven't covered so far and test on Thursday, 8/26.

We will start the CiCi's Sundays on August 29, unless you do not need help yet.

Be safe. Play hard. Go Trojans.

p hat statistics

Barry vs Emmitt

So Emmitt Smith is now in the Hall of Fame and the ongoing debate is once again brought to the surface. Who was better, Barry Sanders or Emmitt Smith? Recently at Mlive.com, I came across an article saying that Barry Sanders was the best to those who live in Kansas, Oklahoma, and Michigan. The fact is, Barry was the better of the two simply because he was better than Smith. No other reason!

So Smith holds the record with 18,355 yards in his career. So what? This means he had to play five more seasons than Sanders did to get a measly 3,086 yard more than Barry's 15,269. Let us continue to compare Emmitt's 15 years as a running back to Barry's 10 years. Emmitt! averaged 1,223.66 yards a season. Sanders averaged 1,526.90 yards. Receiving yards? Emmitt averaged 214.93 yards and Barry averaged 292.10 yards. With 5 more seasons than Barry, Emmitt never hit the 2,000 yard plateau, but Sanders did once. Both of them broke the 1,700 yard marker twice. In 15 seasons, Smith went over 1,400 yards 5 times. Sanders did it 7 times in only ten seasons. In fact, the only place Emmitt actually outshines Barry as a running back is in touchdowns. Emmitt averaged 10.9 rushing TDs a season. Sanders averaged 9.9 TDs. Only a one touchdown difference each season and Emmitt was o n a Superbowl caliber team and the Lions did not use Sanders in goal line situations out of fear he would get hurt.

What did Emmit Smith have to work with? Emmitt Smith always had one of the best offensive lines in the NFL in front of him. Go watch tape of Smith and you will often see him running through holes that Oprah could run through without being touched. Emmitt also had Troy Aikman and Michael Irvin keeping defenses honest.

What did Barry Sanders have to work with? Barry had QB's who were never known as special and one of the worst offensive lines in the NFL when he played. I cannot tell you how many times I have heard people try to say that the Lions line was pretty good then and they would st! ate how many yards Sanders got as proof. Let me make this clear folks. That is a line of pure unintelligent crap! I watched every game through Sanders entire career. I remember very well how bad that line was. People try to blame Sanders for the multiple one yard losses he had, but it was the fault of his offensive line. I cannot tell you how many times I screamed at that TV because Barry was being hit as he was taking the hand-off. Barry did not have a habit of dancing around when there was a hole to take. No, instead, Barry often had to find his own hole that to the normal eye did not exist. Every game you would hear the announcers exclaim how Sanders literally found a sliver of an opening in the line and got through it. Barry often had to make tacklers miss before he even reached the line of scrimmage.

Seriously, if there was ever a legitimate case in the NFL of a single player carrying a team on his back, it was Sanders. If there was ever a case of a runn! ing back who had to gain his yards on his own, it was Barry Sa! nders. H e had a terrible team around him, he had an awful offensive line and yet his numbers per season blows Emmits out of the water.

But Emmitt Smith won three Superbowls! Um, yeah. That's exactly my point! Emmitt had a great team around him. Barry had a bad team around him and still had better numbers than Emmitt.

I recently heard someone on 97.1 the Ticket saying he would rather have Emmitt because when it came to that one yard for a first down, you could count on Emmitt getting it and Barry would often lose a yard.! Again, unintelligent crap! Do you really think that if Barry's offensive line opened up a hole for him, that he would still lose the yard? Does anyone truly believe that Smith would have been dependable in short yardage if he was behind the Lions line? If someone was to say that they would rather have had the Cowboy's offensive line than the Lions line, I would say that was right spot on. There, you would have a case. But to give Smith all the credit for what his line did is ridiculous. To blame Sanders for his bad offensive line is ridiculous. If we could go back and switch the two players around, where Sanders played for the Cowboys and Smith played for the Lions, what do you think would happen? Do you still think that Smith would have three Superbowls? Without his great offensive line, I would not place money down that Smith would even win one rushing title in his career. Not if he had the Lions offensiv! e line blocking for him. What about Sanders? Seriously, if San! ders had the holes to run through that Smith always had, I would not doubt that he would have had at least two more 2,000 yard seasons.

