text:
User:EGM6322S09TIAN

One case
$$\kappa$$ $$= \underline{\kappa} (x,y,u,u_x,u_y)$$ $$\Rightarrow$$

Definition of quasilinear: For a PDE of order n (i.e. highest derivative terms are of order n),coeffients of nth order derivative are functions $$= (x,y,u,u_x,u_y,\frac{\partial^m u}{\partial {x^p y^q}})$$

Here, we assume there are two independent variables, mth order derivative, and $$p+q=m,m<n$$

Another Case
PDEs linear with respect to 2nd derivative, but still non-linear in general:

$$div($$ $$\kappa$$   $$\cdot grad u)+$$ $$f(x,y,u,u_x,u_y)=0$$

Here, $$\kappa =$$ $$\kappa (x,y)$$

$$f(x,y,u,u_x,u_y)=0$$ is nonlinear with respect to argues in general, e.g.

$$div($$ $$\kappa$$   $$\cdot grad u)+$$ $$ax^2+by+\sqrt{u}+(u_x)^4+2(u_y)^2=0$$

Homework
Show it linear to 2nd derivative, but non-linear in general.

To make it clear,

$$D_1(\cdot):=$$ $$div[$$  $$\kappa(x,y)$$   $$\cdot grad (\cdot)]$$

We can do this:

$$D_2(\cdot):=$$ $$D_1(\cdot)+$$ $$(\cdot)^{1/2}+$$ $$[(\cdot)_x]^4+$$ $$[2(\cdot)_y]^2$$

$$D_3(\cdot):=$$ $$D_2(\cdot)+$$ $$ax^2+by$$

P11－2
In $$div(\cdot)$$ an example of   for $$R^m \to R^n$$ $$(M:R^m \to R^n)$$ and $$M$$ ??????????

$$R^m, R^n$$ are space vectors (tensors, matrix). Divide maps vector field (vector-valued function) into a scalar function. In other words, domain and range of $$div(\cdot)$$ are function of spaces.

Coordinate Transformation (continued)
Eq(1)P.9.1

Eq(2)P.8.1

$$x= \phi (\bar{x},\bar{y})$$

$$y= \psi (\bar{x},\bar{y})$$

Linear coordinate transformation Eq(5) P.9-1

$$u(x,y)=$$ $$u($$ $$x= \phi (\bar{x},\bar{y})$$, $$y= \psi (\bar{x},\bar{y}))$$

$$=u(\bar{x},\bar{y})$$,  which is an abuse of notation by using "u".

$$=\bar{u}(\bar{x},\bar{y})$$,  which is a more rigorous notation.

Example
Let $$u(x)=ax+b$$

Condition, $$x=\phi (\bar x)$$ $$=sin \bar x$$

$$u(x)=$$ $$u(\phi (\bar x))$$ $$=asin \bar {x} + b$$

=$$u(\bar x)$$ $$\gets$$  abuse of notation

=$$\bar {u} (\bar x)$$  $$\gets$$  more rigorous

Another One
$$u_x(x,y)=$$ $$\frac{\partial u}{\partial x}(x,y)$$ $$=u_x(\phi(\bar{x},\bar{y}),\psi(\bar{x},\bar{y}))$$ $$= \frac{\partial }{\partial x}$$ $$\bar{u}(\bar{x},\bar{y})$$ $$=\frac{\partial \bar u}{\partial \bar x}$$ $$\frac{\partial \bar x}{\partial x}$$ $$+$$ $$\frac{\partial \bar u}{\partial \bar y}$$ $$\frac{\partial \bar y}{\partial y}$$ $$= \bar{u}_\bar {x}$$ $$\frac{\partial \bar x}{\partial x}$$ + $$\bar{u}_\bar {y}$$ $$\frac{\partial \bar y}{\partial x}$$

Define:

$$\bar x$$ = $$\bar {x} (x,y)$$ = $$\bar {\phi} (x,y)$$

$$\bar y$$ = $$\bar {y} (x,y)$$ = $$\bar {\psi} (x,y)$$

$$u_y(x,y)=$$ $$\frac{\partial }{\partial y}\bar u(\bar {x},\bar {y})$$ = $$= \bar{u}_\bar {x}$$ $$\frac{\partial \bar x}{\partial y}$$ + $$\bar{u}_\bar {y}$$ $$\frac{\partial \bar y}{\partial y}$$

Matrix Form
$$\partial_x u=$$ $$\big\lfloor$$ $$\frac{\partial \bar x}{\partial x}$$ $$\frac{\partial \bar y}{\partial x}$$ $$\big\rceil$$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$ $$(\bar u)$$

HW
Likewise for $$\partial_y $$

$$\partial_y u=$$ $$\big\lfloor$$ $$\frac{\partial \bar x}{\partial y}$$ $$\frac{\partial \bar y}{\partial y}$$ $$\big\rceil$$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$ $$(\bar u)$$

Then,

$$\begin{Bmatrix} \partial_ x \\ \partial_ y \end{Bmatrix} $$ = $$\begin{bmatrix} \frac{\partial \bar x}{\partial x} & \frac{\partial \bar y}{\partial x} \\ \frac{\partial \bar x}{\partial y} & \frac{\partial \bar y}{\partial y} \end{bmatrix} $$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$

$$\begin{bmatrix} \frac{\partial \bar x}{\partial x} & \frac{\partial \bar y}{\partial x} \\ \frac{\partial \bar x}{\partial y} & \frac{\partial \bar y}{\partial y} \end{bmatrix} $$ is known as the Jacobian matrix(sometimes it is defined as transposition of Jacobian matrix).

Easier and more general,

$$(x_1,\cdots,x_n)$$ $$\to$$ $$(\bar{x_1},\cdots,\bar{x_n})$$

Initial notation:$$\bar{x_i}$$ = $$\bar{x_i}$$ $$(x_1,\cdots,x_n)$$

$$J_{n \times n}$$ = $$\begin{bmatrix} \frac{\partial \bar x_i}{\partial x_j} \end{bmatrix}_{n \times n} $$

Here, "$$i$$"is the row index while "$$j$$"is the column index.

Carl Gustav Jacob Jacobi(1804-1851)

Jacobian Matrix was named after Carl Gustav Jacob Jacobi, a 19th century mathematician from Prussia. Born in 1804, Jacobi studied at Berlin University and later went on to teach at Königsberg University. He is known for Jacobi's elliptic functions,Jacobian,Jacobi symbol, and Jacobi identity. He died in Berlin in 1851. source:

=Signatures=

--EGM6322S09TIAN 20:35, 5 February 2009 (UTC) Andy L

title: User:EGM6322S09TIAN


text:
User:GreySmith Institute/GreySmith Institute

GreySmith Institute
The GreySmith Institute is conceptually an independent collaboration within the WikiVersity collaboration. The idea is to create a special interest group, made up of Enthusiasts interested in theorizing about and researching and developing Artificial Consciousness.

As well as the main site Portal:GreySmith Institute which offers a framework for thinking about Artificial Consciousness, GreySmith Institute has sponsored a number of Forums.

 * AC Forum a forum for discussing Artificial Consciousness
 * CompSci Forum a forum for discussion of Computer Science Topics
 * NeuroPsyche Forum a forum for discussion of NeuroScience and Psychology
 * Courseware Forum a forum for discussion of curriculum and Courseware at GreySmith Institute

To correspond directly with the Institute Staff, Please contact User: GreySmith Institute or leave a message on the associated talk page. To pre-register for classes follow the Student Union Link on Portal: GreySmith Institute

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text: Category:Partial differential equations

title: Category:Partial differential equations


text:
Category talk:Resources by type

I don't see why this category should be __hidden__. Any ideas? Hillgentleman | //\\ |Talk 04:43, 5 February 2009 (UTC)

title: Category talk:Resources by type


text:
User:Vsnaragund/Course work

all projects
http://projects.exeter.ac.uk/

ROBOTICS COURSE NOTES
http://arri.uta.edu/acs/jmireles/

http://artikel-software.com/.../robotics-and-intelligent-systems-lecture-note.

http://robotics.cucei.udg.mx/Index_files/page0004.html

http://www.cse.unr.edu/~monica/Courses/CS491-691/

http://www.cs.ait.ac.th/~mdailey/courseware/index.php?action=course&course_id=7&course_page=lecture_notes

http://see.stanford.edu/see/courseinfo.aspx?coll=86cc8662-f6e4-43c3-a1be-b30d1d179743

http://www.cs.cmu.edu/afs/cs/academic/class/...97/.../ALeapCurr.html

http://summerschool2010.ust.hk/

http://ocw.mit.edu/courses/mechanical-engineering/2-12-introduction-to-robotics-fall-2005/lecture-notes/

http://stratasphere.blogspot.com/.../course-notes-on-robotics-theory.html

Theory of plasticity and elasticity OR mechanics of solids
http://home.iitk.ac.in/~pmd/me721.html

http://home.iitk.ac.in/~ag/ME721.htm

http://www.eng.fsu.edu/~garm/egm5671/frames.html

http://www.geotechlinks.com/ln.php

http://www.ce.berkeley.edu/~coby/plas/

http://projects.exeter.ac.uk/fluidflow/ContinuumMechanics/TheoryofElasticity4013/TheoryofElasticity4013.html

http://web.mit.edu/abeyaratne/ElasticSolids-Vol.1-Math.pdf

http://www.me.ust.hk/~meqpsun/Notes/

http://www.math.uci.edu/~fwan/pdf/61_fundamentalsoflineartheory.pdf

http://www.engin.brown.edu/courses/en227/refs.htm

http://imechanica.org/node/354

http://www.mechanics.citg.tudelft.nl/~pierre/

http://www.4shared.com/document/vEZtBC7-/GPH_621_Elasticity_Theory_Cour.html

http://ip-72-167-142-143.ip.secureserver.net/hk/lecture%20notes%20on%20theory%20of%20elasticity-pdf-1.html

http://carbon.ucdenver.edu/~swelch/elasticity/ME5143_s11.pdf

THEORY OF MACHINES AND MECHANISMS
http://mechatronics.atilim.edu.tr/courses/mece303/Lectures/MECE_303_1_10%20%5BUyumluluk%20Modu%5D.pdf

http://www.onesmartclick.com/engineering/kinematics-dynamics-machines.html

http://www.cs.cmu.edu/afs/cs/academic/class/16741-s07/www/lectures.html

title: User:Vsnaragund/Course work


text: Category:Research groups

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text: Category:Wikiversity community

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Wikiversity:Threaded discussions with NavFrames with subst/20090201151334

Exactly. If you have a short comment, just put it on the headline.
20090205061138
 * Comments: --Hillgentleman | //\\ |Talk 06:11, 5 February 2009 (UTC)

 * reply[]

What links here


text:
User:Freakojohn

Hi,

I am freakojohn. I am student of Aerospace Engineering in Madras Institute of Technology,

Anna University, Chennai.

