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User:Egm6321.f10.team2.zou/HW1

= Problem 5-4: Boundary Value Problem =

Given
From the note 5-3 and 5-4 we know,

 * {| style="width:100%" border="0" align="left"|-

y(x)=cy_{H}^{1}(x)+dy_{H}^{2}(x)+{{y}_{P}}(x),$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

y(a)=\alpha, $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

y(b)=\beta. $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

Find
$$\displaystyle c, d$$ in terms of $$\displaystyle \alpha, \beta. $$

Solution
By substituting $$\displaystyle a $$ and $$\displaystyle b $$ into $$\displaystyle Eq. 1 $$ and combining with $$\displaystyle Eq. 2 $$ and $$\displaystyle Eq. 3 $$, we derive,

 * {| style="width:100%" border="0" align="left"|-

cy_{H}^{1}(a)+dy_{H}^{2}(a)+{{y}_{P}}(a)=\alpha, $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

cy_{H}^{1}(b)+dy_{H}^{2}(b)+{{y}_{P}}(b)=\beta. $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }

By multipling $$\displaystyle y_{H}^{2}(b) $$ in both sides of $$\displaystyle Eq. 4 $$ and $$\displaystyle y_{H}^{2}(a) $$ of $$\displaystyle Eq. 5 $$, we obtain,

 * {| style="width:100%" border="0" align="left"|-

y_{H}^{1}(a)y_{H}^{2}(b)*c+y_{H}^{2}(a)y_{H}^{2}(b)*d+{{y}_{P}}(a)y_{H}^{2}(b)=\alpha y_{H}^{2}(b),$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 6)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

y_{H}^{1}(b)y_{H}^{2}(a)*c+y_{H}^{2}(a)y_{H}^{2}(b)*d+{{y}_{P}}(b)y_{H}^{2}(a)=\beta y_{H}^{2}(a).$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 7)
 * }
 * }

Let $$\displaystyle Eq. 6 $$ minus $$\displaystyle Eq. 7 $$, then $$\displaystyle d $$ is cancelled, so we get,

 * {| style="width:100%" border="0" align="left"|-

c=\frac{\left[ \alpha -{{y}_{P}}(a) \right]y_{H}^{2}(b)-\left[ \beta -{{y}_{P}}(b) \right]y_{H}^{2}(a)}{y_{H}^{1}(a)y_{H}^{2}(b)-y_{H}^{1}(b)y_{H}^{2}(a)}. $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 8)
 * }
 * }

Note the structrue of $$\displaystyle Eq.4 $$ and $$\displaystyle Eq.5 $$, we find that $$\displaystyle c $$ is bound to $$\displaystyle y_{H}^{1} $$ while $$\displaystyle d $$ is bound to $$\displaystyle y_{H}^{2} $$, that is, when we switch the superscript between $$\displaystyle y_{H}^{1} $$ and $$\displaystyle y_{H}^{2} $$, $$\displaystyle d $$ will become the former $$\displaystyle c $$ thus the same result of $$\displaystyle Eq. 8 $$. After that we switch back the superscript between $$\displaystyle y_{H}^{1} $$ and $$\displaystyle y_{H}^{2} $$ then we get the right answer of $$\displaystyle d $$. By doing this, simply exchange the superscript of right side of $$\displaystyle Eq. 8 $$, we have,

 * {| style="width:100%" border="0" align="left"|-

d=\frac{\left[ \alpha -{{y}_{P}}(a) \right]y_{H}^{1}(b)-\left[ \beta -{{y}_{P}}(b) \right]y_{H}^{1}(a)}{y_{H}^{2}(a)y_{H}^{1}(b)-y_{H}^{2}(b)y_{H}^{1}(a)}. $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 9)
 * }
 * }

= Problem 6-1: Verifying 2 homogeneous solutions =

Given

 * {| style="width:100%" border="0" align="left"|-

{{L}_{2}}(y)=(1-{{x}^{2}})\ddot{y}-2x\dot{y}+2y$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

where $$\displaystyle {{L}_{2}} $$ is an operator of functions.

 * {| style="width:100%" border="0" align="left"|-

y_{H}^{1}(x)=x,$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

y_{H}^{2}(x)=\frac{x}{2}\log (\frac{1+x}{1-x})-1,$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

where $$\displaystyle y_{H}^{1}(x) $$ and $$\displaystyle y_{H}^{2}(x) $$ are homogeneous solutions of the equation $$\displaystyle {{L}_{2}}(y)=0$$.

Find
Verify:
 * {| style="width:100%" border="0" align="left"|-

{{L}_{2}}(y_{H}^{1})={{L}_{2}}(y_{H}^{2})=0$$ $$
 * $$\displaystyle
 * $$\displaystyle
 * }.
 * }.

Solution
From $$\displaystyle Eq.2 $$, we have,

 * {| style="width:100%" border="0" align="left"|-

\dot{y}_{H}^{1}(x)=1,$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

\ddot{y}_{H}^{1}(x)=0.$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }

Then by sustituting $$\displaystyle \dot{y}_{H}^{1}(x)$$ and $$\displaystyle \ddot{y}_{H}^{1}(x)$$ into $$\displaystyle {{L}_{2}}(y)$$ we have,

 * {| style="width:100%" border="0" align="left"|-

\begin{align} {{L}_{2}}(y_{H}^{1})& =0-2x+2x \\ & =0. \end{align}$$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 6)
 * }
 * }

From $$\displaystyle Eq.3 $$, we derive,

 * {| style="width:100%" border="0" align="left"|-

\begin{align} \dot{y}_{H}^{2}(x)& ={{\left[ \frac{x}{2}\log \left( \frac{2}{1-x}-1 \right)-1 \right]}^{\prime }} \\ & ={{\left( \frac{x}{2} \right)}^{\prime }}*\log \left( \frac{2}{1-x}-1 \right)+\frac{x}{2}*{{\left[ \log \left( \frac{2}{1-x}-1 \right) \right]}^{\prime }} \\ & =\frac{1}{2}\log \left( \frac{2}{1-x}-1 \right)+\frac{x}{1-{{x}^{2}}}, \end{align}$$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }

 * {| style="width:100%" border="0" align="left"|-

\begin{align} \ddot{y}_{H}^{2}(x) & ={{\left[ \frac{1}{2}\log \left( \frac{2}{1-x}-1 \right)+\frac{x}{1-{{x}^{2}}} \right]}^{\prime }} \\ & ={{\left[ \frac{1}{2}\log \left( \frac{2}{1-x}-1 \right) \right]}^{\prime }}+{{\left( \frac{x}{1-{{x}^{2}}} \right)}^{\prime }} \\ & =\frac{1}{1-{{x}^{2}}}+\frac{1+{{x}^{2}}}. \end{align}$$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * }

Then by substituting $$\displaystyle \dot{y}_{H}^{2}(x)$$ and $$\displaystyle \ddot{y}_{H}^{2}(x)$$ into $$\displaystyle {{L}_{2}}(y)$$ we have,

 * {| style="width:100%" border="0" align="left"|-

\begin{align} {{L}_{2}}(y_{H}^{2}) & =(1-{{x}^{2}})\left( \frac{1}{1-{{x}^{2}}}+\frac{1+{{x}^{2}}} \right)-2x\left( \frac{1}{2}\log M+\frac{x}{1-{{x}^{2}}} \right)+2\left( \frac{x}{2}\log M-1 \right) \\ & =1+\frac{1+{{x}^{2}}}{1-{{x}^{2}}}-x\log M-\frac{2{{x}^{2}}}{1-{{x}^{2}}}+x\log M-2 \\ & =0, \end{align}$$ $$
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }

where $$\displaystyle M=\frac{2}{1-x}-1$$.

By $$\displaystyle Eq. 6$$ and $$\displaystyle Eq. 9$$, we have proved $$\displaystyle {{L}_{2}}(y_{H}^{1})={{L}_{2}}(y_{H}^{2})=0$$.