The fact is, Emmitt Smith was a very good running back and maybe even a great one. But with a much more superior team and blocking line in front of him, he still did not out perform Barry Sanders who had a terrible line and team around him. There is just no way that anyone can argue that Emmitt Smith was a better running back and use any real stats to back his argument up. I'm sorry! You can love a player all you want, and that gives you the right to believe he is the best, but if you really want to argue it, then you need evidence, and the numbers back up Barry Sanders!

It is not because I am a Detroit Lions fan that I say this. Trust! me, I have no problem stating that other players are better than what we have had here in Detroit. The ONLY reason I will say that Barry Sanders might have been the best running back of all time and was absolutely head and shoulders better than Emmitt Smith, is because he did more than Smith with less around him.

offensive line hole numbers

Interview with Robert Farrar Capon

An amazing interview, from the website for something called the Chicago Sunday Evening Club (www.csec.org). You can also find a couple of his sermons on their site.

Interview with Robert Farrar Capon
Interviewed by
Floyd Brown

Floyd Brown: Here again is Robert Farrar Capon. I want to thank you for a fine presentation and also say that you are a very challenging man. I have difficulty with many of the things you said, just as you suggested. You told me that if we would follow the commandments everything would be worked out all right, but if we don't follow the commandments here, or anyway we haven't done it....I have got to have a script. You have got to give me a worksheet. What am I to do from day to day?

Robert Farrar Capon: Well, one of the problems with any authentic pronouncement of the gospel is that it introduces us to freedom. The point is that as long as the world runs this show what it tries to say is that if you do something wrong God will get you. What it said in Jesus is, by the blanket absolution of everybody in the death of Christ, that God is not going to get anybody.

For example, who is in heaven? People think it is good guys. There is nobody in heaven but forgiven sinners because th! ere was nobody available to go to heaven except forgiven sinners and there is nobody in hell except forgiven sinners. The difference is that in heaven they accept the forgiveness, in hell they reject it. That's it. You can't get into hell by being bad. You get into heaven by being bad and accepting forgiveness. Now, that does in a way mean you have permission to be bad. If you want to stick your hand in a meat grinder, you are free to do that. It's stupid, but God isn't going to run the universe that way. God is not going to punish. He cares more about relationships than behavior.

Brown: I think I understand philosophically what you are saying here, but it is still hard for us slow learners there in the back row. I! 've got to have a plan here. I know that if I go out a! nd I fig ht and I'm the kind of guy who causes disruptive things, I'm a threat to society. I do bad things and bad things result. I know that if repent of these things, God will forgive me, but if I don't ever repent of these things, what's going to happen?

Capon: He forgave you before you repented. That's crucial. See, that is why it is so outrageous. The gospel is really vulgar, crass and immoral because it says God forgives the world before it repents. In the gospel, repent is always repent and believe. It means turn yourself around from not trusting the forgiveness and trust it. That's it. It doesn't mean that you earn it by repenting. You had it before.

If you do something to me and you are wrong and I am right, you can repent all you want but until I forgive you, it's not going to do you a bit of good. It only helps when I have already forgiven you and you can enter into the restored relationship and turn again to me. Only I can decide to forgive you and God for His own idiot reasons decided to absolve the world. He really did. It's outrageous. It's immoral. It's tough.

Brown: It's outrageous, immoral and very difficult for many of us to comprehend at the level that you have, but I feel assured in listening to you here that I am forgiven and that there is a future for me in the better place because He is going to ! forgive me, but I have got to accept that only through H! im can I get this forgiveness.

Capon: That's the whole point.

Brown: But I've got to understand that we have got to love one another. We've got to follow the commandments if we are going to live together and have a good earth in which to enjoy.