At present, I am in my final year and am doing my project in the dynamic simulation of

the start up process of a gas turbine engine.

My technical area of interest is in aerodynamics and propulsion. Besides, I am also interested

in anything related to Aerospace Engineering.

My general areas of interest is in English grammar, philosophy, science fiction, management,

mathematics, physics, logic.

title: User:Freakojohn


text: Category:GreySmith Institute forums

title: Category:GreySmith Institute forums


text:
User talk:I Am Learning

 Hello I Am Learning, 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

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title: User talk:I Am Learning


text:
Money

Some readings about "money", for beginners and others, considering questions such as:
 * What is money?
 * How does money 'work' or 'not work'?
 * etc.

Theoretical money
Def. a current medium of exchange in the form of coins and banknotes is called money.

title: Money


text:
Spacetime metrics explained for biologists

This is a reading course for the wikipedia article spacetime. Check also spacetime for a lightning overview. As the course progresses, the skeletons may be filled out by participants (see page history) and new resources may be spun off.

Reading list
Basic Supplementary (suggested by mikeu) More
 * spacetime (suggested by User:JWSchmidt)
 * world line
 * Minkowski diagram
 * Ned Wright's Cosmology Tutorial
 * The Light Cone - an illuminating introduction to relativity
 * Wormholes, Time Machines, and the Weak Energy Condition by M. Morris, K. Thorne, and U. Yurtsever (suggested by JWSchmidt)

Motivating questions or ideas

 * Lorentz metric:
 * 1) At the Wikipedia article for world line the term "Lorentz metric" links to Spacetime and on that page there is this sentence, "This means the smooth Lorentz metric $$g$$ has signature $$\left(3,1\right)$$."  The Wikipedia page for Lorentz metric links to Pseudo-Riemannian manifold where it indicates that there are multiple Lorentzian metrics. That page also mentions the "Minkowski metric".  The Wikipedia page for Minkowski metric links to Minkowski space where it says, "the term 'Minkowski space' is also used for analogues in any dimension: n+1 dimensional Minkowski space is a vector space or affine space of real dimension n+1 on which there is an inner product or pseudo-Riemannian metric of signature (n,1)". I would like to know which of these metrics is typically used and I'd like an example of how it is used. --JWSchmidt 17:18, 10 February 2009 (UTC)
 * 2) * Our usual spacetime is (1+3)-dimensional [i.e. n=3]. researchers are evenly split on the sign convention.  There is a rumour that physicists favour (+,-,-,-) and mathematicians favour (-,+,+,+).  This means that the square of distance from the point (t,b,c,d) [i.e. time=t, position= (b,c,d)] to the origin (0,0,0,0) is either (tt-bb-cc-dd) or (-tt+bb+cc+dd).  This structure is called "Lorentz metric".  It differs from the usual Euclidean metric (i.e. Pythagoras theorem) in usual space by a change of sign from + to -.  Hillgentleman | //\\ |Talk 03:09, 11 February 2009 (UTC)
 * 3)  My search for information about metrics started at Time travel and then I went to Wormhole and found the page section there on metrics. Reference #8 on that Wikipedia page links to the article Wormholes, Time Machines, and the Weak Energy Condition by M. Morris, K. Thorne, and U. Yurtsever. Near the bottom of the second column on page 1446 there is an equation for a spacetime metric. Where does that metric come from and how does it relate to others like those mentioned above? --JWSchmidt 14:34, 11 February 2009 (UTC)
 * 4) * [[file:Coordonnees_polaires_plan.png|right|70px]] Cordonnees_spheriques.svg In your reference, $$ds$$ is the "infinitessimal distance" between two points which are "very very" close to each other on a curved space.  The formula "ds^2 = ..." is written in polar coordinates and in terms of differential forms, and it defines a metric in a curved space (manifold) which describes the shape of the "wormhole" they are studying.  The simplest polar coordinate system is on the plane:  $$ r = (x^2 + y^2)^{1/2}, \theta = arctan(y/x)$$.  You get the x and y back by $$ x=r cos\theta , y=r sin\theta$$.  We were talking about a flat Minkowski space, whose metric can be written as $$ ds^2 = dt^2 - dx^2 - dy^2 - dz^2$$ .Hillgentleman | //\\ |Talk 08:23, 12 February 2009 (UTC)

 * 1) Why is ...

Physics

 * spacetime
 * Lorentz transformation
 * speed of light
 * frame of reference
 * velocity and momentum
 * Newton's law of motion

Mathematics

 * vector space
 * metric: (metric)
 * rotation
 * matrix

Basic principles

 * Speed of light is a universal constant, as is demonstrated by the Michelson-Morley experiment
 * principle of relativity

Phenomenology

 * dilation of time
 * mass-energy equivalence
 * causality

Study notes
Spacetime is just space and time put together, i.e., the four-dimensional space given by the three "space"-directions and one "time"-direction.

The first question is, "Why do we do that?" A quick answer is then, "Spacetime is more than just space and time bundled together. In fact, experiments show that spacetime is a more fundamental entity; you cannot really separate time from space. (These directions can "interact".)  The first hints of that fact came from electromagnetism... (More later)"

The second question is: what is a metric in mathematics? A quick answer is that it is a structure in a space with which you can measure the distance between two points. On a straight surface like a flat piece of paper (ie 2-dimensional space), measuring distance is simple: Pythagorean theorem tells us that the distance between two points with coordinate (x,y) (p,q) is $$\sqrt (x-p)^2 + (y-q)^2$$ On a curved surface like a sphere, measuring distance is more involved.

And fast forward to special relativity, as a direct consequence of the fundamental assumption that lightspeed is a universal constant, the metric of the four-dimensional spacetime is given by ...

Homework

 * 1) Expand the study notes above into useful learning resources.
 * 2) Calculate the Lorentzian (+,-,-,-) distance of the points (0,0,0,0) and (1,1,0,0) (i.e. two points which are 1 unit of time apart and 1 unit of space apart).


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User talk:TrevorLocke

 * Hi Trevor;
 * Are you working on the research component for the Budapest assignment? Seems there's a little confusion right now, organizationally. Post to the discussion page for your group.
 * Best! Stevenarntson

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User talk:STRAPPY McSTRAP-ON

 Hello STRAPPY McSTRAP-ON, 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

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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! --Sigma 7 19:40, 5 February 2009 (UTC)

Please see Wikiversity's no personal attacks policy. Comment on content, not on contributors. Personal attacks damage the community and deter users. Note that continued personal attacks will lead to blocks for disruption. Please Assume Good Faith and keep this in mind while editing. --Sigma 7 19:40, 5 February 2009 (UTC)

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User:Tevita

bio
My name is Tevita Tuitupou, and i am a student of The Art Institute of Seattle in the associates program of Multimedia Arts and Animation. I love to draw, hang out and kick it like bruce lee movies with my homies. Used to skateboard and play guitar, still have some skills, but not too much anymore.ya know, kinesthetic amnesia and whatnot. Anyways. thanks for your time :]

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User talk:EGM6322S09TIAN

 Hello EGM6322S09TIAN, 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

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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! --Juan de Vojníkov 20:33, 5 February 2009 (UTC)

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User talk:Tevita Tuitupou

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User talk:Wearyroad

 Hello Wearyroad, 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

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User:LAR1957

LAR1957 has been in higher education for the better part of 15 years. During the time that LAR1957 has been involved in education, a need has arisen to provide efficient, low cost, quality eduation. It has now become critical given current economic times to provide such education both through brick and mortar and computer-based, online means at a low cost with the same, or better, quality than is currently being provided.

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User talk:Bishop J. L. Mathis

 Hello Bishop J. L. Mathis, 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

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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! --AFriedman 22:11, 5 February 2009 (UTC)

 Hi , I am Percy. Nice to meet you. I love the beach, swimming, fishing, and I am currently doing some research at Wikiversity on oceanography. I am also learning to play piano. What do you like? Can I be your mascot?

Bishop J. L. Mathis
Hi, I have nominated this page: Bishop J. L. Mathis for deletion. I dont thing so it is an educational resource. Note that advertising doesnt have a place on Wikiversity. --Juan de Vojníkov 00:05, 6 February 2009 (UTC)

 * This page is still currently under construction as we still are gathering useful facts and information about Bishop J. L. Mathis and his organizations and community impact. If you allow this page to develop you will see that it's apart of a network of facts and useful knowledge about some of Bishop Mathis' organizations (check out The Birthing Of God International Fellowship page) and community activities.
 * If you're thinking about making the page into an educational resource, please let us know ASAP (1) the educational purpose of the resource, (2) why biographical information about this Bishop should be part of the resource, and (3) why the article as it currently appears would not be a duplication of a Wikipedia-type article or another Wikimedia resource. If Bishop Mathis is notable enough for Wikipedia, I don't see how the Wikiversity article as it appears now would be fundamentally different from a Wikipedia article about Bishop Mathis.  See also What Wikiversity is not.  --AFriedman 20:47, 6 February 2009 (UTC)

OK. Lets see. I have informed the community, about your report, here: Requests for Deletion. Have a good day.--Juan de Vojníkov 19:51, 6 February 2009 (UTC)

title: User talk:Bishop J. L. Mathis


text:
User:Dabongo

Knowledge is king - so here I am at Wikiversity. It's not the best place for a ADHD person to try to focus... but I have fun trying..

In the beginning, I didn't have the resources for the education I wanted - much less any direction on what I was to do in life... So I'm very motivated to be able to use Wikiversity - and without having to sell my house to pay tuition...

If I need to gain information, or learn a process - I seek, find, verify and then apply the information... If everything works as expected, I move on...otherwise, I start over... usually at a wiki site ;)

To all the sharing 'thinkers' - I appreciate the access to your knowledge...