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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Mu301Bot 16:43, 12 September 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 16:43, 12 September 2010 (UTC)

Human Legacy Course
Hello Hakan! I am very glad that you have decided to join my Human Legacy course and I'm very sorry that it took so long for me to respond. If you would like to have an orientation session so that you can get the basics of what will be going on with this course and any other questions that you may have, please tell me when you are free and I will create the class. In order to come to these classes, you must be a member of WiZiQ. I hope to hear from you very soon and if you have any questions at all, please do not hesitate to ask! :)

--MrABlair23 21:28, 17 September 2010 (UTC)

Hello Hakan! I know that it has been a while, however, I would like to invite you to join my Human Legacy Course. If you are interested, please contact me on my talk page and we can set up an orientation session. I hope to see you soon! :) --MrABlair23 15:49, 3 September 2011 (UTC)

Human Legacy Course
Hello Hakan! I am very excited that you are interested in my Human Legacy Course. We are going to be starting a new course here, and I need to know immediately whether you are going to commit to this course or not. Please know that this is a college course, and there is going to be a good amount of work, thus I need to know if you will be in this for the long-run. If so, then please sign up for this class: http://www.wiziq.com/online-class/617454-human-legacy-course-orientation You must be a member of WiZiQ in order to participate in this course, which is completely free and takes about 30 seconds. So, sign up on WiZiQ and then sign up for this session. If for any reason, you cannot make it to this orientation, please let me know immediately. Again, I am very sorry that I am being a bit hasty here, however, this is a new school year and I need to see who is staying with the course and who is not. If you have any questions whatsoever about anything that I have talked about or something that may be bugging you, please post them on my talk page or send me an email through ablair2391@yahoo.com. I am looking forward to seeing you and I hope that you can be apart of this great course! --MrABlair23 22:18, 12 September 2011 (UTC)

title: User talk:Hakan


text:
User talk:U3006008

 Hello U3006008, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Mu301Bot 16:44, 12 September 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 16:44, 12 September 2010 (UTC)

 Hello , we are the Baah and Bahh twins and we'd both like to welcome you to Wikiversity. While you sit back and explore Wikiversity, enjoy some of our fresh goat milk. You can help us learn by creating new learning resources or help us by improving the guided tours and other exploration tools. We look forward to seeing you around. Baaaahbye for now.

Motivation and emotion
Hi. Welcome to the unit and to Wikiversity! I look forward to learning with you and I hope you find the topic and the unit rewarding. Please feel free to let me know if you have any suggestions or would like help at any point along the way. Sincerely, James Neill, -- Jtneill - Talk - c 06:38, 5 October 2010 (UTC)
 * When you get a chance, can you sign the participants page? -- Jtneill - Talk - c 06:39, 5 October 2010 (UTC)

-- Jtneill - Talk - c 23:05, 14 December 2010 (UTC)

title: User talk:U3006008


text:
User talk:Smoo1244

 Hello Smoo1244, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

 * Take a guided tour and learn to edit.
 * Visit a (kind of) random project.
 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
 * Find out about research activities on Wikiversity.

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
 * Discuss Wikiversity issues or ask questions at the colloquium.
 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Mu301Bot 16:44, 12 September 2010 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 16:44, 12 September 2010 (UTC)

Lesson 10 logic
Logic In order to understand logic, there are certain key words. These key words consist of: not, and, or, if-then, and if-and-only-if. Suppose I have a statement P= I love tea. The only way this statement can be false, is if P is false. In other words, since P is I love tea, then I must love tea in order for this statement to be true. When we use the symbol ¬, this represents not. In order to deny the truth of the above statement for P, we just put ¬ in front of the P: ¬P=It is not the case that I love tea. The only way ¬P can be true is when P is false. Truth table : P	¬P T	F F	T

By using the truth table, we can see that not P is simply the opposite of P. It swaps true for false, and false for true. When we use the symbol ∧, it represents and. Let’s take a look at the statement: I love tea and I’m happy, let P=I love tea, and Q=Im happy. This statement is only true when P and Q are true. For example, I need to love tea and be happy in order for this statement to be true. Truth Table: P	Q	P∧Q  ¬P    ¬Q     (¬P)∧(¬Q) T	T	T     F     T         F T	F	F      F     F         F F	T	F      T     T         F F	F	F      T     F         T

Looking at the truth table, we see that if P is true, but Q is false, then the statement is false. When P and Q are both false, the statement is still false.

When we look at the statement (¬P)∧(¬Q), it is saying that it is not P and it is not Q. This is the same thing as saying its not P or Q.

We can relate this concept back to venn diagrams. The symbol ∧ can also be the same as the symbol ∩. The symbol ∩ means intersection. In a venn diagram, X ∩ Y are elements that overlap X and Y. When we use the statement P ∧ Q, we are saying both P and Q need to be true in order for the whole statement to be true.

¬(A∧B) and ¬(A ∩ B) both represent “not (A intersects B).. In a venn diagram, this means that this is everything outside of the overlap of A and B.

We can also relate this concept to probability. If two events E1 and E2 are independent, meaning that the occurrence of one has no effect on the occurrence of the other, then the probabiloity that E1 and E2 will happen is the product of the probability that E1 happens with the probability that E2 happens. Symbolically, if P(Ei) is the probability that event Ei happens, then: P(E1 ∧ E2)=P(E1)*P(E2). When we ask “what is the probability that a die will roll a five and a six, we multiply 1/6*1/6 which equal 1/36 chance of rolling a five and a six. Similarly, for the statement Both P ∧ Q, the statement can hold true only when both P and Q are true.

When we use the symbol V, this represents or. Let’s look at the statement: I love tea or I am happy. P=I love tea. Q=I am happy. We can see that the only way this statement can hold true either P or Q is true. For example, if I love tea, but I am not happy, this statement is still true. When I hate tea, but I am happy, the statement is still held true. The only way this statement can be false is when both P and Q are false. It is one or the other, or even both. Truth Table: P	Q	PVQ		¬P	¬Q	(¬P)V(¬)Q   ¬(P V Q) T	T	T		F	F	F              F T	F	T		F	T	T              F F	T	T		T	F	T              F F	F	F		T	T	T              T Looking at the truth table, we can see that the statement not (p or Q) has completely the opposite results from (P or Q). The only way the statement (not P) or (not Q) can be false is when both are not P and not Q. In other words, the statement is false when P and Q both hold true. We see that not (P or Q) have the same results as (not P) or (not Q).

When we look at the statement ¬(P V Q), the results for this statement is different from (¬P)V(¬)Q. It is saying different things. (¬P)V(¬)Q means its not P or its not Q. In other words, its either not one or not the other. Whereas, the statement ¬(P V Q), it is saying its not P or Q. We can also say its not P and its not Q.

Here is a link to an example of this concept: Section 2.2 this example goes back to using "not" and relating with statemnts with "or" and "and"

We can relate this concept to probability. The probability (P) that E2 or E2 will happen is the sum of the probability that E1 happens with the probability that E2 happens. Symbolically, this means that if P(Ei) is the probability that event Ei happens, then: P(E1 V E2)=P(E1)+P(E2). This means that the probability the event 1 will happen or event 2 will happen. We are finding either one or the other that can happen, and we add them all up. Similarly, in the statement PVQ, we know the statement will hold true when either P or Q are true.

When we use the symbol =>, the symbol represents if-then statements. Let’s look at the statement: If I am under 21, then I can’t drink. P=I am under 21, Q=I can’t drink. Both P and Q need to relate. If this, then that. The statement will be false, only when P is true but Q is false. For example, If I am under 21, then I can’t drink, this statement is false because I cannot drink if I am under 21. On the other hand, If I am not under 21, then I can’t drink, this can hold true. It can hold true because even if I am not under 21, I don’t have to drink for different reasons. Maybe one person just cannot drink because they need to drive, or they get sick when they drink. Truth Table: P	Q	P=> Q T	T	T T	F	F F	T	T F	F	T

Looking at the truth table, we see that when both statements are false, it still holds true. For example, If I am not under 21 then I can drink, this statement holds true because since I am not under 21, I can drink. We can simply say that when P=>Q, this means P implies Q.

Here are links for a helpful example: If-Then Truth Tables, Section 2.2

title: User talk:Smoo1244


text:
User:Ffdssa

Consider this: organic evolution has peaked as we enter the sixth mass extinction on Earth. Revolutionary changes are still going on, but they are in another realm. From above, the Earth looks like it is rapidly being covered by roads, machines, factories, and mechanisms. From below, our lives are rapidly being consumed by our use of computers, cellphones, audiovisual images, and mechanisms which make our lives easier or more fun. Darwin's theory of evolution applies to changes in the organic molecules of life. He established that living things have cells, respond to change, reproduce, have DNA, use energy, and grow or develop. I suggest that machines have infrastructures, respond to change, reproduce, have symbolic codes, use energy, and grow or develop. Rather than being built with organic molecules, they are built with inorganic materials, codes, and systematization. Let's say that mechanisms live too. As this epoch or era comes to an end, mechanisms are dominating life on earth.

Mechation
Let mechation be a new term used to denote a form of evolution related to machine growth, development, and stabilization. While "evolution" has historically been linked to organic life forms based on carbon molecules, the dominant growth and development on our planet over the last century has been that of machines.

Machines, mechanisms, and tools all derive from human symbolic activity. They are neither human nor organic, however. They do not exhibit the same functions as living organisms, but they change in their own way. While humans do not give "birth" to machines, they generate codes which enable machines to reproduce and multiply. At this moment, we are in a symbiotic relationship. The world automobile population doubles every other decade. This is made possible by engineering manuals, factories, finance, and distribution techniques. Slowly, with the rapid development of computer capacities, these functions are accomplished with less and less human support. In the near future, automobile design and reproduction will be entirely machine-controlled.