Capon: That would work but that won't do the job. Only He can do the job.


least common denominator worksheet

C > Mathematics sample source codes(Volumes & Areas)

Volumes & Areas

/PROGRAM TO CALCULATE AREA,VOLUME,PERIMETER OF A PARTICULAR 
 GEOMETRIC SHAPE/

#include< stdio.h>
#include< conio.h>
#include< math.h>
#define PI 3.14159
char ch;
main()
 {

clrscr();

  textcolor(4);
  intro();
  getch();
  textcolor(7);
  clrscr();
  do
   {
      ch=menu();
    switch(ch)
     {
       case 'a':
       case 'A':
               clrscr();
               square();
               getch();
               break;
       case 'b':
       case 'B':
               clrscr();
               rect();
               getch();
               break;
       case 'c':
       case 'C':
               clrscr();
               circl();
               getch();
               break;
       case 'd':
       case 'D':
               clrscr();
               tri();
               getch();
               break;
       case 'e':
       case 'E':
               clrscr();
               rom();
               getch();
               break;
       case 'f':
       case 'F':
               clrscr();
               para();
               getch();
               break;

       case 'g':
       case 'G':
               clrscr();
               tra();
               getch();
               break;
       case 'h':
       case 'H':
               clrscr();
               qua();
               getch();
               break;
       case 'i':
       case 'I':
               clrscr();
               semicir();
               getch();
               break;
       case 'j':
       case 'J':
               clrscr();
               msector();
               getch();
               break;

       case 'k':
       case 'K':
                      clrscr();
              sphere();
              getch();
              break;
       case 'l':
       case 'L':
               clrscr();
               cone();
               getch();
               break;
       case 'm':
       case 'M':
               clrscr();
               cyll();
               getch();
               break;

       case 'n':
       case 'N':
               clrscr();
               cube();
               getch();
               break;
       case 'o':
       case 'O':
               clrscr();
               cuboid();
               getch();
               break;
       case 'p':
       case 'P':
               clrscr();
               hemisphe();
               getch();
               break;

       case 'q':
       case 'Q':
               exit(1);
     }
   } while(ch!='Q'||ch!='q');
      getch();
 }
  intro()
   {
     int i;
     clrscr();
     printf("



");
     textcolor(2);


cprintf("#################################################################
###############");
     textcolor(4);
     printf("



       PROGRAM TO CALCULATE AREAS , VOLUMES ,
CIRCUMFERENCES ");
     printf("
      
=====================================================
");
     printf("
               OF VARIOUS GEOMETRIC SHAPES");
     printf("
               ===========================

");
     textcolor(2);

cprintf("#################################################################
###############");
     getch();

     printf("





 Program developed and designed
by...

                ");
     printf("WWW");

   }
  menu()
   {
      clrscr();
      textcolor(7);
      printf("                 MENU
             Two Dimensional Shapes.
           
             -----------------------
           
             A.SQUARE
             B.RECTANGLE
           
             C.CIRCLE
             D.TRIANGLE
           
             E.RHOMBUS
             F.PARALLELOGRAM
           
             G.TRAPEZIUM
             H.QUADRILATERAL.
           
             I.SEMICERCLE
             J.SECTOR
");
      printf("
             Three Dimensional Shapes.
          
             -------------------------
          
             K.SPHERE
             L.CONE
             M.CYLLINDER
          
             N.CUBE
             O.CUBOID
             P.HEMISPHERE
          
             Q.QUIT
             Enter Your Choice :");
      scanf("%c",&ch);
     return(ch);
   }