Personal thought - ADHD is not a disability in itself. It's others inability to deal with someone who has ADHD, that's the real disability.... And by the way, it's not my attention deficit disorder - I'm just ignoring you....

title: User:Dabongo


text:
User talk:Dabongo

 Hello Dabongo, 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

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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! --Juan de Vojníkov 23:54, 5 February 2009 (UTC)

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User:Kevinborja

bio
My name is Kevin Borja I was born in Altamirano City in Guerrero, Mexico I moved to the US when I was 12 and i like art, that’s one of the reasons why i attend the Art Institute of Seattle. I live in Kent Washington, before i lived in Puyallup, a town which i hated with a passion since I was the only Mexican there; also people were not that friendly. But anyways yeah, I like music and movies and that type of "stuff"... Also sorry if you find mistakes or if my vocabulary isn't that complex, keep in mind that Spanish is my first language.

midterm
Well, I didn't like the Bunyons Chess piece. I found that name awkward, "bunyons" I honestly didn’t know what it meant but as I researched the artist I found that he got the name from a famous logger named Paul Bunyon. After all the research I still think the piece is ugly but now at least I know where the name came from. The logs hanging with pieces of metal here and there were not as appealing to me, honestly I didn’t hate it but that was my least favorite one and since I only got a look at half of the park I didn’t have many choices to hate on, I didn’t know the other side was part of the park. Also some of his other art weren't as ugly I also Learned that he was a chinese-italian-american artist or at least that is what Wikipedia said. Well at least now I know why I don't like it and I somehow able to appreciate the piece a little better, when I went back it did remind me of a logger's house and like I said I appreciate it more than the first time i went to the park.

final
For my first assignment I decided to paint abstract art, something I’m not good at. I don’t see the world that different than the average person, so painting blobs of paint that look good does not come easy for me. I decided to paint something every two weeks and in between them I’m going to study different styles of art also I plan to visit several museums since I’ve never been to one, I just hadn't had the will to go to one but now I'll do it for school.

By the end of this quarter, I want to: Paint abstract

The research component of the goal is to: Find different styles of abstract art Week 2: Buy supplies

Week 3: Paint, something that I would regularly paint

Week 4: Study Cubism

Week 5: Paint something in Cubism

Week 6: Study Neoplasticism

Week 7: Pain something in Neoplasticism

Week 8: Paint something combining all of what I’ve learned

title: User:Kevinborja


text:
LifeHacks

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Olin's Founding Precepts describe an Olin engineer with an assortment of important skills and experiences. The Precepts also aspire to change engineering education to reach these objectives. “[C]hanges ... include interdisciplinary and integrated teaching, hands-on learning and research opportunities for students, improved communication skills, [and] students working as members of teams ...” At the heart of each of these goals is a fundamental capability to work with information and turn it into knowledge - identifying, searching for, collecting, triaging, analyzing, presenting, and sharing the vast amount of information available to today's problem-solvers. While Olin aspires to teach many of these skills through disciplinary exercises in the classroom, developing and reflecting upon “information literacy” can benefit from a focused co-curricular experience. By focusing on some of these ideas, Olin students can become more effective and efficient at managing information in today's world.

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title: LifeHacks


text:
User:EGM6322.S09.TIAN

One case
$$\kappa$$ $$= \underline{\kappa} (x,y,u,u_x,u_y)$$ $$\Rightarrow$$

Definition of quasilinear: For a PDE of order n (i.e. highest derivative terms are of order n),coeffients of nth order derivative are functions $$= (x,y,u,u_x,u_y,\frac{\partial^m u}{\partial {x^p y^q}})$$

Here, we assume there are two independent variables, mth order derivative, and $$p+q=m,m<n$$

Another Case
PDEs linear with respect to 2nd derivative, but still non-linear in general:

$$div($$ $$\kappa$$   $$\cdot grad u)+$$ $$f(x,y,u,u_x,u_y)=0$$

Here, $$\kappa =$$ $$\kappa $$ $$(x,y) $$ $$f(x,y,u,u_x,u_y)=0$$ is nonlinear with respect to argues in general, e.g.

$$div($$ $$\kappa$$   $$\cdot grad u)+$$ $$ax^2+by+\sqrt{u}+(u_x)^4+2(u_y)^2=0$$

Homework:Show The Linearity Of The Equation Above

Show it linear to 2nd derivative, but non-linear in general.

To make it clear,

$$D_1(\cdot):=$$ $$div[$$  $$\kappa$$ $$(x,y)$$   $$\cdot grad (\cdot)]$$

We can do this:

$$D_2(\cdot):=$$ $$D_1(\cdot)+$$ $$(\cdot)^{1/2}+$$ $$[(\cdot)_x]^4+$$ $$[2(\cdot)_y]^2$$

$$D_3(\cdot):=$$ $$D_2(\cdot)+$$ $$ax^2+by$$

The definition of linearity: $$\mathfrak{L} \left( \alpha u + \beta v \right) = \alpha \mathfrak{L} \left( u \right) + \beta \mathfrak{L} \left( v  \right)$$, where $$\forall$$ $$u,v: \Omega \rightarrow \mathbb{R} $$ and $$\forall$$ $$\alpha, \beta \in \mathbb{R}$$

Using this definition of linearity, the above expression for $$D(u)$$ is given as: $$D_1(\cdot) \left( \alpha u + \beta v\right) = div \left[ \mathbf{\kappa} \cdot grad \left( \alpha u + \beta v \right) \right]$$

$$grad(\cdot)$$ is linear $$grad(u) = \frac {\partial u}{\partial x_i} e_i$$ and $$\frac {\partial u}{\partial x_i} (\cdot)$$ is linear $$\therefore$$ $$grad \left( \alpha u + \beta v \right)$$ = $$\alpha \frac {\partial u}{\partial x_i}$$+ $$\beta \frac {\partial v}{\partial x_i}$$= $$  \alpha   grad(u) + \beta  grad(v)$$

Matrix (tensor) multiplication is a linear operator $$\bar{A} \cdot \left( \alpha \bar{x} + \beta \bar{y} \right) = \alpha \bar{A} \bar{x} + \beta \bar{A} \bar{y}$$

$$\therefore$$ $$\mathbf{\kappa} \cdot grad(u) = \alpha \mathbf{\kappa} \cdot grad(u) + \beta \mathbf{\kappa} \cdot grad(v)$$

$$div(\cdot)$$ is linear because it is another differential operator let $$\bar{a}, \bar{b}: \Omega$$ $$\mathbb{R}^3$$ and $$\alpha, \beta \in \mathbb{R}$$

$$\therefore$$ $$div \left( \alpha \bar{a} + \beta \bar{b} \right) = \frac {\partial }{\partial x_i} \left( \alpha a_i + \beta b_i \right) = \alpha \frac {\partial a_i}{\partial x_i} + \beta \frac {\partial b_i}{\partial x_i}$$

Taking all this into consideration, the definition of linearity has been proven.

$$D_1 \left( \alpha u + \beta v \right) = \alpha div \left[ \mathbf{k} \cdot grad(u) \right] + \beta div \left[ \mathbf{k} \cdot grad(v) \right]$$ ,which means, the 2nd derivative part is linear.

Then,

$$D_2(\alpha u + \beta v) =$$ $$D_1(\alpha u + \beta v)+$$ $$(\alpha u + \beta v)^{1/2}+$$ $$[(\alpha u + \beta v)_x]^4+$$ $$2[(\alpha u + \beta v)_y]^2$$

$$\alpha D_2( u ) =$$ $$\alpha D_1( u )+$$ $$\alpha( u )^{1/2}+$$ $$[\alpha( u )_x]^4+$$ $$2[\alpha( u )_y]^2$$

$$\beta D_2( v ) =$$ $$\beta D_1( v )+$$ $$\beta( v )^{1/2}+$$ $$[\beta( v )_x]^4+$$ $$[2\beta( v )_y]^2$$

Obviously,

$$D_2(\alpha u + \beta v) \neq$$ $$\alpha D_2( u ) +$$ $$\beta D_2( v ) $$

$$\therefore$$, $$D_2(\cdot)=$$ $$D_1(\cdot)+$$ $$(\cdot)^{1/2}+$$ $$[(\cdot)_x]^4+$$ $$[2(\cdot)_y]^2$$ is non-linear.

Similarly, we can prove that:

$$D_3(\cdot)=$$ $$D_2(\cdot)+$$ $$ax^2+by$$ is non-linear.

$$\therefore$$, the equation is linear to 2nd order derivative but non-linear in general.

Coordinate Transformation (continued)
In $$div(\cdot)$$ an example of   for $$\mathbb{R}^m$$  $$\to$$ $$\mathbb{R}^n$$  $$(M:\mathbb{R}^m \to \mathbb{R}^n)$$.

$$\mathbb{R}^m, \mathbb{R}^n$$ are space vectors (tensors, matrix). Divide maps vector field (vector-valued function) into a scalar function. In other words, domain and range of $$div(\cdot)$$ are function of spaces.

$$x= \phi (\bar{x},\bar{y})$$

$$y= \psi (\bar{x},\bar{y})$$

Linear coordinate transformation Eq(5) P.9-1

$$u(x,y)=$$ $$u($$ $$x= \phi (\bar{x},\bar{y})$$, $$y= \psi (\bar{x},\bar{y}))$$

$$=u(\bar{x},\bar{y})$$,  which is an abuse of notation by using "u".

$$=\bar{u}(\bar{x},\bar{y})$$,  which is a more rigorous notation.

Example
Let $$u(x)=ax+b$$

Condition, $$x=\phi (\bar x)$$ $$=sin \bar x$$

$$u(x)=$$ $$u(\phi (\bar x))$$ $$=asin \bar {x} + b$$

=$$u(\bar x)$$ $$\gets$$  abuse of notation

=$$\bar {u} (\bar x)$$  $$\gets$$  more rigorous

Another One
$$u_x(x,y)=$$ $$\frac{\partial u}{\partial x}(x,y)$$ $$=u_x(\phi(\bar{x},\bar{y}),\psi(\bar{x},\bar{y}))$$ $$= \frac{\partial }{\partial x}$$ $$\bar{u}(\bar{x},\bar{y})$$ $$=\frac{\partial \bar u}{\partial \bar x}$$ $$\frac{\partial \bar x}{\partial x}$$ $$+$$ $$\frac{\partial \bar u}{\partial \bar y}$$ $$\frac{\partial \bar y}{\partial y}$$ $$= \bar{u}_\bar {x}$$ $$\frac{\partial \bar x}{\partial x}$$ + $$\bar{u}_\bar {y}$$ $$\frac{\partial \bar y}{\partial x}$$

Define:

$$\bar x$$ = $$\bar {x} (x,y)$$ = $$\bar {\phi} (x,y)$$

$$\bar y$$ = $$\bar {y} (x,y)$$ = $$\bar {\psi} (x,y)$$

$$u_y(x,y)=$$ $$\frac{\partial }{\partial y}\bar u(\bar {x},\bar {y})$$ = $$= \bar{u}_\bar {x}$$ $$\frac{\partial \bar x}{\partial y}$$ + $$\bar{u}_\bar {y}$$ $$\frac{\partial \bar y}{\partial y}$$

Matrix Form
$$\partial_x u=$$ $$\big\lfloor$$ $$\frac{\partial \bar x}{\partial x}$$ $$\frac{\partial \bar y}{\partial x}$$ $$\big\rceil$$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$ $$(\bar u)$$

Homework:Likewise For $$\partial_y $$

Likewise for $$\partial_y $$

$$\partial_y u=$$ $$\big\lfloor$$ $$\frac{\partial \bar x}{\partial y}$$ $$\frac{\partial \bar y}{\partial y}$$ $$\big\rceil$$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$ $$(\bar u)$$

Then,

$$\begin{Bmatrix} \partial_ x \\ \partial_ y \end{Bmatrix} $$ = $$\begin{bmatrix} \frac{\partial \bar x}{\partial x} & \frac{\partial \bar y}{\partial x} \\ \frac{\partial \bar x}{\partial y} & \frac{\partial \bar y}{\partial y} \end{bmatrix} $$ $$\begin{Bmatrix} \partial_ {\bar x} \\ \partial_ {\bar y} \end{Bmatrix} $$

$$\begin{bmatrix} \frac{\partial \bar x}{\partial x} & \frac{\partial \bar y}{\partial x} \\ \frac{\partial \bar x}{\partial y} & \frac{\partial \bar y}{\partial y} \end{bmatrix} $$ is known as the Jacobian matrix(sometimes it is defined as transposition of Jacobian matrix).