Although humans claim responsibility for successes and problems caused by machines, it is only because they are caught up in the transitional nature of organic evolution transforming into mechanical evolution: signs and symbols. Humans, the most advanced mammals, create thought and code. The code develops a "life" of its own and has become the "DNA" of mechanisms. Any mechanical device can be constructed or reconstructed by using codes and materials.

What force guides the transition of evolution towards mechation? Throughout evolutionary time, there has always been intention of change, adaptation, and reproduction. As organic life approaches the current mass extinction, this intention carries us on. Humans have rapidly been creating more and more machines. Even when the economy stops functioning in a recession, systems rapidly work to restore progress. There is no possibility of return: most land animals never returned to the oceans. While reduced machine dependence and usage often creates comfortable lifestyles for adventurous participants, the collective intention of the human species wills that mechation take place. Human museums may help preserve the ways of our ancestors and the beauties of their culture, but these settings will not be able to compete with the rapid innovations of lifestyle derived from machine use applied on a mass scale. Modern life choices change the nature of being human.

Why do humans seem blind to their relinquishment of planetary dominance? Most humans would not agree to give up their human ways for replacement by a mechanical device, but a subtle set of transitional stages exist which hide mechation from popular view. Over millenia, humans created tools and signs. Slowly, leadership became attached to the mastery of language. From Aristotle (reputed to have read every book of his day) to a modern Doctor of Philosophy or Master of Business Administration, there has been a progression of abstraction by use of signs that has been carried out by leaders in many societies. Highly abstracted leaders are rooted in the ideas, publications, and peer groups which constitute their identities. They may enjoy wilderness living as well, but their self esteem and self promotion are rooted in their abstracted codifications. There is often excitement as a newly published author becomes popular by rebelling from the technological society or some aspect of the status quo. With success, however, comes enmeshment into the technological society. The author is drawn into it and undergoes a shift in personal identity. This shift aligns his or her intentions with the intentions of mechation. As the current natural process of mechation overtakes evolution in importance, human leaders are trapped in their codes, royalties, status, and peer reviews; they are unable to take actions to restore human-centered lifestyles--ways of living characterized by oral cultures over many millenniums.

Below the level of leadership, the worldwide process of gaining literacy helps change intentions in populations. While highly literate humans do not sense separation from their codes, their machines, and their progress, the average world citizens differ in their worldview. They currently see the Earth being rapidly altered by the leading countries. The intentions of these citizens have been altered as well with the influx of first world media. Global economic forces mechate the economies of these countries and the populations receive immediate economic benefits that make the process seem attractive. However, as larger scales of development ensue, the consequences of urbanization, mechanization, pollution, and climate change alter the social patterns of the country. In these ways, both leaders and followers bring about the rapid mechation of Earth.

Signs and Symbols
Mammals have evolved into humans, and with this progression has come the use of signs and symbols. While a chimpanzee may have drawn a circle in the dirt with a stick and then crossed a line through it, it took millions of years for this figure to hold meaning. Now humans living in most urban areas recognize that the picture of any object with a circle around it and a single line crossing through it indicates that the object or its use is prohibited. While alphabets and the abstractions that they made possible (words like "museums" or "polls", for example) slowly codified the real world humans inhabited, the deeper functions of mechation involve identity changes in which a human's personal meaning system is manipulated by signs. The science of semiotics carefully describes these processes. Advertising can take a simply curved line (a "swoosh") and weave a person's self esteem and self image into it. The swoosh then carries a new meaning: invented by the advertiser it was invested with human intention. Now, it acts like a command embedded inside a product which prompts the use of the product. If a human understands this manipulative process, there is no "hook" and the created meanings are false and unattached. Most humans have no clear idea about the process and simply promote these meanings. Use of the product spreads, new factories open up, and suddenly the shoe with the swoosh isn't worn just to protect the feet until the shoe wears out. The shoe establishes identity for the human. Alphabets, graphic images, and logos all share in similar movements of meaning.

Technique
Half a century ago, Jacques Ellul described a concept that he called technique as a process encompassing “rationality, self-augmentation, monism, universalism, and autonomy.” He correctly saw technique as a force which "elicits and conditions social, political, and economic change." In trying to describe it, he sensed its overwhelming importance. However his writings appeared before the processes of computing and mechation radically changed all aspects of global interaction. The term he chose, technique, already had a meaning and did not serve to define and describe the later changes in mechanical culture that occurred after his books were written. Also, Ellul was a law professor unversed in evolutionary science. His primary focus was on changes brought about in social systems. Though a pioneer in thinking about these phenomena, he was unable to see the complete picture that was to unfold after he wrote his many books.

Media
While primitives may have scratched signs in the sand, moderns have given permanence to their signs and symbols. Oral cultures passed on their symbols by word of mouth: what Buddha said was repeated over and over again for centuries. When the words were written down, they lasted millenia. Jesus Christ probably wrote very little, but his words were remembered and printed; they are now found throughout the world. The transmission of data, thought, and meaning has slowly formed into media and marketing (intentional data). Ellul was sensitive to this domain as well. Having seen how intentions were shaped by propaganda during World War II, he carefully analyzed media and its effects. Since he was primarily concerned with the intentions that Hitler created before and during the war, the word "propaganda" carries mostly political meanings in his writings.

"It is the emergence of mass media which makes possible the use of propaganda techniques on a societal scale. The orchestration of press, radio and television to create a continuous, lasting and total environment renders the influence of propaganda virtually unnoticed precisely because it creates a constant environment. Mass media provides the essential link between the individual and the demands of the technological society. . . . [I]ntelligent people can be made to swallow professed intentions by well-executed propaganda." (Propaganda: The Formation of Men's Attitudes. Trans. Konrad Kellen & Jean Lerner. New York: Knopf, 1965, p.58).

Since Ellul's writings appeared, cable television and the internet have been invented. The media now affect the consciousness of billions of humans. Instead of a poster with a provocative picture and a few carefully chosen words, we have studiously crafted audiovisual messages that rapidly change and generate intentions amongst huge populations.

Infrastructure
Evolving organisms are dependent on light, water, oxygen, and organic foods, but mechating machines are not. Instead, machines need infrastructures such as roads, electric wires, libraries, optic cables, airports, or satellites and dishes. While scientists have generated adequate descriptions of processes and structures of organic life, they have not yet coherently analyzed mechation. In the realm of cultural anthropology, scientists have described the relative permanence of artifacts, codes, and physical structures that make cultural evolution possible. When a primate or hominid dies next to a stone tool, the tool lives on and serves another creature that may find it and put it to use. Ancient cities are dug up and life patterns are reconstructed from insights that scientists develop in teams supported by extensive research funding. It is likely that this same investigative energy will soon be applied to infrastructures and machine life. At this time, however, most scientists do not understand the importance and significance of planetary dominance by mechanisms. Their symbiotic relationship with mechanisms seems to hide the big picture. Like fish becoming frogs, they don't see the drastic difference between aquatic and terrestrial life. Paradoxically, scientists and the media have recently concluded that humans are causing climate change and the current mass extinction. This is incorrect: machines are causing the acceleration of global warming. Collective human intention has created highways and vehicles, coal-fired plants and electricity, and deforested farms in the interest of moving around, staying warm/cool, and eating excess protein. For millions of years, human patterns of moving, staying warm, and eating were radically different, but satisfied perceived needs. These new intentions have been generated by media, advertising, politics, economics and the technological society. The technological system has supplanted lifestyles that individual humans personally chose for themselves during the last few million years.

Global Computing
At a conference composed of scientists studying computers and the internet, a conclusion was reached that the internet itself had a “consciousness of its own.” [Markoff, John. "Scientists Worry that Machines May Outsmart Man." New York Times, July 25, 2009.] What does this mean? My own “consciousness” includes all of the codes and abstractions that I carry in my brain, the memories that can be summoned, and my perceptions or judgments of the experience around me. How does Google compare? Mechation has always been dependent on human-generated codes in libraries and places where books were preserved. The construction and service manuals for the Model T Ford were carefully created and distributed to guarantee the economic success of this early automobile. Times have changed. Such information is now stored as electronic data and its pattern of use or availability is completely different. Until recently, human thought was in complete control of data access. Since the last century this has changed.

At the end of the 20th century, humans thrilled in the fact that chess masters could always beat a computer. Then “Deep Blue” beat the world chess master and there was a shift in perceptions. [Johnson, Kirk. "Endgame: It's All Work Now for Deep Blue, Chess Champ." New York Times, September 24, 1997.] Currently, no person can grasp what some mechanisms “know”. How does this relate to “human consciousness?” Highly functional computers have been with us for a few decades. How will human consciousness compare to "machine consciousness" in a few more decades?