           /*****   SUB FUNCTIONS  *****/
           /*****    2 D SHAPES    *****/

        square()
         {
           float s,a,p;int i,j;
           printf("
 Enter side of square:");
           scanf("%f",&s);
           a=s*s;
           p=4*s;
           printf("
     Perimeter of square  : %.3f units",p);
           printf("
     Area of square       : %.3f sq.units",a);
           printf("
 Square is ...
            ");
           for(i=1;i<=s;i++)
         {
           textcolor(10);
           for(j=1;j<=s;j++)
            cprintf("ÛÛ");
            printf("
            ");
          }
           return(0);
         }
        rect()
         {
          float a,p,l,b;   int i,j;
           printf("
 Enter length and breadth of rectangle:
Length:");
           scanf("%f",&l);
           printf("
Breadth:");
           scanf("%f",&b);
           a=l*b;
           p=2*(l+b);
           printf("
     Perimeter of rectangle  : %.3f units",p);
           printf("
     Area of rectangle       : %.3f sq.units",a);
           printf("
 Rectangle is...
        ");
           for(i=1;i<=b;i++)
         {
           textcolor(4);
           for(j=1;j<=l;j++)
            cprintf("ÛÛ");
            printf("
        ");
          }
           return(0);
         }
       tri()
        {
         float area,p;
         float a,b,c,s;
         printf("
Enter three sides of triangle:");
         scanf( "%f%f%f",&a,&b,&c);
         p=a+b+c;
         s=p/2;
         area=sqrt(s*(s-a)*(s-b)*(s-c));
         printf("
    Perimeter of triangle : %.3f units",p);
         printf("
    Area of a triangle    : %.3f sq.units",area);
        }
       rom()
        {
          float s,d1,d2,a,p;
          printf("
Enter side and diagonals of a rhombus:
Side:");
          scanf("%f",&s);
          printf("
Diagonal :");scanf("%f",&d1);
          printf("
Diagonal :");scanf("%f",&d2);
          a=0.5*d1*d2;
          p=4*s;
          printf("
    Perimeter of rhombus   :%.3f units",p);
          printf("
    Area of rhombus        :%.3f sq.units",a);
        }
       circl()
        {
         float r,a,p;
         printf("Enter radius of circle:");
         scanf("%f",&r);
         a=PI * r * r;
         p=2 * PI * r;
         printf("
    Circumference of circle : %.3f units",p);
         printf("
    Area of circle          : %.3f sq.units",a);
        }
       para()
        {
         float a,p,base,h,l,b;
         printf("Enter height,length,breadth of parallalogram :
" );
         printf("
Height :"); scanf("%f",&h);
         printf("
Base or Length :"); scanf("%f",&l);
         printf("
Breadth :"); scanf("%f",&b);
         base=l;
         a=base*h;
         p=2 * ( l + b );
         printf("
    Perimeter of parallalogram :%.3f units",p);
         printf("
    Area of parallogram        :%.3f sq.units",a);

        }


       tra()
        {
         float a,b,d,are;
         printf("Enter height and lengths of two parallel sides:
Height :");
         scanf("%f",&d);
         printf("Side:"); scanf("%f",&a);
         printf("Side:"); scanf("%f",&b);
         are=0.5 * d * (a+b);
         printf("
    Area of trapezium : %.3f sq.units",are);
        }
      qua()
       {
        float a,b,area,d;
        printf("Enter diagonal and perpendicular distances from opposite
vertices:
");
        printf("Diagonal :"); scanf("%f",&d);
        printf("
Distance :"); scanf("%f",&a);
        printf("
Distance :");scanf("%f",&b);
        area= 0.5 * d * (a + b);
        printf("
    Area of quadrilateral : %.3f sq.units", area);
       }
      semicir()
       {
         float a,p,r;
         printf("Enter radius of semicircle:");
         scanf("%f",&r);
         a=0.5* PI * r * r;
         p= (PI * r ) + (2 * r);
         printf("
    Circumference of semicircle : %.3f units",p);
         printf("
    Area of semicircle          : %.3f sq.units",a);
       }

      msector()
       {
         float x,r,temp,a,p;
         printf("Enter radius and angle of sector:");
         printf("
Radius :");
         scanf("%f",&r);
         printf("
Angle(in degrees) :");
         scanf("%f",&x);
         temp= x/360;
         a= temp * (PI * r * r);
         p= temp * (2 * PI * r);
         printf("
    Circumference of sector : %.3f units",p);
         printf("
    Area of sector          : %.3f sq.units",a);
       }