Easier and more general,

$$(x_1,\cdots,x_n)$$ $$\to$$ $$(\bar{x_1},\cdots,\bar{x_n})$$

Initial notation:$$\bar{x_i}$$ = $$\bar{x_i}$$ $$(x_1,\cdots,x_n)$$

$$J_{n \times n}$$ = $$\begin{bmatrix} \frac{\partial \bar x_i}{\partial x_j} \end{bmatrix}_{n \times n} $$

Here, "$$i$$"is the row index while "$$j$$"is the column index.

Carl Gustav Jacob Jacobi(1804-1851)

Jacobian Matrix was named after Carl Gustav Jacob Jacobi, a 19th century mathematician from Prussia. Born in 1804, Jacobi studied at Berlin University and later went on to teach at Königsberg University. He is known for Jacobi's elliptic functions,Jacobian,Jacobi symbol, and Jacobi identity. He died in Berlin in 1851. source:

=Signatures=

--EGM6322.S09.TIAN 20:35, 5 February 2009 (UTC) Miao Tian

=Complete Form Of Matrix=

$$\alpha = \beta + \gamma$$

$$\beta$$ = $$\left \lfloor \partial_{\bar{x}} \; \partial_{\bar{y}} \right \rfloor $$ $$\mathbf{J} \mathbf{J^T}\begin{Bmatrix}\partial {\bar{x}}\\\partial {\bar{y}}\end{Bmatrix}$$

$$= \left \lfloor \partial_r \; \partial_{\theta} \right \rfloor $$ $$\frac {1} {r^2} $$ $$\begin{bmatrix} rc & rs\\ -s & c \end{bmatrix} $$ $$\begin{bmatrix} rc & -s\\ rs & c \end{bmatrix} $$ $$\begin{Bmatrix}\partial_r \\\ \partial_{\theta}\end{Bmatrix}$$

$$= \left \lfloor \partial_r \ \partial_{\theta} \right \rfloor $$ $$\begin{Bmatrix}\partial_r \\\ \partial_{\theta}\end{Bmatrix}$$

$$= \partial_{rr} +$$ $$\frac {1} {r^2} $$ $$\partial_{\theta \theta} $$

Note: $$\left \lfloor \partial_{\bar{x}} \ \partial_{\bar{y}} \right \rfloor $$$$\mathbf{J} \mathbf{J^T}$$ hold fixed, no further differentiate.

Three Methods To Figure Out $$\gamma$$
Method One:

$$\gamma =$$ $$= \left \lfloor \partial_r \ \partial_{\theta} \right \rfloor $$ $$\mathbf{J} \mathbf{J^T}$$ $$\begin{Bmatrix}\partial r \\\ \partial {\theta}\end{Bmatrix}$$

Method Two:

$$= \left \lfloor \partial_x \ \partial_y \right \rfloor $$ $$\mathbf{J} (x,y)$$ $$\begin{Bmatrix}\partial r \\\ \partial {\theta}\end{Bmatrix}$$

Method Three:

re-expect result in $$( r, $$ $$\theta$$ )

$$= \left \lfloor \partial_x \ \partial_y \right \rfloor $$ $$\mathbf{J} (r,\theta)$$ $$\begin{Bmatrix}\partial_r \\\ \partial_{\theta}\end{Bmatrix}$$

expressing result in $$( r, $$ $$\theta$$ )

Let us use Method Three:

$$= \left \lfloor \partial_x \ \partial_y \right \rfloor $$ $$\mathbf{J^T}$$ = $$= \left \lfloor \partial_x \ \partial_y \right \rfloor $$ $$\begin{bmatrix} c & -\frac {s}{r}\\ s & \frac {c}{s} \end{bmatrix} $$ = $$= \left \lfloor ( \partial_x c + \partial_y s) \;  (-\partial_x (\frac {s}{c})) + \partial_y (\frac {c}{r}) \right \rfloor $$

$$\partial_x c =$$ $$\frac{\partial}{\partial x}$$ $$cos {\theta}(x,y)$$ = $$\frac{\partial}{\partial r}$$ $$( cos {\theta})$$ $$\frac{\partial r}{\partial x}$$ + $$\frac{\partial}{\partial {\theta}}$$ $$( cos {\theta})$$ $$\frac{\partial {\theta}}{\partial x}$$

$$\partial_x f(r,{\theta})$$ = ($$\frac{\partial}{\partial r} \; f$$) $$\frac{\partial r}{\partial x} $$ + $$\frac{\partial f}{\partial {\theta}} $$ $$\frac{\partial {\theta}}{\partial x} $$

$$\frac{\partial {\theta}}{\partial x} $$ = $$\frac{\partial}{\partial x} $$ $$tan^{-1}$$ $$( \frac{y}{x} )$$ =$$J_{21} (r,{\theta})$$ = $$\frac{\partial {\bar{x_2}}}{\partial {x_1}} $$

$$J_{21}=$$ $$-\frac {sin{\theta}} {r}$$ $$\partial_x cos {\theta} $$ = $$(-sin{\theta})$$ $$(-\frac {s}{r})$$ = $$\frac {s^2}{r}$$

$$\partial_y sin {\theta}$$ = $$\frac {c^2}{r}$$

$$\Rightarrow$$ $$\partial_x c + \partial_y s$$ = $$\frac {1}{r}$$

$$\partial_x (\frac {s}{r})=$$ $$\frac{\partial} {\partial {r}} $$ $$(\frac {s}{r})$$ $$\frac{\partial r }{\partial x} +$$ $$\frac{\partial} {\partial {\theta}} $$ $$(\frac {s}{r})$$ $$\frac{\partial {\theta} }{\partial x} $$

= $$-\frac {2sc} {r^2}$$

Similarly, $$\partial_y (\frac {c}{r})=$$ $$\frac{\partial} {\partial {r}} $$ $$(\frac {c}{r})$$ $$\frac{\partial r }{\partial y} +$$ $$\frac{\partial} {\partial {\theta}} $$ $$(\frac {c}{r})$$ $$\frac{\partial {\theta} }{\partial y} $$

= $$-\frac {2sc} {r^2}$$

Homework: The Complete Form Of $$\gamma$$ $$\gamma =$$ $$\begin{bmatrix} (\phi_{xx} \partial_{\bar{x}} + \psi_{xx} \partial_{\bar{y}}) & (\phi_{xy} \partial_{\bar{x}} + \psi_{xy} \partial_{\bar{y}}) \\ (\phi_{xy} \partial_{\bar{x}} + \psi_{xy} \partial_{\bar{y}}) & (\phi_{yy} \partial_{\bar{x}} + \psi_{yy} \partial_{\bar{y}}) \end{bmatrix} $$

Homework:Derive LP p.14 (1.2.13) $$A=a \phi_x^2 + 2b \phi_x \phi_y +c \phi_y^2$$

$$ B=a \phi_x \psi_x + b( \phi_x \psi_y +\phi_y \psi_x ) + c \phi_y \psi_y  $$

$$C=a \psi_x^2 + 2b \psi_x \psi_y +c \psi_y^2$$

$$AC - B^2 =$$ $$(a \phi_x^2 + 2b \phi_x \phi_y +c \phi_y^2)$$ $$(a \psi_x^2 + 2b \psi_x \psi_y +c \psi_y^2)$$ - $$[a \phi_x \psi_x + b( \phi_x \psi_y +\phi_y \psi_x ) + c \phi_y \psi_y ]^2 $$

=$$a^2 \phi_x^2 \psi_y^2 + 2ab \phi_x \phi_y \psi_y^2 + ac \phi_y^2 \psi_y^2 + 2ab \phi_x^2 \psi_x \psi_y + 4b^2 \phi_x \phi_y \psi_x \psi_y + 2bc \phi_y^2 \psi_x \psi_y +ac \phi_x^2 \psi_y^2 +2bc \phi_x \phi_y \psi_y^2 + c^2 \phi_y^2 \psi_y^2 $$ -

($$a^2 \phi_x^2 \psi_x^2 +b^2 \phi_x^2 \psi_y^2 +b^2 \phi_y^2 \psi_x^2 +2b^2 \phi_x \phi_y \psi_x \psi_y + c^2 \phi_y^2 \psi_y^2 +2ab \phi_x^2 \psi_x \psi_y + 2ab \phi_x \phi_y \psi_x^2 +2ac \phi_x \phi_y \psi_x \psi_y +2bc \phi_x \phi_y \psi_y^2 +2bc \phi_y^2 \psi_x \psi_y$$)

= $$(ac-b^2)(\phi_x \psi_y - \phi_y \psi_x)$$

Lecture 24
$$\tau (div (grad \omega))+ p(x,y) = m W_tt$$

Here, $$div (grad \omega)= \omega_{xx}+\omega_{yy}$$, $$m$$ is mass/unit area.