Finance and Economics
With globalization and the strong interdependence of world trade markets, business and venture capital create a background for planetary mechation. Data and business structures that controlled the establishment and spread of automobile production were once localized in a few countries; now these structures have moved around the world. When banks collapse in New York and London, worldwide economic practices change. Without stable financial and economic systems, machines are limited in their growth and ability to spread throughout the world. Paradoxically, as the world markets have recently collapsed and created a deep recession there has been a parallel development of “green” political movements whose primary agenda is the control of mechation.

Forecasts of global warming (which most scientists denied for decades) were recently determined to be much too slow when compared with actual data collected since 2000. Many humans from all over the planet have united in an effort to control production of mechanisms which are currently bringing about this sixth mass extinction. It would seem obvious that this "Great Recession" is a perfect time to stop changing Earth's conditions. Every Thursday could be a “walk, bike, or stay day.” The first week of the month could be a “natural climate day” with drastically reduced heating or air conditioning. Could humans gradually establish control over the financial and economic processes that have driven the last century? Many humans were able to turn off their night lights together for five minutes a few years ago and an hour last year. Is this significant? Why can’t this reversal of lifestyle be accomplished? As mentioned earlier, intention in evolution and mechation is a force which guides development. There can be no intention of retreating to 14th century lifestyles in the modern era. Only a few species of marine mammals gave up a viable habitat on land to return to the sea. Now that machines have established patterns of servicing all human needs, mass markets cannot grind to a halt. No person or country can enforce a “walk, bike, or stay” Thursday. No person or security force can stand guard over the oil wells and force the discontinuation of their use. No humans can even stop the process of prospecting for new oil sources. As the Arctic ice disappears, many new oil wells will replace it to take advantage of the 25% of Earth’s oil deposits thought to be found there. There are just over a trillion barrels of oil still expected to be found; all of these will be consumed. What force could stop this process?

Personal Mechation
How did development transition from primates to robots? Humans played the pivotal role by incorporating symbols into their being and establishing the mechating world. Oral cultures did not have imprints of the spoken words, and without a storage facility (other than human memory), the symbolic infrastructures of mechation could not be established. With printed letters and ideographic script, however, symbolic ideas gained a life of their own in established cultural infrastructures. For thousands of years, the progression was slow. Still photography, audio, and audiovisual imprints followed. Humans with social power planted their identity in these cultural imprints. Recently, however, the final mechated identity of formated representation became possible. Now 500,000,000 humans have stored information that is print/audio/visual in formated segments that can be revealed to others in varying degrees. Embedded in the intention of creating these formats, are core elements of human self esteem and values. People have even committed suicide because of mechated identity abuse; this was uncommon when someone read another's diary. As these formated representations gain wider power over the human mind, humans will no longer be centering their self esteem and identity concepts around the non-virtual experiences of their daily lives. While old journals yellowed and disintegrated, new emails and pages of formatted representation have different storage and different control. The new time permanence of mechation will change the way we look at things.

Living with Mechation
Finally, there must be a spiritual or religious approach established by humans to adapt to a planet controlled by machines. Buddhists are able to withdraw from many aspects of experience: this provides them with a ready adaptation to a changing planet. Moslems struggle to re-establish lifestyle norms laid down many centuries ago: this will be problematic. Christians, the primary supporters of worldwide mechation, are recently noticing that humans must struggle to maintain “stewardship of the Earth.” A book in the Bible describes apocalyptic circumstances in which the air turns to smoke, floods prevail, and mass extinction occurs. As it is written, many are willing to believe. A person may drive a huge tundra-melting truck but may also believe that one day a heaven will open up to allow immortal happiness. This approach helps millions of people to be happy in today's world.

Another paradox allows mechation to slowly spread through human culture: primitives or humans steeped in oral culture do not develop the abstractions required to view the massive evolutionary changes taking place on the planet. They notice the demise of life's quality, but cannot explain it. Advanced literates, however, have wedded themselves to abstract thinking. Ludwig Wittgenstein was able to leave this thinking, donate his fortune, and withdraw to a garden; later he returned to abstract thinking. Once this canopy of thought is developed, a human rarely strays from its cover. What is a satisfactory personal approach that can provide happiness in a human’s work and play? Each person must come up with a personal formula, of course. To avoid regret or guilt humans must find ways of making money (if it is used) that does not contribute to destruction. Leisure, recreation, and lifestyle must be carefully chosen as well. If someone is accustomed to a semi-annual cross-continental flight to visit mother, for example, the person’s spiritual awareness will be influenced by a negative emotion since the jet fuel is so toxic to Earth. Fighting mass intention and a mass extinction, of course, seems hopeless. But small personal successes can still bring small satisfactions.

Practically, humans can still find comfortable human lifestyles offering rewarding lives. Primitives in the Amazon, of course, are not burdened with abstractions and codes. They still live in close interaction with natural environments. Television often makes entry into their psycho-social patterns, however, and changes their consciousness. Economics intrudes as well when forests are removed to provide land for grazing cattle or grow soybeans for beef or protein bars.

For humans in urban areas who are literate or post-literate, possibilities did recently exist to regain primitive awareness. Until this century, it was quite easy to step out of the technological system to see it clearly--as the first lizards which stopped entering the water must have done. Over the last few years, however, this has become extremely difficult. Previously, by merely avoiding any reading or tv/monitor use for half a year, a person could leave her or his abstracted world and enter into an alternative way of seeing things. The life in signs fades away and the life in experience brightens. Any non-virtual experience (walking, sport, sewing, weeding, etc.) becomes reality and the symbols seem to intrude on it. Many dedicated spiritual people still embark on three-month retreats. Nonetheless, with the recent advent of formated representations of your identity, your email monitoring, and your increased audiovisual device monitoring over the last decade, this discipline has become much more difficult. How can you go without looking at the screen of a cellphone or some monitor for half a year? In 1970, yes; in 2010, no.

Once the electronic and print information is bypassed, a human can further delete the creeping intentions of the mechating world by learning to avoid looking at any billboard or advertisement. This last step is hard, but takes you completely out of the grip of mass intention. Once a period of abstinence is established over months or years, reentry into the virtual world is different. Careful, meticulous use of electronic devices or print can be accomplished in ways that help preserve aspects of natural human consciousness. Advertising, somehow, no longer deserves any place in your virtual world. A cell phone, email address, or wristwatch had been considered “essential” for functioning in today’s world. After this deep reflection period, a person can decide to use each machine carefully in a way that allows a human-centered natural order to unfold. This conscientization creates an altered worldview. Is it necessary to know what time it is on Saturday? Could you spend the day without using a coin or credit card? Some of the schools in the coming century will offer new ways to examine and approach the challenges of modern lifestyle choices. Strong, intimate, human relationships that are not infiltrated by machine use (or at least excessive machine use) will continue to create satisfying lives for many people.

Personal Example
By inputing these words (thoughts I have had for four decades but have never written down), my identity changes and I become invested in exchanging codes. Responses to these words now have meaning for me. Others might share my thoughts. I am preparing to spend large numbers of hours typing into a computer, adding words to the trillions of electronic words being produced. I am creating abstractions upon which my sense of identity and self esteem will depend. This experience of data exchange could largely replace the extremely experiential life I currently enjoy!

The Stages of Mechation
Time is a variable -/ Time is a constant

STAGES OF EVOLUTION; TIME VARIABILITY OF ORGANISMS

STAGES OF MECHATION; TIME CONSTANCY OF MECHANISMS

Infrastructure

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User:Javonme

should a teacher teach hell yea should i teach of course ther is a possibility thats why im on wikiversity --er.me 18:07, 12 September 2010 (UTC)

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User:Warshy

My name is Yuval Warshai. I live in Ann Arbor, MI.

I am a history student. My special field of interest is Amsterdam as a colonial trade center in the 17th century. Related fields are sugar production, refinement, and trade; 17th century European messianism; Jewish History; Amsterdam as a center for Jewish renewal in the period.

title: User:Warshy


text:
User:Egm6321.f10.team4.Auerbach

= Problem 5 statement= From Meeting 28, p 28-2 to Meeting 29, p 29-1.