       /******** 3 DIMENSIONAL SHAPES  *********/

       sphere()
        {
          float lsa,tsa,v,r;
          printf("Enter radius of sphere :");
          scanf("%f",&r);
          tsa=4*PI*r*r;
          v=(4.0/3.0)*PI*r*r*r;
          printf("
    Total surface area of sphere   :%.3f sq.units",tsa);
          printf("
    Volume of sphere               :%.3f cu.units",v);
        }
       cone()
        {
         float h,r,s ,v,tsa,lsa;
         printf("Enter base radius ,height, slant height of cone :");
         printf("
Radius :"); scanf("%f",&r);
         printf("
Height :"); scanf("%f",&h);
         printf("
Slant height :"); scanf("%f",&s);
         tsa=PI * r *(s+r);
         lsa=PI * r * s;
         v=(PI * r * r * h)/3;
         printf("
    Total surface area of cone    :%.3f sq.units",tsa);
         printf("
    lateral surface area of cone  :%.3f sq.units",lsa);
         printf("
    Volume of cone                :%.3f cu.units",v);
        }
       cyll()
        {
           float lsa,tsa,v,r,h;
           printf("Enter height and radius of cyllinder");
           printf("Height :"); scanf("%f",&h);
           printf("Radius :"); scanf("%f",&r);
           lsa=2*PI*r*h;
           tsa=2*PI*r*(h+r);
           v=PI*r*r*h;
           printf("
    Total surface area of cyllinder  :%.3f sq.units",tsa);
           printf("
    Curved surface area of cyllinder :%.3f sq.units",lsa);
           printf("
    Volume of cyllinder              :%.3f cu.units",v);
        }
       cube()
        {
          float  lsa,tsa,v,s,d;
          printf("Enter side of cube :");
          scanf("%f",&s);
          d=s*sqrt(3);
          lsa=4 * s * s;
          tsa=6 * s * s;
          v= s * s * s;
          printf("
    Diagonal of cube              :%.3f units",d);
          printf("
    Total surface area of cube    :%.3f sq.units",tsa);
          printf("
    lateral surface area of cube  :%.3f sq.units",lsa);
          printf("
    Volume of cube                :%.3f cu.units",v);
        }
       cuboid()
        {
         float lsa,tsa,v,l,b,d,h;
         printf("Enter length,breadth,height of cuboid :");
         printf("
Length :");  scanf("%f",&l);
         printf("
Breadth :");  scanf("%f",&b);
         printf("
Height :");  scanf("%f",&h);
         d=sqrt(l*l + b*b + h*h );
         lsa =2 * h *( l+b );
         tsa = lsa + 2 * l * b;
         v=l*b*h;
         printf("
    Diagonal of cuboid              :%.3f units",d);
         printf("
    Total surface area of cuboid    :%.3f sq.units",tsa);
         printf("
    lateral surface area of cuboid  :%.3f sq.units",lsa);
         printf("
    Volume of cuboid                :%.3f cu.units",v);
        }
       hemisphe()
        {
             float lsa,tsa,v,r;
          printf("Enter radius of hemisphere :");
          scanf("%f",&r);
          tsa=3*PI*r*r;
          lsa=2*PI*r*r;
          v=(2.0/3.0)*PI*r*r*r;
          printf("
    Total surface area of hemisphere    :%.3f sq.units",tsa);
          printf("
    lateral surface area of hemisphere  :%.3f sq.units",lsa);
          printf("
    Volume of hemisphere                :%.3f cu.units",v);
        }

lateral surface area

The Edmonton Eulers Method

Hey everyone, it's MrSiwWy here as the scribe for March 18's class on Euler's method. I know I started this scribe post pretty late, but I just got home from the fashion show at school, which was definitely an enjoyable occasion. I really found this topic quite interesting, so I'll very much enjoy explaining his method as intricately as possible. Now with classes only every second day, I didn't think scribe duties would remain so frequent, though the class is indeed quite minuscule in comparison to the class size first semester. Oh yes, and before I begin, I think i must note that all explanations will be accompanied by an example furthering my explanation in a different text colour. Text in black will be initial explanations, while text in green will pertain to explanations using an example for the first part of the post and text in blue will pertain to explanations using an example for th! e second part of the post. Hope it works out well. Enjoy!