Wave Equation In 1-D Space (actually a 2-D (x,t) Problem)
$$\tau \omega_{xx} - m \omega_{tt} +p =0$$

$$A= \begin{bmatrix} a & b \\ b & c \end{bmatrix} $$, $$detA=ac-b^2$$

In this case, $$a= \tau >0, b=0, c=-m<0 $$

$$detA=- \tau m <0 \Rightarrow hyperbolic$$

1-D space
$$\frac{d}{dx} (\kappa \frac{du}{dx}) + f = C \frac{du}{dt}$$

Here, $$\kappa is heat conductivity, f is heat source, C is heat capacity$$

We assume $$\kappa$$ is constant.

$$\kappa u_{xx} - C u_t +f =0$$

$$a= \kappa, b=0,  c=0 \Rightarrow  detA=0\Rightarrow parabolic$$

2-D space
$$\frac{d}{dx} (\kappa \frac{du}{dx}) + f = C \frac{du}{dt}$$

We assume $$\kappa$$ is constant here.

$$\kappa (u_{xx} + u_{yy}) - C u_t +f =0$$

General to 3 independent variables (x,y,z)

$$\big\lfloor \partial_x \; \partial_y \;\partial_z  \big\rceil \begin{bmatrix} A_{11} & A_{12} & A_{13}\\ A_{21} & A_{22} & A_{23}\\ A_{31} & A_{32} & A_{33} \end{bmatrix} \begin{Bmatrix} \partial_x u \\ \partial_y u \\ \partial_z u \end{Bmatrix} $$

Here,$$ \begin{bmatrix} A_{11} & A_{12} & A_{13}\\ A_{21} & A_{22} & A_{23}\\ A_{31} & A_{32} & A_{33} \end{bmatrix} = [A_{ij}]_{3 \times 3}$$

In 2-D case, $$A_{ij}=0 \; \forall \; i,j \; except \; A_{11} = A_{22}= \kappa >0 \Rightarrow detA=0 \Rightarrow parabolic$$

Solution of unsteady heat equation without heat source, which means $$(f=0)$$ in polar coordinate.
Separation of Variables.

$$\frac {1}{r} \frac {\partial} {\partial r} (r \frac {\partial u} {\partial r})$$ $$+ \frac {1}{r^2} \frac {\partial^2 u}{\partial^2 \theta}$$ $$= \frac {\partial u}{\partial t}(1)$$

Here, $$\frac {1}{r} \frac {\partial} {\partial r} (r \frac {\partial u} {\partial r})$$ $$+ \frac {1}{r^2} \frac {\partial^2 u}{\partial^2 \theta}$$ $$=div (grad u)$$

$$u(r,\theta,t)=R(r)\Theta (\theta) T(t)\;(2)$$

Plug $$(2)$$ into $$(1)$$:

$$\frac {1}{rR} \frac {\partial} {\partial r} (r \frac {dR} {dr})$$ $$+ \frac {1}{r^2 \Theta} \frac {d^2 \Theta}{d \theta^2 \theta}$$ $$- \frac {1}{T} \frac {dT}{dt}=0$$

Homework:Expand $$\; T^* $$ in terms of $$cos \theta$$ $$T^* (\theta)= \frac {3T_o}{2} + \frac {T_o}{2} cos{2 \theta}$$

Expand it:

$$T^* (\theta)= \frac {3T_0}{2} + \frac {T_0}{2} (2 cos^2 \theta -1)$$ $$=T_0+T_0 cos^2 \theta$$

lecture 27
$$\bar u$$ $$(r, \theta)=$$ $$R(r) \Theta (\theta)= \frac {1}{k} R(r)\Theta (\theta)$$

Since $$k$$ is arbitrary, select $$k=1 $$

Now why $$B=B(\rho), C=C(\rho)$$?

Hint:

General initial condition : $$u(r, \theta, t_0)= {\bar u} (r, \theta)$$

Simplify $$u(r, \theta ,t_0)={\bar u (\theta)}$$

$$u(r, \theta_1 ,t_0)={\bar u (\theta_1)}$$

$$u(r, \theta_2 ,t_0)={\bar u (\theta_2)}$$

$${\bar u} (\theta)= \Theta (\theta)= \frac {1}{k} \Theta (\theta) k$$

Let $$\frac {1}{k} \Theta (\theta) = \Theta (\theta)$$,

$$k=T(t_0)$$

$$\begin{cases} {\bar u} (\theta_1)= Bsin(\sqrt{\rho} \theta_1)+Ccos(\sqrt{\rho} \theta_1)\\ {\bar u} (\theta_2)= Bsin(\sqrt{\rho} \theta_2)+Ccos(\sqrt{\rho} \theta_2) \end{cases}$$

Then we can solve B, C and finally we will find that B and C are functions of $$\rho$$

$$B=B(\rho, \theta_1, \theta_2)$$

$$C=C(\rho, \theta_1, \theta_2)$$

HW 2
Bessel Function:

$$z^2 \frac {d^2w}{dz^2} + z \frac {dw}{dz} + (z^2-\nu^2)w=0$$

We have one solution $$J_{\nu}(z)$$:

When $$\nu = $$integer n,

$$J_n(z)= \frac {1}{\pi} \int_{0}^{\pi} cos(zsin \theta -n \theta)d \theta$$

In $$J(z)=z_{\alpha} \sum_{k=1}^{\infty} \alpha_k z^k$$ form, we can write $$J_n(z)$$as:

$$J_n(z)= \sum_{m=0}^{\infty} (-1)^m \frac {z^{n+2m}}{2^{n+2m}m!\Gamma(n+m+1)}$$

The other solution is to let $$\nu = -n$$:

$$J_{-n}(z)= \sum_{m=0}^{\infty} (-1)^m \frac {z^{-n+2m}}{2^{-n+2m}m!\Gamma(-n+m+1)}$$

Verify it :

$$z^2 \frac {d^2J_{-n}(z)}{dz^2}=$$ $$ \sum_{m=0}^{\infty}(-n+2m)(-n+2m-1) (-1)^m \frac {z^{-n+2m}}{2^{-n+2m}m!\Gamma(-n+m+1)}$$

$$z \frac {dJ_{-n}(z)}{dz}=$$ $$ \sum_{m=0}^{\infty}(-n+2m)(-1)^m \frac {z^{-n+2m}}{2^{-n+2m}m!\Gamma(-n+m+1)}$$

lecture 32
(1)$$div (\underline {v}) = \frac {\partial v_i}{\partial x_i}$$ $$= \frac {\partial v_i}{\partial x_i} \delta_{ij}$$ $$= \frac {\partial v_i} {\partial \overline {x_k}} \frac {\partial \overline {x_k}} {\partial x_j}\delta_{ij}$$

(2)$$\underline {J} = \begin{bmatrix} \frac {\partial \overline {x_i}}{\partial x_j} \end{bmatrix} $$ $$= \begin{bmatrix} C & S \\ -\frac {S}{r} & \frac {C}{r} \end{bmatrix} $$

(3)$$\frac {\partial v_1}{\partial x_1} = \frac {\partial v_x}{\partial x}= \frac {\partial v_x}{\partial r} \frac {\partial r}{\partial x} + \frac {\partial v_x}{\partial \theta}  \frac {\partial \theta}{\partial x} $$

$$\frac {\partial \overline {x_1}}{x_1} = J_{11}=C$$

$$\frac {\partial \overline {x_2}}{x_1} = J_{21}= -\frac {S}{r}$$

(4)$$\underline {v}=v_x \underline {i}+ v_y \underline {j}=$$ $$v_r(c \underline {i} + s \underline {j})+ v_{\theta}(-rs \underline {i} + rc \underline {j})$$ $$=(cv_r-rsv_{\theta}) \underline {i} + (sv_r-rcv_{\theta}) \underline {j} $$

Here we have,

$$\underline {e_r}=c \underline {i} + s \underline {j}$$

$$\underline {e_{\theta}}=-rs \underline {i} + rc \underline {j}$$

$$v_x=cv_r-rsv_{\theta}$$

$$v_y=sv_r-rcv_{\theta}$$

from equation (3),

$$\frac {\partial v_x}{\partial r}= \frac {\partial}{\partial r}(cv_r-rsv_{\theta})$$

Similarly,

$$\frac {\partial v_x}{\partial \theta}= \frac {\partial}{\partial \theta}(cv_r-rsv_{\theta})$$

So we have,

$$\frac {\partial v_1}{\partial x_1}= \frac {\partial v_x}{\partial x}=$$ $$[\frac {s^2}{r} v_r +c^2 \frac {\partial v_r}{\partial r}- \frac {cs}{r} \frac {\partial v_r}{\partial \theta}] + [-rcs \frac {v_{\theta}}{r}+ s^2 \frac{\partial v_{\theta}}{\theta}]$$

$$\frac {\partial v_2}{\partial x_2}= \frac {\partial v_y}{\partial y}=$$ $$[\frac {c^2}{r} v_r +s^2 \frac {\partial v_r}{\partial r}+ \frac {cs}{r} \frac {\partial v_r}{\partial \theta}] + [rcs \frac {v_{\theta}}{r}+ c^2 \frac{\partial v_{\theta}}{\theta}]$$

$$div (\underline {v}) = \frac {\partial v_x}{\partial x} + \frac {\partial v_y}{\partial y}= \frac {1}{r} \frac {\partial}{\partial r}(rv_r)+ \frac {\partial v_{\theta}}{\partial \theta}$$

Differnce between the above expression and that in the book In the book,

$$\underline {e_r}=c \underline {i} + s \underline {j}$$

$$\underline {e_{\theta}}=-s \underline {i} + c \underline {j}$$

not,

$$\underline {e_r}=c \underline {i} + s \underline {j}$$

$$\underline {e_{\theta}}=-rs \underline {i} + rc \underline {j}$$

So now we have,

$$\underline {v}=v_x \underline {i}+ v_y \underline {j}=$$ $$v_r(c \underline {i} + s \underline {j})+ v_{\theta}(-s \underline {i} + c \underline {j})$$ $$=(cv_r-sv_{\theta}) \underline {i} + (sv_r-cv_{\theta}) \underline {j} $$

$$\frac {\partial v_x}{\partial r}= \frac {\partial}{\partial r}(cv_r-sv_{\theta})=c \frac {\partial v_r}{\partial r} - s \frac {\partial v_{\theta}}{\partial r}$$

$$\frac {\partial v_x}{\partial \theta}= \frac {\partial}{\partial \theta}(cv_r-sv_{\theta})=-sv_r+c \frac {\partial v_r}{\partial \theta} - cv_{\theta}-s \frac {\partial v_{\theta}}{\partial \theta}$$

$$\frac {\partial v_y}{\partial r}= \frac {\partial}{\partial r}(sv_r+cv_{\theta})=s \frac {\partial v_r}{\partial r} +c \frac {\partial v_{\theta}}{\partial r}$$

$$\frac {\partial v_y}{\partial \theta}= \frac {\partial}{\partial \theta}(sv_r+cv_{\theta})=cv_r+s \frac {\partial v_r}{\partial \theta} - sv_{\theta}+c \frac {\partial v_{\theta}}{\partial \theta}$$