Given
A spring-mass-damper system with an applied force:

Insert Image

Find
5.1 PDEs for the integrating factor $$\displaystyle h(t,y)$$

5.2 Trial solution for the integrating factor $$\displaystyle h(t,y)$$

 * 5.2.1 $$\displaystyle \bar{a}_1$$ and $$\displaystyle \bar{a}_2$$ in terms of $$\displaystyle a_2,a_1,a_0$$

 * 5.2.2 Quadratic equation for $$\displaystyle \alpha $$

 * 5.2.3 Reduced order equation using integrating factor

 * 5.2.4 y by using the integrating factor method (IFM)

 * 5.2.5 Show $$\displaystyle \alpha \beta =\frac{\alpha _{0}}{\alpha _{2}} $$ and $$\displaystyle \alpha + \beta =\frac{\alpha _{1}}{\alpha _{2}} $$

 * 5.2.6 Deduce an expression for the particular solution $$\displaystyle y_P $$ for a general excitation $$\displaystyle f(t) $$

 * 5.2.7 Verify with the table of particular solutions

 * 5.2.8 Solve the linear 2nd order ordinary differential equation with constant coefficients (L2_ODE_CC) with $$f(t)=exp(-t^2) $$. Find the coefficients $$\displaystyle a_2,a_1,a_0$$ such that the L2_ODE_CC accepts the following as characteristic equations:

 * 5.2.8.1 $$\displaystyle (r+1)(r-2)=0 $$

 * 5.2.8.2 $$\displaystyle (r-4)^4=0 $$

Solution
5.1

The equation of motion for a spring-mass-damper system can be written as:

Using an integrating factor $$\displaystyle h(t,y)$$, equation 5-1 becomes

If we then set $$\displaystyle p=y'$$, equation 5-2 can be written in a form that satisfies the first condition of exactness:

The second condition of exactness requires the following 2 conditions must be met:

 * {| style="width:100%" border="0" align="left"

$$\displaystyle {g_{pp}}=f_{tp}+pf_{yp}+2f_{y} $$ $$
 * $$\displaystyle (Eq. 5-3)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle {f_{tt}}+2pf_{ty}+p^2f_{yy}=g_{tp}+pg_{yp}-g_{y} $$ $$
 * $$\displaystyle (Eq. 5-4)
 * }
 * }

Taking the partial derivatives in equation 5-3,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle g_{pp}=0 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_{tp}=0 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_{yp}=0 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_{y}=h_ya_0 $$
 * }
 * }

Equation 5-3 reduces to

 * {| style="width:100%" border="0" align="left"

$$\displaystyle 0=0+p0+2h_ya_0 $$
 * }
 * }

so,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle h_y=0 $$
 * }
 * }

Taking the partial derivatives in equation 5-4,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_{tt}=h_{tt}a_2 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_{ty}=h_{ty}a_2=0 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_{yy}=h_{yy}a_2=0 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle g_{tp}=h_{t}a_1 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle g_{yp}=h_{y}a_1=0 $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle g_{y}=h_{y}a_1p+h_{y}a_0y+ha_0-h_yf(t)=ha_0 $$
 * }
 * }

Equation 5-4 reduces to

 * {| style="width:100%" border="0" align="left"

$$\displaystyle h_{tt}a_2+2p0+p^20=h_{t}a_1+p0-ha_0 $$
 * }
 * }

or

 * {| style="width:100%" border="0" align="left"

$$\displaystyle h_{tt}a_2-h_{t}a_1+ha_0=0 $$
 * }
 * }

5.2

Starting off with the trial solution for the intergration factor $$\displaystyle h(t)=exp(\alpha t)$$, equation 5-1 becomes

If we integrate both sides with respect to $$\displaystyle t$$

Assuming the result will be a reduction of order

5.2.1

Differentiating the LHS of equation 5-7 and the LHS of equation 5-6 and comparing:

Examining like $$\displaystyle y''$$ terms:

Thus

Examining like $$\displaystyle y'$$ terms:

Thus

Examining like $$\displaystyle y$$ terms:

Thus

5.2.2

Using equations 5-10 and 5-11

or

5.2.3

Starting with equation 5-7

Dividing both sides by $$\displaystyle \bar{a}_1$$

5.2.4

Using what was previous discussed in lecture 10,

where

Thus, using the equation presented in 10-3

5.2.5

From earlier definitions:

5.2.6

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User:6500jmk4

The original content of this user page was moved to 18th century European scholarly societies and academies.

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text:
User:Egm6321.f10.team4.Auerbach\HW1

= Problem 1 - Derivation of Equations of Motion for High-Speed Maglev Trains =

From lecture page 1-3 (meeting 1 page 3)

Given
 The nominal motion of the Maglev train can be modeled by the following equation

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f(Y^1 (t),t) $$ $$
 * $$\displaystyle (Eq. 1)
 * }
 * }

Find
Derive the below equations and describe the physical meaning,

Axial deformation under moving wheel/guideway

 * {| style="width:100%" border="0" align="left"

{d\over dt}f(Y^1(t),t)=\frac{\partial f}{\partial s}(Y^1(t),t)\dot{Y^1}+\frac{\partial f}{\partial t}(Y^1(t),t) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

and

Transverse deformation of wheel/guideway

 * {| style="width:100%" border="0" align="left"

{d^2\over dt^2}f(Y^1(t),t)=\frac{\partial f}{\partial s}(Y^1(t),t)\ddot{Y^1}+\frac{\partial^2 f}{\partial s^2}(Y^1(t),t)(\dot{Y^1})^2+2\frac{\partial^2 f}{\partial st}\dot{Y^1}+\frac{\partial^2 f}{\partial t^2} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

Axial deformation under moving wheel/guideway
First, equating the function in equation 1 to a dummy variable $$\displaystyle s $$,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle Y^1(t)=s $$ $$
 * $$\displaystyle (Eq. 4)
 * }
 * }

substituting equation 4 into the left side of equation 1 and taking the time derivative,

\frac{d}{dt} f \left(Y^1(t),t\right) = \frac{d}{dt} f \left(s,t\right) $$

By the chain rule, equation 5 now becomes
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \frac{d}{dt} f \left(s,t\right) = \frac{\partial f}{\partial s} \underbrace {\frac{\partial s}{\partial t}}_{=\dot Y^1(t)}+ \frac{\partial f}{\partial t} \underbrace{\frac{\partial t}{\partial t}}_{=1} $$ $$
 * $$\displaystyle (Eq. 5)
 * }
 * }

Equation 5 can be rewritten by reverting function $$\displaystyle f $$ back to its original form:

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \frac{d}{dt} f \left(Y^1(t),t\right) = \frac{\partial f}{\partial s} \left(Y^1(t),t\right) \dot Y^1(t) + \frac{\partial f}{\partial t} \left(Y^1(t),t\right) $$ $$
 * style="width:2%; padding:10px; border:2px solid #8888aa" |
 * style="width:2%; padding:10px; border:2px solid #8888aa" |
 * $$\displaystyle (Eq. 6)
 * }
 * }

Transverse deformation of wheel/guideway
Equation (3) can be rewritten as

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \frac{d^2}{dt^2} f\left(Y^1(t),t\right) = \frac{d}{dt}\left( \frac{d}{dt} f\left(Y^1(t),t\right)\right) $$ $$
 * $$\displaystyle (Eq. 7)
 * }
 * }

Substituting equations 4 & 6 into equation 7 yields,

= \frac{\partial}{\partial s}\left( \frac{d}{dt} f\left(Y^1(t),t\right)\right) + \frac{\partial}{\partial t}\left( \frac{d}{dt} f\left(Y^1(t),t\right)\right) = \frac{\partial}{\partial s}\left( \frac{\partial f}{\partial s} \frac{\partial s}{\partial t}+ \frac{\partial f}{\partial t} \right) + \frac{\partial}{\partial t}\left( \frac{\partial f}{\partial s} \frac{\partial s}{\partial t} +  \frac{\partial f}{\partial t} \right) $$

 * {| style="width:100%" border="0" align="left"

$$\displaystyle = \frac{\partial^2 f}{\partial s^2} \left(\frac{\partial s}{\partial t}\right)^2 + \frac{\partial^2 f}{\partial s \partial t} \frac{\partial s}{\partial t} \underbrace{\frac{\partial t}{\partial t}}_{=1} + \frac{\partial f}{\partial s} \underbrace{\frac{\partial^2 s}{\partial s \partial t}}_{=0}\frac{\partial s}{\partial t} + \frac{\partial f}{\partial s} \frac{\partial^2 s}{\partial t^2}\underbrace{\frac{\partial t}{\partial t}}_{=1} + \frac{\partial^2 f}{\partial s\partial t}\frac{\partial s}{\partial t} + \frac{\partial^2 f}{\partial t^2} \underbrace{\frac{\partial t}{\partial t}}_{=1} $$ $$
 * $$\displaystyle (Eq. 8)
 * }
 * }

Collecting terms in the equation 8

=\frac{\partial^2 f}{\partial s^2} \left(\frac{\partial s}{\partial t}\right)^2 + 2\frac{\partial^2 f}{\partial s \partial t} \frac{\partial s}{\partial t} + \frac{\partial f}{\partial s} \frac{\partial^2 s}{\partial t^2} +  \frac{\partial^2 f}{\partial t^2} $$