Scribe
~~~~~~

I can't remember exactly how class started, though I do recall it initiated with the usual abstract chatter and various technological utility exposures by Mr. K. But what I do remember, is beginning the actual lesson with a very fundamentally elegant and quite remarkable equation; Euler's identity.

Though we didn't go in depth into what Euler's identity is and how it was formulated, but we did vaguely discuss the implications of the identity. The sheer elegance of the equation derives from the fact that it contains and also intertwines the destiny of five of the most important constants in mathematics: 0, 1, (pi), i, and e. Euler's ident! ity is as follows:


Now we transitioned into the basis of the day's topic: Euler's method. I think it's quite a useful technique, and is a very innovative technique with easy implementation (at our level at least). We started off with a demonstration of Euler's method without any formal introduction quite yet. This demonstration can be found here. If you follow the link, it might ease the subsequent explanations tremendously.

- First off, imagine that you are given an initial value problem. Recall that an initial value problem is a problem! in which you are given a differential equation to solve as usual, but you are also given a point that exists on the parent function/solution to the differential equation.

*In this case, as used by the aforementioned demonstration, take the differential equation to be y'(t) = 1 - t + 4y(t) and the initial point to be y(0) = 1. This means that at t = 0, y(t) = 1. Following the above link will drastically clarify this example. Also, take note that we know the point (0,1) on the differential equation solution, and therefore have an exact solution and not just a general one. A general solution only represents the family of functions that could fit the solution for the differential equation. An exact one means that it's only specific function, and not a whole family.

- Now, there is an important idea that I must stress in order for Euler's method to be utilized easily, so pay attention in case you missed it ! in class. We must find a way to get another point on the pare! nt funct ion, which can be easily determined by plugging in the initial value/point into the differential equation to solve for the slope of the line tangent to the function at that point. Using this slope we can use our classic definition of slope to yield the next point that exists on the function y(t) given a certain step.

*The point (0,1) is known to lie on the function y(t), but how are we possibly going to get another point on this function? Well, as I stated earlier, since we know the differential equation, we can plug in the point (0,1) into the differential equation (which is y'(t) = 1 - t + 4y(t) in this case) and determine the slope of the line tangent to the function at that point. This is because the differential equation will solve for y'(t), which is the derivative of y(t) or rather the instantaneous rate of change of y(t) at a given t. This is particularly useful since using our rather classic definition of "slope" (rise over run) will yield our next point. By plugging in the initial point into the differential equation as follows, we can determine the required slope:

y'(0) = 1 - (0) + 4(1)
y'(0) = 5

Using this slope with the "old-school" rise over run definition of slope, we can easily determine the next point. But be careful, you must pay careful attention to the steps or the scale of each axis to correctly apply this definition. Since the steps we will be using in this case are 0.1, that means that instead of the function increasing upwards by 5 and increasing rightwards by 1, the function will i! ncrease upwards by 0.5 as it travels rightwards by 0.1. This ! means th at the next point will be (0.1, 1.5). Using the next button on the demonstration page will automatically graph the next point on the function.

- Now that we have two points on the graph, we can easily repeat the above process to determine any subsequent points and find an accurate portrayal of the solution. The only problem is that you must use a sufficient amount of steps by decreasing the amount of change along the x-axis (or in this case t) so that each point will be closer to each other and each subsequent derivative will be more accurate than with little points. I advise using this website or this website to help grasp this concept. Review one of t! hese sites to further your understanding of what I have just said. Also, concerning this idea, I tend to think of Euler's method as being quite similar to how an integral works. In an integral, you must let the dx values (or dt) get as close to 0 as possible, so as to increase how accurate the solution truly is or how well the integral fits the actual shape of the function. This is exactly how Euler's method works.