And we have, $$\underline {J} = \begin{bmatrix} \frac {\partial \overline {x_i}}{\partial x_j} \end{bmatrix} $$ $$= \begin{bmatrix} C & S \\ -\frac {S}{r} & \frac {C}{r} \end{bmatrix} $$

$$div (\underline {v}) = \frac {\partial v_x}{\partial x} + \frac {\partial v_y}{\partial y}

= \frac {\partial v_x}{\partial r} \cdot \frac {\partial r}{\partial x} +\frac {\partial v_x}{\partial \theta} \cdot \frac {\partial \theta}{\partial x} +\frac {\partial v_y}{\partial r} \cdot \frac {\partial r}{\partial x} +\frac {\partial v_y}{\partial \theta} \cdot \frac {\partial \theta}{\partial y}$$

$$=c(c \frac {\partial v_r}{\partial r} - s \frac {\partial v_{\theta}}{\partial r})-\frac {s}{r}(-sv_r+c \frac {\partial v_r}{\partial \theta}

- cv_{\theta}-s \frac {\partial v_{\theta}}{\partial \theta})

+s(s \frac {\partial v_r}{\partial r}

+c \frac {\partial v_{\theta}}{\partial r})

+\frac {c}{r}(cv_r+s \frac {\partial v_r}{\partial \theta}

- sv_{\theta}+c \frac {\partial v_{\theta}}{\partial \theta})

$$

$$=c^2 \frac {\partial v_r}{\partial r} - cs \frac {\partial v_{\theta}}{\partial r}+ \frac {s^2}{r}v_r -\frac {sc}{r} \frac {\partial v_r}{\partial \theta} + \frac {sc}{r} v_{\theta} + \frac {s^2}{r} \frac {\partial v_{\theta}}{\partial \theta} + s^2 \frac {\partial v_r}{\partial r} +sc \frac {\partial v_{\theta}}{\partial r} + \frac {c^2}{r} v_r + \frac {cs}{r} \frac {\partial v_r}{\partial \theta} - \frac {cs}{r} v_{\theta}+ \frac {c^2}{r} \frac {\partial v_{\theta}}{\partial \theta}$$

=$$\frac {\partial v_r}{\partial r}+ \frac {1}{r} v_r + \frac {1}{r} \frac {\partial v_{\theta}}{\theta}$$

=$$\frac {1}{r} \frac {\partial}{\partial r}(rv_r)+ \frac {1}{r} \frac {\partial v_{\theta}}{\theta}$$

That is the expression from the book.

Verify the d'Alembert solution is the solution of Wave Equation

The classic wave equation is,

$$c_0^2 w_{xx}=w{tt}$$

Initial Condition:

$$w(x,0)=f(x)$$

$$w_t(x,0)=g(x)$$

the solution is:

$$w(x,t)=\frac {1}{2} [f(x-c_0t)+f(x+c_0t)] + \frac {1}{2c_0} \int_{x-c_0t}^{x+c_0t} g(\xi)	d \xi$$

Plug the solution into the wave equation,

$$\frac {\partial w}{\partial x}=\frac {1}{2} [f^'(x-c_0t)+f^'(x+c_0t)]+\frac {1}{2c_0}[g(x+c_0t)-g(x+c_0t)]$$

$$\frac {\partial^2 w}{\partial x^2}=\frac {1}{2} [f^{}(x-c_0t)+f^{}(x+c_0t)]+\frac {1}{2c_0}[g^'(x+c_0t)-g^'(x+c_0t)]$$

$$\frac {\partial w}{\partial t}=\frac {1}{2} [c_0f^'(x-c_0t)+c_0f^'(x+c_0t)]+\frac {1}{2c_0}[c_0g(x+c_0t)-c_0g(x+c_0t)]$$

$$\frac {\partial^2 w}{\partial x^2}=\frac {1}{2} [c_0^2f^{}(x-c_0t)+c_0^2f^{}(x+c_0t)]+\frac {1}{2c_0}[c_0^2g^'(x+c_0t)-c_0^2g^'(x+c_0t)]$$

Then it's easy to see that

$$c_0^2w_{xx}=w_{tt}$$

lecture 37

Cases $$\lambda_1 \lambda_2 >0$$ and $$\lambda_1 \lambda_2 <0$$,

$$\lambda_1 \lambda_2 >0$$is the case of ellipse

$$\lambda_1 \lambda_2 <0$$is the case of hyperbola

In both of these two cases:$$\lambda_1 \lambda_2 \neq0$$

Geometric interpretation:

Eigenvalue problem $$\Leftrightarrow$$ Rotation of $$(x,y)$$to$$(\overline {x},\overline{y})$$which are parallel to principal axes of conics. Orthogonal of $$\underline {V}$$ $$(\underline {v} \ \underline {v}^T$$ $$=\underline {I})$$

Next Step: Get rid of linear terms in

$$\left \lfloor \overline {x} \ \overline {y} \right \rfloor$$ $$\underline {\Lambda}$$ $$	\binom{\overline {x}}{\overline {y}}   $$ + $$\left \lfloor \overline {d} \ \overline {e} \right \rfloor$$ $$	\binom{\overline {x}}{\overline {y}}   $$ +$$f=0$$ Equation(1)

Translation of Coordinate System.

Define the new coordinate system $$(\overline{\overline {x}} \ \overline{\overline {y}}) $$as:

$$	\binom{\overline{\overline {x}}}{\overline{\overline {y}}}$$ = $$\binom {\overline {x}+r}{\overline {y}+s}$$

(r,s)are unknowns.It's the "center" of ellipse or hyperbola.

$$\binom {\overline {x}}{\overline {y}}$$ = $$	\binom{\overline{\overline {x}}-r}{\overline{\overline {y}}-s}$$

Plugging it into Equation (1), we obtain:

$$\lambda_1 (\overline{\overline{x}}-r)^2+\lambda_2 (\overline{\overline{y}}-s)^2$$ $$+\overline {d} (\overline{\overline{x}}-r)+\overline {e} (\overline{\overline{y}}-s) +f =0$$

Find Out r and s Expanding

$$\lambda_1 (\overline{\overline{x}}-r)^2+\lambda_2 (\overline{\overline{y}}-s)^2$$ $$+\overline {d} (\overline{\overline{x}}-r)+\overline {e} (\overline{\overline{y}}-s) +f =0$$

We obtain:

$$\lambda_1 \overline {\overline {x}}^2 + \lambda_2 \overline {\overline {y}}^2$$ $$+(\overline {d}- 2 \lambda_1 r )\overline {\overline {x}}$$ $$+(\overline {e}- 2 \lambda_2 s )\overline {\overline {y}}$$ $$+(\lambda_1 r^2 + \lambda_2 s^2 - \overline {d} r -\overline {e} s +f)=0$$

Because we need to get rid of linerar terms,

$$ \overline {d} - 2 \lambda_1 r =0$$

$$ \overline {e} - 2 \lambda_2 s =0$$,

Finally we have:

$$r= \overline {d} / 2 \lambda_1$$

$$s= \overline {e} / 2 \lambda_2$$

Find Out g $$\lambda_1 (\overline{\overline{x}}-r)^2+\lambda_2 (\overline{\overline{y}}-s)^2=g$$

Comparing it to

$$\lambda_1 \overline {\overline {x}}^2 + \lambda_2 \overline {\overline {y}}^2$$ $$+(\lambda_1 r^2 + \lambda_2 s^2 - \overline {d} r -\overline {e} s +f)=0$$

we get,

$$g=-(\lambda_1 r^2 + \lambda_2 s^2 - \overline {d} r -\overline {e} s +f)$$

Parabola PDE Now we have $$\lambda_1 u_{xx} + e u_y =h$$ (1)

and we want $$u_{\xi \xi} - u_{\eta} =g$$(2)

Rewriting (1) in matrix form, we have:

$$\left \lfloor \partial {x} \ \partial {y} \right \rfloor$$ $$\begin{bmatrix} \lambda_1     &  0      \\ 0             & 0 \end{bmatrix} $$ $$\begin{bmatrix} \partial_x u           \\ \partial_y u            \end{bmatrix} $$ $$+ \left \lfloor 0 \ e \right \rfloor$$ $$\begin{bmatrix} \partial_x u           \\ \partial_y u            \end{bmatrix}=g $$(3)

We have already derived that,

$$\begin{bmatrix} \partial_x            \\ \partial_y \end{bmatrix} $$ = $$J_{\beta} \begin{bmatrix} \partial_{\xi}            \\ \partial_{\eta} \end{bmatrix} $$ (4)

$$J_{\beta}= \begin{bmatrix} 1/ \sqrt{\lambda_1}     &  0      \\ 0             & 0 \end{bmatrix} $$(5)

Plugging (4) and (5) into (3), we obtain:

$$\left \lfloor \partial {\xi} \ \partial {\eta} \right \rfloor J_{\beta}^T$$ $$\begin{bmatrix} \lambda_1     &  0      \\ 0             & 0 \end{bmatrix} J_{\beta}$$ $$\begin{bmatrix} \partial_{\xi} u           \\ \partial_{\eta} u            \end{bmatrix} $$ $$+ \left \lfloor 0 \ e \right \rfloor J_{\beta}$$ $$\begin{bmatrix} \partial_{\xi} u           \\ \partial_{\eta} u            \end{bmatrix}=g $$

$$\left \lfloor \partial {\xi} \ \partial {\eta} \right \rfloor \begin{bmatrix} 1/ \sqrt{\lambda_1}     &  0      \\ 0             & 0 \end{bmatrix}$$ $$\begin{bmatrix} \lambda_1     &  0      \\ 0             & 0 \end{bmatrix} \begin{bmatrix} 1/ \sqrt{\lambda_1}     &  0      \\ 0             & 0 \end{bmatrix}$$ $$\begin{bmatrix} \partial_{\xi} u           \\ \partial_{\eta} u            \end{bmatrix} $$ $$+ \left \lfloor 0 \ e \right \rfloor J_{\beta}$$ $$\begin{bmatrix} \partial_{\xi} u           \\ \partial_{\eta} u            \end{bmatrix}=g $$

The above equation is:

$$u_{\xi \xi} - u_{\eta} =g$$, which is exactly we want.

title: User:EGM6322.S09.TIAN


text:
User:Baurairakesh

Hi this is RAKESH BAURAI

HERE FOR THE QUEST OF KNOWLEDGE --Baurairakesh 03:08, 6 February 2009 (UTC)

title: User:Baurairakesh


text:
User:Until It Sleeps

Ohai! You've probably seen me down at Wikipedia, which is where I spend the vast majority of my time. I'll come here occasionally though.