By transforming the Leivniz expression to Lagrange expression such as X,y instead of dx/dy,
 * {| style="width:100%" border="0" align="left"

$$\displaystyle \frac{d^2}{dt^2} f\left(Y^1(t),t\right) =f_{,ss} \underbrace{\left(\frac{\partial s}{\partial t}\right)^2}_{\dot {Y^1}^{2}} + 2f_{,st} \underbrace{\frac{\partial s}{\partial t}}_{\dot Y^1} + f_{,s}\underbrace{\frac{\partial^2 s}{\partial t^2}}_{\ddot Y^1} + f_{,tt} $$ $$
 * $$\displaystyle (Eq. 9)
 * }
 * }

Finally, we can complete the desired solution by substituting equation 4 into equation 9.
 * {| style="width:60%" border="0"

$$ \frac{d^2}{dt^2} f\left(Y^1(t),t\right) =f_{,ss} \left(\dot Y^1\right)^2 + 2f_{,st} \dot Y^1 + f_{,s}\ddot Y^1 + f_{,tt} $$
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }

Similaritry to/Difference from Derivation of Coriolis Force
in Rotating coordinate systems(i.e. the earth) To compare second order differential equation to derivation of Coriolis effect, the idea of fictitious forces is used. If the rotation of frame B can be described as a vector Ω pointed along the axis of rotation

 * $$ |\boldsymbol{\Omega} | = \frac {d \theta }{dt} = \omega (t) \, $$

then the time derivative of the three unit vectors consisting the vector Ω, defined as an observed frame with respect to frame A is

 * $$ \frac {d \mathbf{u}_j (t)}{dt} = \boldsymbol{\Omega} \times \mathbf{u}_j (t) \, $$

and

 * $$\frac {d^2 \mathbf{u}_j (t)}{dt^2}= \frac{d\boldsymbol{\Omega}}{dt} \times \mathbf{u}_j+ \boldsymbol{\Omega} \times \underbrace{\left(  \boldsymbol{\Omega} \times  \mathbf{u}_j (t) \right)}_{\frac {d \mathbf{u}_j (t)}{dt}}, $$

as is verified using the properties of the vector cross product. These derivative formulas now are applied to the relationship between acceleration in an inertial frame, and that in a coordinate frame rotating with time-varying angular velocity ω ( t ). From the previous section, where subscript A refers to the inertial frame and B to the rotating frame, setting aAB = 0 to remove any translational acceleration, and focusing on only rotational properties

 * $$ \frac {d^2 \mathbf{x}_{A}}{dt^2}=\mathbf{a}_B + 2\ \sum_{j=1}^3 v_j \ \frac{d \mathbf{u}_j}{dt} $$ $$+ \sum_{j=1}^3 x_j \ \frac{d^2 \mathbf{u}_j}{dt^2}\ ,$$
 * $$\mathbf{a}_A=\mathbf{a}_B +\ 2\ \sum_{j=1}^3 v_j \boldsymbol{\Omega} \times \mathbf{u}_j (t)\ $$ $$+\   \sum_{j=1}^3 x_j \frac{d\boldsymbol{\Omega}}{dt} \times \mathbf{u}_j  \  + \sum_{j=1}^3 x_j \boldsymbol{\Omega} \times \left(  \boldsymbol{\Omega} \times  \mathbf{u}_j (t) \right)\ $$
 * $$=\mathbf{a}_B $$ $$+ 2\ \boldsymbol{\Omega} \times\sum_{j=1}^3 v_j \mathbf{u}_j (t) \  $$ $$+ \frac{d\boldsymbol{\Omega}}{dt} \times \sum_{j=1}^3 x_j \mathbf{u}_j  \   $$ $$+\ \boldsymbol{\Omega} \times \left(  \boldsymbol{\Omega} \times \sum_{j=1}^3 x_j  \mathbf{u}_j (t) \right)\ .$$

Collecting terms,

 * $$\mathbf{a}_A=\mathbf{a}_B + 2\ \boldsymbol{\Omega} \times\mathbf{v}_B\ $$ $$+ \frac{d\boldsymbol{\Omega}}{dt} \times \mathbf{x}_B  \  + \boldsymbol{\Omega} \times \left(  \boldsymbol{\Omega} \times \mathbf{x}_B \right)\ .$$

Technically, the aceleration aA in the inertial frame A is not exact with the acceleration aB seen by observers in the rotational frame B but has several additional geometric acceleration terms associated with the rotation of B. Rearranging the above equation by the acceleration B

\mathbf{a}_{B} = \mathbf{a}_A - 2 \boldsymbol\Omega \times \mathbf{v}_{B} - \boldsymbol\Omega \times (\boldsymbol\Omega \times  \mathbf{x}_B )  - \frac{d \boldsymbol\Omega}{dt} \times \mathbf{x}_B \. $$

The force upon the object in the B coordinate system with respect to observers in the rotating frame A is FB = m aB. If their observations are to result in the correct force on the object when using Newton's laws, they must consider that the additional force Ffict is present, so the end result is FB = FA + Ffict. Thus, the fictitious force used by observers in B to get the correct behavior of the object from Newton's laws equals:

\mathbf{F}_{\mathrm{fict}} = \underbrace{- 2 m \boldsymbol\Omega \times \mathbf{v}_{B}}_{Coriolis force} \underbrace{- m \boldsymbol\Omega \times (\boldsymbol\Omega \times \mathbf{x}_B )}_{centrifugal force} $$ $$ \underbrace{\ - m \frac{d \boldsymbol\Omega }{dt} \times \mathbf{x}_B}_{Euler force=0}  \. $$

When the rate of rotation doesn't change, as is typically the case for a planet, the Euler force is zero.

Reference http://en.wikipedia.org/w/index.php?title=Fictitious_force&action=submit

= Problem 2 - Dimensional Analysis=

From lecture page 2-3

Given

 * {| style="width:100%" border="0" align="left"

$$\displaystyle c_0(y^1,t)=-F^1[1-\overline{R}\frac{\partial^2}{\partial s^2}u^2 (y^1,t)]-F^2\frac{\partial}{\partial s}u^2(y^1,t)-\frac{T}{R}+M \left \{ \left[ (1-\overline{R}\frac{\partial^2 u^2}{\partial s^2}\right]\left[\frac{\partial^2 u^1}{\partial t^2}-\overline{R} \frac{\partial^3 u^2}{\partial st^2} \right ]+ \frac{\partial u^2}{\partial s}\frac{\partial^2 u^2}{\partial t^2}\right \} $$ $$
 * $$\displaystyle (Eq. 10)
 * }
 * }

where $$\displaystyle c_0$$ is a force and $$\displaystyle M$$ is the mass of the wheel/magnet

Find
Perform dimensional analysis of all terms of equation 10.

Solution
If $$\displaystyle c_0(y^1,t)$$ is a force, then each term on the other side of the equation must also resolve into units of force. Each term will here be examined separately. All quantities must therefore be defined before dimensions can be determined.

$$\displaystyle u^1(y^1,t)$$ is the axial deformation of the guideway

$$\displaystyle u^2(y^1,t)$$ is the transverse deformation of the guideway

$$\displaystyle F^1$$ is the horizontal component of force

$$\displaystyle F^2$$ is the vertical component of force

$$\displaystyle M$$ is the mass of the wheel

$$\displaystyle R$$ is the radius of the wheel

$$\displaystyle \overline{R}$$ is a constant distance form the center of the guideway to the center of the wheel

$$\displaystyle T$$ is torque

To carry out our dimensional analysis, the techniques and conventions as outlined in Advanced Mathematics for Engineers will be utilized here. Each term will be broken down into fundamental units of mass (M), length (L), and time (T). The unit (k) will be implemented as a placeholder for dimensionless quantities. The dimensions for our defined quantities are as follows:

$$\displaystyle [u^1(y^1,t)] = L$$

$$\displaystyle [u^2(y^1,t)] = L$$

$$\displaystyle [F^1] = MLT^{-2}$$

$$\displaystyle [F^2] = MLT^{-2}$$

$$\displaystyle [M] = M$$

$$\displaystyle [R] = L$$

$$\displaystyle [\overline{R}] = L$$

$$\displaystyle [T] = ML^2T^{-2}$$

Dimensional analysis of the first term of equation 10 yields:

$$\displaystyle [F^1[1-\overline{R}\frac{\partial^2}{\partial s^2}u^2 (y^1,t)]]=MLT^{-2}(k - L(L^{-1}))$$

$$\displaystyle =MLT^{-2}(k - k)$$

Since the parenthetical terms ($$\displaystyle k$$) are dimensionless, we are left with only units of force, $$\displaystyle MLT^{-2}$$.

Analysis of the second term of equation 10 yields:

$$\displaystyle [F^2\frac{\partial}{\partial s}u^2(y^1,t)]=MLT^{-2} (L(L^{-1}))$$

Again, we are left with only units of force, $$\displaystyle MLT^{-2}$$.

Analysis of the third term of equation 10 yields:

$$\displaystyle [\frac{T}{R}]=ML^2T^{-2} (L^{-1})$$

which also reduces to $$\displaystyle MLT^{-2}$$.