*Each time that you press the next button on the above demonstration, the graph will further the use of Euler's method and graph the next point on the parent function, thereby creating an appr! oximate graph of said function. But notice how choppy each se! gment lo oks, even though as a calculus student(and others =p) you should recognize the function to be curved.

Once we were introduced to Euler's method using a bevy of demonstrations and tools to ease the idea of his method to us, we were asked to apply what we had just learned to a problem. This can be seen on the following slide:


In the above slide, all that we really did was find a way (basically on our own) to efficiently repeat the process I detailed above. Though there were some alterations in this problem.

*Basically, when you were given the initial point, you could plug the point into the differential equation (which is y' = y - x this time) to find th! e deriva tive of the function at that point. This derivative will be m, or the slope of the tangent line at that point, which can be used by rearranging the m = Î"y/Î"x equation into Î"y = m * Î"x. Since m has just been calculated, and Î"x (which is the! step as I mentioned above) is given in the question as 0.25. Calculating Î"y will give us the change in y from the first point to the next point given a certain step, which means we'll know the next points x-coordinate (the first point x-coordinate plus the step) and y-coordinate (the first point's y-coordinate plus the Î"y calculated). Thus, this "next" point will be our "initial point" in the next part of the solution. If you use the above slide to help with understanding this idea, then each row will be one iteration of determining the solution to the differential equation. An iteration means a complete round of doing something, such as the process that is being repeated within a loop (which can be taken as the process I detailed above in the first detailed section of this scribe post).

But how can we make this process simpler and reduce the irksomeness of the entire process, especially for cases with a lot more repetitions? One way that we worked out during class involved using the store function in our calculators. This method can act! ually have several approaches, but basically you can utilize your calculator's store functions in many ways to achieve the same thing. Here's basically what you do:


- Store the initial y value into any variable in your calculator, say A.

- Input this variable into the differential equation on your calculator, and multiply this new expression by the step, and finally add A to this whole thing and store the new answer back into A. It might be hard at first to type this all in within one shot, but it is doable if you do it enough. Below is an example of how it should look in your calculator using the above question.

*Applying this step to the slide above, here's what it would look like in your calculator:
(((A - 0)0.25) + A) -> A

- Simply repeat this line using the [2nd] then [enter] function in your calculator, each time changing the x value according to how the point has changed.

*Again applying this step to the slide above, here's what the next line would look like:
(((A - 0.25)0.25) + A) -> A!

Using this meth! od yield ed the answers shown in the above slide, which could be taken as solved since the last point on the interval asked for (which was [0,1]) was determined, the question was answered. Though, Mr. K wrote down the exact answer to the problem at the bottom of the slide, which wasn't that close to the answer we arrived at.

So then we tried using more segments to approximate a sol! ution that is much closer than achieved above. We did this by using our new found method of numerically solving initial value problems with Euler's method, we attempted another problem. Though it may look quite empty, all of the work was quickly repeated on our calculators using a method roughly equivalent to the one above, and we all arrived at the same answers as shown in the following slide. I suggest trying it out on your own for some practice. (note: The question is basically the exact same as the first, but it uses far more segments and a much smaller step).


Just before class ended, Mr. K distributed the "EULER" calculator program for us to use to quickly solve problems involving Euler's method.


I will post the algorithms and full code for the program here when I get the full version again, since someone accidentally erased a line in the program and I can't remember what th! at line was.

Okay, that's all for my scribe for now! . I sti ll have some stuff to edit, but it's getting pretty late now and I don't want to be late for Chemistry again tomorrow (I bet people in Chem would doubt that). Anyway, the next scribe will be:
Tim-MATH-y!
Well good night everyone, see you all in class tomorrow! Please just talk to me or comment if there are any questions, complaints, anxieties, confusions, etc. =p Good bye all!

initial value problem calculator