title: User:Until It Sleeps


text:
Template:What

[ what? ]

title: Template:What


text:
User:Until It Sleeps/signature.css

 Until It Sleeps

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User talk:Augur~enwikiversity

Welcome
Hello Augur, 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
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Welcome
Hello Until It Sleeps, 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
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Welcome
Hello Kevinborja, 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
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Welcome
Hello Baurairakesh, 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
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Welcome
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 Hello IbrahimShareef, 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

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User talk:Hillgentleman/20090206041513

You are welcome!
20090206042318
 * Comments:

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 * reply[]

What links here

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User talk:Metroid690~enwikiversity

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Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Metroid690. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Metroid690~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

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User talk:Hillgentleman/20090206

Deletionism
deletionism can "make a smaller part of wikiversity more orderly" <-- Yes, "make things orderly" is part of what we do, but it has to be balanced against other things. Learning, exploration, discovery, discussions, research and education are often messy processes. If an editor, acting in good faith, makes a contribution to Wikiversity then we should first try to build upon that contribution, not show that our first reaction is an attempt to destroy that contribution. --JWSchmidt 20:47, 9 September 2008 (UTC)

 * Thanks, guys. Hillgentleman|Talk 16:09, 11 September 2008 (UTC)
 * Just thought I'd clarify. The Jade Knight 07:59, 12 September 2008 (UTC)

 * In my practice as an educator, if a student submits a problematic piece of work (no matter how appalling), I ask them to substantiate their remarks with evidence and reasoning. This is the Maieutic Method, introduced into the education culture by none other than Socrates, himself.  If the student has no concept of evidence-based reasoning, then the Maieutic Method further engages the student in step-by-step construction of the evidence-driven reasoning process.  —Moulton 13:47, 12 September 2008 (UTC)

Re: blocking John
It's really just to give us some time to breathe and start discussing. John tends to dominate discussions because he has time and zeal, and we really need to have some discussions to get the project back on track. I'll lift the block when I feel he's ready to talk, but he needs some time.

I'm completely aware of how ugly this whole thing is, but it really is the right thing to do. --SB_Johnny talk 23:17, 19 September 2008 (UTC)

 * Hi Hillgentleman, you're right to be concerned. I do endorse those actions and comments - as I have been working closely with the other bureaucrats on these matters for the last week or so. But I can assure you that none of us feel that this is an ideal situation. It must be very confusing for people who are not following IRC 24/7, and who have not been following all the activity documented in John's review. As SB_Johnny says above, John's block is a temporary measure to allow the wider community to have input on issues arising from the past month or so. And this will be happening on-wiki - we have simply been too swamped to be able to do this in anything like an ideal, wiki-like manner. Cormaggio talk 09:18, 22 September 2008 (UTC)

Wicked. -- Jtneill - Talk - c 07:32, 29 September 2008 (UTC)
 * Tx to your help, I got it working : Social psychology (psychology)/Participants. My next challenge: adding in the sizes of each user's subpages. Of course I could add them manually. Do you know of a better way? -- Jtneill - Talk - c 10:09, 29 September 2008 (UTC)
 * Ask your students to do it themselves and give them extra credits. Hillgentleman|Talk 10:20, 29 September 2008 (UTC)
 * Tx for this & esp. the subpages link suggestion for the SPP/Participant - it works nicely. -- Jtneill - Talk - c 09:31, 30 September 2008 (UTC)

Curriculum Vitaes
In this thread, you write of the importance of posting one's Curriculum Vitae, as a means of disclosing one's credentials and bona fides. I agree with the importance of providing an accurate CV. As you know, I am also concerned with the unseemly practice of adversarial editors (i.e. those representing other schools of thought) tampering with or otherwise redacting an authentic scholar's CV. To my mind, it is corrosive of an academic culture when a participant who arrives at Wikiversity with no recognizable identity as a bona fide scholar and no published CV undertakes to tamper with, redact, or otherwise deface the CV of a bona fide scholar affiliated with bona fide institutions of higher learning. It is further infuriating when the custodians of WV, who frankly should know better, disrupt the process of sober scholarly review by binding and gagging authentic scholars from well-known institutions of higher learning while willfully ignoring the authentic questions placed before them. —Moulton 12:45, 30 September 2008 (UTC)

 * There is a problem, however, that some wikiversitians/wikimedians may consider Moulton a "rogue" scholar. The importance of a link to a personal blog in a CV is, in at least the minds of some concerned people, less than the risk of privacy violation.  (You claimed that there is nothing in your blog that violates the foundation privacy principles; some claimed that there is.   I am not yet sure what the truth is.  Hopefully the truth will out. ) Hillgentleman|Talk 13:19, 30 September 2008 (UTC)

 * If they have such a thesis, Hillgentleman, let them present their views in a fair review, supported by evidence, analysis, and reasoning.

 * As to my credentials as a scholar, I graduated in 1968 from the University of Nebraska with High Distinction, earning a BS in Electrical Engineering, where I ranked #1 in a class of 400 students in the School of Engineering.  In 1969, I earned an MSEE from Stanford University.  In 1975, I earned a Ph.D. in Systems Theory from Stanford University.  I was a Distinguished Member of Technical Staff at AT&T Bell Laboratories.

 * For the past 20 years I have been a volunteer science educator at the Boston Museum of Science. For the past nine years, I have been a Visiting Scientist in the Affective Computing Research Group at the MIT Media Lab.  I was awarded the Best Theory Paper at the 2001 International Conference on Advanced Learning Technologies.  Are those the characteristics of a "rogue" scholar?

 * Moreover, there are no privacy violations on Moulton Lava, full stop. The burden of proof is on the those who make such absurd allegations.  You asked me that question on August 12th, and I forthrightly responded to it, demonstrating conclusively that there was no such privacy violation as alleged by Jimbo Wales, who was mindlessly repeating what others had whispered to him.

 * JWSchmidt has likened the behavior of those making such absurd claims to a "red scare" reminiscent of the McCarthy era. I ask you, Hillgentlemen, have these Wikimedians no decency?  At long last, have they no integrity or decency?

 * Moulton 13:57, 30 September 2008 (UTC)

huh?
huh?Emesee 02:30, 7 October 2008 (UTC)

Photo licensing
Hi Hillgentleman - yes, it's always worth contacting the author of a photo to see if they can set it free. :-) Some links that might be helpful to you would be on permissions: w:Wikipedia:Example requests for permission (sample emails for this kind of thing), and w:Wikipedia:Confirmation of permission. Links about licencing include: commons:Commons:Licensing and commons:Commons:First steps/License selection - though I'm still not sure they're as user-friendly as they should be (given that copyright can be so confusing). I'd say you should recommend a dual-licence (maybe GFDL & CC-BY-SA) for ease of reuse. If you think the links above (or others you find) are too complicated, you can explain the absolute basics in your email - without scaring him off, obviously! One last thing to bear in mind is not to point at too many WMF projects - maybe Commons would be the best project to link to (including help pages), since that's probably where our images should be. Ok, hope that helps - thanks for taking the time to do this. Cormaggio talk 09:02, 13 October 2008 (UTC)

noindex
Can I ask if you have a specific reason for using the magic word directly rather than in an easily accountable way? – Mike.lifeguard | @en.wb 03:12, 16 October 2008 (UTC)
 * Yes, you can. It is my talk page and I organise it the way I like.  But if you really want to know, I don't like redundant templates, and then noindex means noindex, and a "whatlinkshere" is still an index.  Thanks for asking. Hillgentleman | //\\ |Talk 03:22, 16 October 2008 (UTC)
 * I wonder whether you see an issue with this "index" (or indeed Special:Search/noindex) then? While I agree that your userspace is yours to do with as you will (within community norms), I would still like to understand your rationale, since I've never encountered anyone who expressed anything other than full support for using the magic word in an accountable way. The magic word is to stop search engines from indexing certain sensitive pages, and (I think) should be used in a conservative and open way. Using a template increases transparency while maintaining identical functionality. – Mike.lifeguard | @en.wb 18:13, 16 October 2008 (UTC)
 * A user talk page is not a learning resource and it serves no educational purpose for google to index it. I have said enough.  I have never encountered anyone who insisted so much on using a template on my talk page.  Have a good day. Hillgentleman | //\\ |Talk 05:32, 17 October 2008 (UTC)