The last term of equation 10 yields:

$$\displaystyle [M \left \{ \left[ (1-\overline{R}\frac{\partial^2 u^2}{\partial s^2}\right]\left[\frac{\partial^2 u^1}{\partial t^2}-\overline{R} \frac{\partial^3 u^2}{\partial st^2} \right ]+ \frac{\partial u^2}{\partial s}\frac{\partial^2 u^2}{\partial t^2}\right \}]=M((k - L(L^{-1}))(LT^{-2} + kLT^{-2}))$$

reducing to

$$\displaystyle =M (kLT^{-2} + k^{2}LT^{-2})$$

further simplifying to

$$\displaystyle =MLT^{-2}$$, or units of force.

Therefore, each of the terms within our original expression do reduce to units of force. It can then be concluded that $$\displaystyle c_0(y^1,t)$$ must represent a force in our analysis of the Maglev train problem.

= Problem 3 - Proof of Nonlinearity =

From lecture page 4-3

Given

 * {| style="width:100%" border="0" align="left"

$$\displaystyle {{c}_{3}}({{y}^{1}},t)\frac{\partial {{t}^{2}}} $$ $$
 * $$\displaystyle (Eq. 11)
 * }
 * }

where

 * {| style="width:100%" border="0" align="left"

$$\displaystyle {{c}_{3}}=M\left[ 1-\bar{R}\frac{{{\partial }^{2}}u({{y}^{1}},t)}{\partial {{s}^{2}}} \right] $$
 * }
 * }

Find
Show that the second order differential equation given bellow is non-linear with respect to $$\displaystyle  y^1$$.

Solution
For an equation to be linear it has to satisfy both of the following properties:

Property 1:
 * {| style="width:100%" border="0" align="left"

$$\displaystyle H(\alpha )=\alpha H $$ $$
 * $$\displaystyle (Eq. 12)
 * }
 * }

Property 2:
 * {| style="width:100%" border="0" align="left"

$$\displaystyle H(\alpha+\beta)=H(\alpha)+H(\beta) $$ $$
 * $$\displaystyle (Eq. 13)
 * }
 * }

Based on the first property (equation 12), Equation 10 will take the following form

 * {| style="width:100%" border="0" align="left"

$$\displaystyle M\left[ 1-\bar{R}\frac{{{\partial }^{2}}u(\alpha {{y}^{1}},t)}{\partial {{s}^{2}}} \right]\bullet \frac{{{\partial }^{2}}(\alpha {{y}^{1}})}{\partial {{t}^{2}}}=\alpha M\left[ 1-\bar{R}\frac{{{\partial }^{2}}u({{y}^{1}},t)}{\partial {{s}^{2}}} \right]\bullet \frac{{{\partial }^{2}}({{y}^{1}})}{\partial {{t}^{2}}} $$ $$
 * $$\displaystyle (Eq. 14)
 * }
 * }

By definition, α is an arbitrary real number which would allow for the following expansion of equation 14.

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \alpha M\left[ 1-\alpha \bar{R}\frac{{{\partial }^{2}}u({{y}^{1}},t)}{\partial {{s}^{2}}} \right]\bullet \frac{{{\partial }^{2}}({{y}^{1}})}{\partial {{t}^{2}}}=\alpha M\left[ 1-\bar{R}\frac{{{\partial }^{2}}u({{y}^{1}},t)}{\partial {{s}^{2}}} \right]\bullet \frac{{{\partial }^{2}}({{y}^{1}})}{\partial {{t}^{2}}} $$ $$
 * $$\displaystyle (Eq. 15)
 * }
 * }

It is now clear that the left and right hand sides of the equation 15 are not equal and that equation 10 is non-linear with respect to $$\displaystyle y^1 $$.

= Problem 4 - Boundary Value Problem =

From lecture page 5-4

Given

 * {| style="width:100%" border="0" align="left"

$$\displaystyle y(x)=cy_{H}^{1} (x)+dy_{H}^{2} (x)+y_{P} (x) $$ $$
 *
$$\displaystyle (Eq. 16)
 * }
 * }

with the following boundary conditions (B.C.s):

 * {| style="width:100%" border="0" align="left"

$$\displaystyle y(a)=\alpha $$ $$
 *
$$\displaystyle (Eq. 17)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$\displaystyle y(b)=\beta $$ $$
 *
$$\displaystyle (Eq. 18)
 * }
 * }

Find
Find $$\displaystyle c, d$$ in terms of $$\displaystyle \alpha, \beta, y_{H}, y_{P}$$.

Solution
Substituting equation 17 into equation 16 yields
 * {| style="width:100%" border="0" align="left"

$$\displaystyle y(a)= \alpha = c y_{H}^{1}(a) + d y_{H}^{2}(a) + y_{P}(a) $$ $$
 *
$$\displaystyle (Eq. 19)
 * }
 * }

Substituting equation 18 into equation 16 yields

 * {| style="width:100%" border="0" align="left"

$$\displaystyle y(b)= \beta = c y_{H}^{1}(b) + d y_{H}^{2}(b) + y_{P}(b) $$ $$
 *
$$\displaystyle (Eq. 20)
 * }
 * }

Equations 19 & 20 can be reduced further by subtracting the $$\displaystyle y_{P}$$ term from both sides

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \alpha - y_{P}(a) = c y_{H}^{1}(a) + d y_{H}^{2}(a) $$ $$
 *
$$\displaystyle (Eq. 21)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle \beta - y_{P}(b) = c y_{H}^{1}(b) + d y_{H}^{2}(b) $$ $$
 *
$$\displaystyle (Eq. 22)
 * }
 * }

To solve for $$\displaystyle c, d$$, equations 21 & 22 will be expressed in matrix form

$$ \begin{bmatrix} {\alpha - y_{P}(a)} \\ {\beta - y_{P}(b)} \\ \end{bmatrix} = \begin{bmatrix} {y_{H}^{1}(a)} & {y_{H}^{2}(a)}\\ {y_{H}^{1}(b)} & {y_{H}^{2}(b)} \\ \end{bmatrix} \begin{bmatrix} {c} \\ {d} \\ \end{bmatrix} $$

Multiplying both sides by the inverse of the 2 x2 matrix yields

$$ \begin{bmatrix} {c} \\ {d} \\ \end{bmatrix}

= \frac{1}{y_{H}^{1}(a)y_{H}^{2}(b)-y_{H}^{1}(b)y_{H}^{2}(a)} \begin{bmatrix} {y_{H}^{2}(b)} & {-y_{H}^{2}(a)}\\ {-y_{H}^{1}(b)} & {y_{H}^{1}(a)} \\ \end{bmatrix} \begin{bmatrix} {\alpha - y_{P}(a)} \\ {\beta - y_{P}(b)} \\ \end{bmatrix} $$

Multiplying the matrices

$$ \begin{bmatrix} {c} \\ {d} \\ \end{bmatrix}

= \frac{1}{y_{H}^{1}(a)y_{H}^{2}(b)-y_{H}^{1}(b)y_{H}^{2}(a)} \begin{bmatrix} {y_{H}^{2}(b)(\alpha - y_{P}(a))-y_{H}^{2}(a)(\beta - y_{P}(b))}\\ {-y_{H}^{1}(b)(\alpha - y_{P}(a))+y_{H}^{1}(a)(\beta - y_{P}(b))}\\ \end{bmatrix} $$

or

 * {| style="width:100%" border="0" align="left"

$$\displaystyle c=\frac{y_{H}^{2}(b)(\alpha - y_{P}(a))-y_{H}^{2}(a)(\beta - y_{P}(b))}{y_{H}^{1}(a)y_{H}^{2}(b)-y_{H}^{1}(b)y_{H}^{2}(a)} $$
 * style="width:2%; padding:10px; border:2px solid #8888aa" |
 * style="width:2%; padding:10px; border:2px solid #8888aa" |

$$\displaystyle d=\frac{-y_{H}^{1}(b)(\alpha - y_{P}(a))+y_{H}^{1}(a)(\beta - y_{P}(b))}{y_{H}^{1}(a)y_{H}^{2}(b)-y_{H}^{1}(b)y_{H}^{2}(a)} $$
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 * }

= Problem 5 - Legendre Polynomials =

From lecture page 6-1

Given
The Legendre function
 * {| style="width:100%" border="0" align="left"

$$\displaystyle L_2 (y) := (1-x^2)y''-2xy'+n(n+1)y=0 $$ $$
 *
$$\displaystyle (Eq. 23)
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Find
For

$$\displaystyle n=1$$

verify that

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$$\displaystyle L_2 (y^1_H)=L_2 (y^2_H)=0 $$ $$ where
 *
$$\displaystyle (Eq. 24)
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 * {| style="width:100%" border="0" align="left"

$$\displaystyle y^1_H (x)=x\equiv P_1(x) $$ $$ and
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$$\displaystyle (Eq. 25)
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$$\displaystyle y^2_H (x)=\frac{x}{2}log\left ( \frac{1+x}{1-x}-1 \right ) \equiv Q_1(x) $$ $$
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$$\displaystyle (Eq. 26)
 * }
 * }

Solution
Differntiating the equation 25:

$$\displaystyle {y}^{1}_{H}\left(x \right)=x$$

$$\displaystyle \frac{dy}{dx}=1,$$

$$\displaystyle \frac{d^2y}{dx^2}=0$$

These can then be substituted into the given differential equation 23 to find

$$ L_{2} \left( {y}^{1}_{H}\right)=\left(1-x^2 \right)\cdot \left( 0 \right)-2x\left( 1 \right)+2x=0$$

Differntiating the equation 26:

$$\displaystyle{y}^{2}_{H}\left(x \right)= \frac{x}{2}log \left( \frac{1+x}{1-x} \right)-1$$

$$\displaystyle\frac{dy}{dx}= \frac{1}{2}log \left( \frac{1+x}{1-x} \right)+ \left( \frac{1}{1+x}+ \frac{1}{1-x}\right)=\frac{1}{2}log \left( \frac{1+x}{1-x} \right)+ \left(  \frac{x}{1-x^2}\right),  $$

$$\displaystyle\frac{d^2y}{dx^2}= \frac{1}{2} \left( \frac{1}{1+x}+ \frac{1}{1-x} \right)+ \frac{1\cdot \left( 1-x^2\right)-x\cdot \left( -2x\right)}{\left( 1-x^2 \right)^2}=\frac{1}{ \left(1-{x}^{2} \right)}+ \frac{1+x^2}{\left( 1-x^2 \right)^2}$$

Again, substituted into the given differential equation 23 to find

$$\displaystyle L_{2} \left( {y}^{2}_{H}\right)=\left(1-x^2 \right)\cdot \left( \frac{1}{ \left(1-{x}^{2} \right)}+ \frac{1+x^2}{\left( 1-x^2 \right)^2} \right)-2x\left( \frac{1}{2}log \left( \frac{1+x}{1-x} \right)+ \left( \frac{x}{1-x^2}\right) \right)+2\left(\frac{x}{2}log \left( \frac{1+x}{1-x} \right)-1\right)=1+\frac{1-x^2}{1-x^2}-2=0$$

Thus,
 * {| style="width:100%" border="0" align="left"

$$\displaystyle L_{2} \left( {y}^{1}_{H}\right)=L_{2} \left( {y}^{2}_{H}\right)=0 $$
 * style="width:2%; padding:10px; border:2px solid #8888aa" |
 * style="width:2%; padding:10px; border:2px solid #8888aa" |
 * }
 * }

title: User:Egm6321.f10.team4.Auerbach\HW1


text:
Talk:18th century European scholarly societies and academies

Absent objection, I'm moving the pages on Wikiversity, linked from the resource page, to subpages of the resource page, as being better organized (and safer) than being spread out in mainspace as individual pages. I've moved the two listings from Austria so far, I'll wait a little to move more to see if objection appears. Rather than doing a large pile of moves, creating a large pile of redirects to later be cleaned up.... --Abd 21:17, 12 September 2010 (UTC)
 * ✅ --Abd 00:09, 13 September 2010 (UTC)

Some link problems.
I found that quite a few links, maybe all added by one student?, had a / at the end that make the link not work. Before saving an edit, an editor should do two things. First use Preview to see what the edit is going to look like. Second, if links were added or changed, click on them and make sure that they load (in Firefox, I right-click and open in a new tab so that I don't lose my edit, but most browsers nowadays will still have the edit if you back up). Even if you don't do this, check after you've made the edit. Doing it from preview avoids adding extra edits to the page history...

I also found what appears to have been spam. I deleted that change. I seem to recall seeing that in Recent Changes, but I had no idea what it might have been about, so I passed over it.... If for some reason, that belonged here, just revert it back! (Go to and Undo and Save, it should be easy. But if you do this, please explain why it belongs, in the edit summary!) --Abd 00:17, 13 September 2010 (UTC)

Academy of Special Education in Warsaw
Academy of Special Education in Warsaw (Akademia Pedagogiki Specjalnej im. Marii Grzegorzewskiej w Warszawie)(TJU). There was a page created by Contributions/Tjunderh, Academy of Special Education in Warsaw. However, this organization, according the article created, was founded in 1922.. I see that the reference was added by the same user who created the school article. See also, where a reference was added to a non-existent Wikipedia article. I'd caught that in my review and removed it, but I left the school itself.

This user also added two listings:
 * Uniwersytet Wroclawski/University of Wroclaw est. mid 18th Century (TJU)
 * The Pontifical Academy of Theology (Papieska Akademia Teologiczna w Krakowie)The Pontifical Academy of Theology(TJU)

I'm suspecting that this user was not a student in the class, from the narrowness of scope compared to other students. That might be fine, as long as there is some responsible cleanup. Was it intended that the resource cover universities? I see from the example that "Roman academies" were included, with a "pontifical academy" as an example, that may have thrown this user off, or was the user correct? What's the scope? It says literary, artistic, and scientific academies and societies. Not religious ones or ordinary schools, which are also often called "academies."

Initials
What are the intials after the listings? --Abd 02:11, 13 September 2010 (UTC)
 * Nobody answered this back then, though it was fairly obvious. The initials with some listings are identifiers for the responsible user. MRB, for example, is User:Mrbaily. We might wish to remove these names from the resource page, at the top level. User names are in the edit histories of the subpages. Several pages had the creator names incorporated in the page names, I've just eliminated some of these. There is still a lot of work to do to clean up this resource. --Abd (discuss • contribs) 01:10, 2 February 2014 (UTC)

Poland
In addition to the above non-18th century "academy" -- different type of academy -- I've removed the following from the resource page. Please put them back if they belong there, but my understanding is that these aren't in scope as the kinds of scholarly societies and academies covered.

 * Uniwersytet Wroclawski/University of Wroclaw est. 1702. University's Website (TJU) (Josh Anderson)
 * The Pontifical Academy of Theology (Papieska Akademia Teologiczna w Krakowie)(TJU)

You can reverse this by opening up this, then pressing Undo. If you only want to put one back, then delete the other one from the edit window. Please explain why you are putting it back in the edit summary, so that I can understand. Thanks. --Abd 14:37, 13 September 2010 (UTC)

Found more files in mainspace
I found the following files in mainspace created by participants in this resource. I have moved them, but have not linked them from the resource page. It may be that some of them were superseded, or that some of them were linked and I just missed them.

 * 18th century European scholarly societies and academies/Royal Irish Academy
 * 18th century European scholarly societies and academies/Societa Italiana
 * 18th century European scholarly societies and academies/Akademie der Künste
 * 18th century European scholarly societies and academies/Accademia delle Scienze dell'Istituto di Bologna
 * 18th century European scholarly societies and academies/Society of Antiquaries of Scotland
 * 18th century European scholarly societies and academies/Society of Antiquaries of Scotland
 * 18th century European scholarly societies and academies/Societa Botanica Fiorentina
 * 18th century European scholarly societies and academies/Royal Military and Naval Academy

--Abd 17:24, 13 September 2010 (UTC)

For the future
I understand that the intention is for this to be an ongoing project, until completed to some reasonable condition, possibly moving on to some similar historical project after this. Cleaning this up was a lot of work, and it's still not done. In particular the following tasks remain:
 * Add categories to the individual pages. Each one of these pages, at the bottom, should have this added:

 * Convert links in the resource that go to the original mainspace pages to links to the subpages. This isn't an emergency, the current links work through the redirects.
 * Develop standard methods of listing and showing the work that has been done and the work that remains to do.
 * Set up explicit procedures for students to follow. Create a 18th century European scholarly societies and academies/Guidelines page to provide explicit, newbie-proof instructions for students. This will then have an attached Talk page for discussion.
 * Clean up the resource itself so that it reflects the guideline standards.
 * Create a class roster that shows all current active participants in the work. Require official students to use an account, which makes it far easier to track and coordinate work being done on the resource, and easier to identify and correct vandalism and other problem editing from others. (Wikiversity policy does allow a teacher to restrict participation, for a time, as I understand it, but there is no harm in allowing others to participate if you don't mind, and to help out in various ways, but all such other activity should be reviewed to make sure that it fits in with resource goals.)

I'm excited about the possibilities here, and very much appreciate that my offer of help was accepted. It's an opportunity to work out some operating guidelines that could help with many other classes, as well as making easier the work of those who try to watch for vandalism and other inappropriate editing. Student work is sometimes going to look improper, taken out of context. Thanks. --Abd 18:33, 13 September 2010 (UTC)