Wikiversity: scope (versus?) organisation
"he has been trying to make wikiversity more accessable and useful to more people" <-- "more people"? More than what? In my view, Wikiversity is still embryonic, with 99.9999% of its form, content and participants yet to be seen. Seven years after its start, Wikipedia is still struggling to understand and reduce barriers to participation. I have spent years thinking about where wiki content comes from and the barriers that keep people from editing wiki websites. In my view, it is people like McCormack who are the main barrier to wider participation in wikis in general and at Wikiversity in particular. The history of Wikipedia is the main source of information for analysis of barriers to wiki participation. It is useful to compare participation and the rate of community growth at Wikipedia and its forks. For example, compare the growth of Wikipedia to the growth of Citizendium. Citizendium is somewhere in the middle between the Nupedia model of online encyclopedia production and the Wikipedia model. Nupedia was highly restrictive in terms of who could create content and how content was created. Wikipedia has the very open "everyone can edit" approach. Citizendium makes use of wiki technology but puts many restrictions on the content creation process. Citizendium has a very limited scope compared to Wikipedia and it will never do what Wikipedia can do. Yes, Citizendium will also do some things that Wikipedia cannot do, but if our concern is the involvement of "more people" then it is clear that Wikipedia will always have much higher rates of participation and content creation than a restrictive project such as Citizendium. McCormack wants Wikiversity to be a restrictive wiki built on a Citizendium-like model. He imagines that a few educators should control the creation of content at Wikiversity in the same way that Larry Sanger selects experts who control content creation at Citizendium. The problem for McCormack is that Wikiversity is a Wikimedia sister project that has the "everyone can edit" approach. McCormack worked very hard to subvert the "everyone can edit" approach and he has tried to install his approach of an "a few educators are in control" model. Of course, I challenged him and told him that I would not allow him to subvert the Wikiversity "everyone can edit" approach and he called me a troll and said he would never talk to me again. He ignored me and continued his personal mission to turn Wikiversity into a restrictive wiki that does not welcome self-identified students. When I continued to prevent him from subverting Wikiversity he put together a pile of false and distorted charges against me. Those false and distorted charges have been used to "justify" blocking, banning and de-sysoping me. I've put much thought into the questions of how to grow Wikiversity and how to get "more people" to edit at Wikiversity. My view is that Wikiversity should welcome everyone who wants to use wiki technology and we should be a center of learning about wiki and how to participate in wiki communities and we should do what we can do to help all new visitors explore their learning goals at Wikiversity. This kind of "open door policy" is what the Foundation had in mind when it approved the Wikiversity project. McCormack has never been content to work within this "big tent" strategy of the approved Wikiversity project proposal and the policies that have been developed at Wikiversity. He feels free to ignore civility and call me a troll and publish false charges against me. He feels free to ignore the deletion policy. He feels free to conspire with other custodians off wiki to get me banned, blocked and de-sysoped. Beyond his blatant violations of policy and his attempt to subvert the Wikiversity mission, I have no objection to McCormack working to facilitate the participation of educators at Wikiversity, but he has also worked very hard to prevent new visitors who self-identify as students from feeling welcomed to participate at Wikiversity....that is what I object to. In my view, as long as we keep the doors of Wikiversity wide open then the accessibility and usefulness of Wikiversity will be maximized. Yes, there is a role to be played by restrictive wikis and there are other wikis such as WikiEducator. If McCormack wants to create a restrictive wiki he should go somewhere where a restrictive model of wiki participation has been adopted, he should not try to subvert the Wikiversity mission and turn Wikiversity into a restrictive wiki where only educators are in control. I've written extensively about McCormack's attempts to destroy Wikiversity's long-standing cultural practice of welcoming new visitors who self-identify as students and how I worked to block his attempt to destroy the system we had for inviting students to participate at Wikiversity as editors. For more details, see User:JWSchmidt/Blog/19 October 2008 and the pages that are linked to from that page. "topic:" and "school:" namespaces <-- I would have welcomed McCormack's input on the problems associated with these namespaces if he had been willing to discuss the importance of content development projects at Wikiversity. As far as I can tell, McCormack objects to the idea that non-educators are free to create and participate in Wikiversity content development projects.....as he has said, if we open the door to participation then "silliness might occur". My views are totally different. I'm not afraid to let students have fun. Letting students have fun is exactly how Wikiversity will grow. Preventing students from having fun and exploring their personal learning goals will stifle Wikiversity. "how McCormack's contributions adversely affect free participation in Wikiversity" <-- A very large number of new visitors and potential participants at Wikiversity are self-identified students. It is vital to Wikiversity that we welcome self-identified students on the Main Page and that we have an efficient system designed to invite them to edit and help them participate constructively at Wikiversity. McCormack has systematically worked to disrupt the system by which Wikiversity welcomes self-identified students and invites them to participate at Wikiversity by editing and exploring their learning goals. So far I have had some luck in prevented McCormack from accomplishing some of his efforts that adversely affect free participation in Wikiversity. Many of his damaging changes to Wikiversity still stand and should be repaired. It is not clear that all the damage he has done to Wikiversity will ever be repaired. An active process of driving away long-term Wikiversity participants continues and new outsiders with no interest in the Wikiversity mission are being recruited to be custodians. "McCormack's contribution is positive" <-- Maybe some day he will delete or subvert a page that you think is of central importance to Wikiversity, call you "troll", publish a long list of false charges against you and have you blocked and de-sysoped....if so, you might attain a new perspective. Short of that, try reading what McCormack has written on wiki about his vision for restricting participation at Wikiversity. --JWSchmidt 16:36, 20 October 2008 (UTC)

For what it's worth, I agree with you, Hillgentleman (and disagree with JWSchmidt, but what else is new?) The Jade Knight (d'viser) 22:49, 20 October 2008 (UTC)

 * John, Let us look at the whether "McCormack wants Wikiversity to be a restrictive wiki built on a Citizendium-like model. He imagines that a few educators should control the creation of content at Wikiversity in the same way that Larry Sanger selects experts who control content creation at Citizendium."  Is it true? Can you show what you mean by examples?   As far as I can tell, McCormack objects to the idea that non-educators are free to create and participate in Wikiversity content development projects.....as he has said, if we open the door to participation then "silliness might occur".  <-- did you take that out of context? Hillgentleman | //\\ |Talk 23:30, 20 October 2008 (UTC)

Closure for Mike.lifeguard
Hi Hillgentleman. The policy actually asks that a b'crat close the discussion after five days (see forth step here). The questions being asked of Mike are generally about things that happened well before his probationary period, so if there were issues they should have been brought up during that period so that he could have time to work things out with whomever expressed the concerns. --SB_Johnny talk 21:36, 16 November 2008 (UTC)
 * It says after five days but it doesn't say "and not longer". Bureaucrats are not bound by this policy to terminate the discussion right now.  As the discussion is still "hot", bureaucrats should use their good judgements not to stop the discussion prematurely.  After all, we all want to be sure that Mike.lifeguard is really going to be a good custodian. Hillgentleman | //\\ |Talk 21:40, 16 November 2008 (UTC)
 * Indeed, but the 'crats may close them if they see the conversation is pretty much done and has a conclusive sentiment :-). There was a discussion on #wikiversity-en this morning between Jtniell, myself, cormaggio, and mikeu, and it seemed good to close. I'm rather under the impression that JWSchmidt will not support under any circumstances, and that there's pretty much nothing Mike could say to change his mind. It's fine to oppose, but not always fine to hold things up. You can ask for a review (darklama or erkan probably have the irc log if you want them), but you shouldn't revert... I'm un-reverting now, but feel free to continue the conversation with Mike if you're curious about something. --SB_Johnny talk 22:24, 16 November 2008 (UTC)

What is the Scope of Wikiversity?
Hillgentleman, what do you make of this?

  Is it within the scope and remit of a custodian to arbitrarily and summarily delete the work of another scholar here, without notice, without discussion, and without due process? It occurs to me that Jimbo and Darklama are jointly establishing a disturbing precedent that does not bode well for an authentic learning community.
 * 13:57, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/Archive"  (Beyond scope)
 * 13:55, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/Archive 8.9.14"  (Beyond scope)
 * 13:54, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/Ethic Models & Resource Links"  (Beyond scope)
 * 13:53, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/Meta-Wiki"  (Beyond scope)
 * 13:53, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/MetaArchive"  (Beyond scope)
 * 13:51, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/dnull1"  (Beyond scope)
 * 13:50, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/Mu"  (Beyond scope)
 * 13:49, 15 December 2008 Darklama (Talk | contribs) deleted "User talk:Moulton/NewYorkBrad's Principles"  (Beyond scope)

—Moulton 23:23, 15 December 2008 (UTC)

Forum question
Hi HG. I was thinking of setting it up so that there's a DPL list on the main forum page to track the most recently active "threads" (pages), but was just about to try to fins someone to set up the preload. commons:COM:RFCU uses more or less what I had in mind, though is it possible to have it preload the inclusion to the target page as well? --SB_Johnny talk 12:44, 4 January 2009 (UTC)

 * Hi. I am not sure I understand what you want.  What do you mean by the "inclusion" and the "target page"?  But, of course, a preload turns up only when you open a new page or a new section. Hillgentleman | //\\ |Talk 01:46, 5 January 2009 (UTC)

 * Well, if you look at the commons page, you'll see that the actual "new cases" are subpages, which are in turn included on a subpage that's in turn included on a subpage of the RFCU page. Could it be set up so that when you hit the button it not only creates the new page (the sub-sub page), but at the same time includes it on the forum page (the subpage), so that it's a one-step creation? IOW, at the same time it preloads the {page content}, it would also add {:/page content} to the subpage that shows the active threads? (I'm guessing the answer is "no", now that I think about it).--SB_Johnny talk 12:22, 5 January 2009 (UTC)

 * You can only save one page every time you press a save button. There is no way you can go around it within mediawiki (think of, not the least, GFDL!) and you may try to use e.g. a firefox macro to handle it. Hillgentleman | //\\ |Talk 12:40, 5 January 2009 (UTC)

 * Ah ok :-). I was just thinking that would be easier for new users who aren't familiar with inclusion and such. We could probably make some instructions pop up similar to how bcp3 does it if he wants to use inclusion (if it's just a list of threads, the DPL will suffice). Thanks anyway. --SB_Johnny  talk 13:05, 5 January 2009 (UTC)

 * Transclusion is an important part of mediawiki (which makes it much more powerful than knol!) and for me the best way for a beginner to learn it is to use it and look at it as it is and not to mystify it. Hillgentleman | //\\ |Talk 00:55, 6 January 2009 (UTC)

 * But, of course, you can play some tricks with templates (e.g. with the timestamp) and provide links and hints at the newly created page. Hillgentleman | //\\ |Talk 00:57, 6 January 2009 (UTC)

 * Well, let's see if something gets started using the "forum-as-learning-model" :-). If Thewinster doesn't start something, I might want to get something going along those lines about collaborative creation of hotbuttonish content... see my recent contribs on Wikipedia and you'll guess what I have in mind ;-). --SB_Johnny talk 01:24, 6 January 2009 (UTC)

title: User talk:Hillgentleman/20090206


text:
User talk:RamRod~enwikiversity

 Hello RamRod, 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! -- UntilItSleeps 04:37, 6 February 2009 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called RamRod. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name RamRod~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:48, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:18, 19 April 2015 (UTC)

title: User talk:RamRod~enwikiversity


text:
User:Apis~enwikiversity

Hi!

title: User:Apis~enwikiversity


text:
User talk:Salauwale

 Hello Salauwale, 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! --Juan de Vojníkov 08:13, 6 February 2009 (UTC)

title: User talk:Salauwale


text:
User talk:Apis~enwikiversity

 Hello Apis, 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! --Juan de Vojníkov 08:14, 6 February 2009 (UTC)

Your account will be renamed
Hello,

The developer team at Wikimedia is making some changes to how accounts work, as part of our on-going efforts to provide new and better tools for our users like cross-wiki notifications. These changes will mean you have the same account name everywhere. This will let us give you new features that will help you edit and discuss better, and allow more flexible user permissions for tools. One of the side-effects of this is that user accounts will now have to be unique across all 900 Wikimedia wikis. See the announcement for more information.

Unfortunately, your account clashes with another account also called Apis. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Apis~enwikiversity that only you will have. If you like it, you don't have to do anything. If you do not like it, you can pick out a different name.

Your account will still work as before, and you will be credited for all your edits made so far, but you will have to use the new account name when you log in.

Sorry for the inconvenience.

Yours, Keegan Peterzell Community Liaison, Wikimedia Foundation 23:28, 17 March 2015 (UTC)

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:03, 19 April 2015 (UTC)

title: User talk:Apis~enwikiversity