text:
User:CainanMartens

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

Read/Understand Sir Thomas More's book, Utopia
 * Research Component

I will research More's philosophy as displayed in the dialogue of his book. I will also research Thomas More himself and the life that he lived. I know currently that he is known to be very contradictory which makes his philosophy hard to understand. I want to know what caused him to be contradictory. I expect this to be displayed in his life style, and the environment that he was born into.
 * week 1

Research the author; Thomas More. Who is he? Where did he come from? What's his background?
 * week 2

Research the time era Thomas More grew up in. In this case the renaissance era. What were some ideas and happenings of this time?
 * week 3

Start reading Thomas More's Utopia. Read book 1 of Utopia. (finish if possible) Book 1: 52 pages. Start a journal and think critically about the views being displayed by More in his book.
 * week 4

Start book 2. Book 2: 78 pages.(Catch up and finish book 1 if i didn't in week 3.) Continue the journal, relate to the text, and work toward a conclusion.
 * week 5

Read book 2, finish book 2? Draw a first conclusion on the thoughts of Thomas More and his Utopia. (This would be a rough draft of ideas.)
 * week 6

Draw up the final conclusion on the story and it's ideas. Answer: How does it apply to modern government/society?
 * week 7

Draw final conclusion on More himself. Answer: What caused his ideas to contradict one another? Why did he choose to do this?
 * week 8

Organize conclusions in an "A to B" fashion and create note cards for presentation.

Final Presentation

 * Topic (10%)

To read and understand Sir Thomas More's Utopia, and to relate it to current events.

 * Research (20%)

<>

 * 1) Internet site:
 * 2) Book:
 * 3) Scholarly Journal:
 * 4) Other (interview, TV show,etc):

 * Your accomplishment (20%)

As it is with philosophy, it is hard to say whether or not i have moved forward or backward. I was able to read the book Utopia, and found its views to be very interesting, and worth consideration. The only achievement i know i have with no doubt in my mind, is I have pressed forward to viewing better forms of society. Before, I could see problems in systems, but would have no idea how to go about forming any of my own better versions of these systems. After reading this book, I am no longer afraid to speak of new ideals and try and form a better kind of society from my discoveries. I do not expect to write any amazing pieces of revolutionary work, but it does help me to better understand the big picture.

As i was reading the book Utopia, I became interested in many other medias that spoke about government and society. I was able to see the documentary, recommended to me by my teacher Mr. Arntson, The Power of Nightmares, which speaks of a very interesting view of a utopia. I looked back on my older readings of Plato's Republic, and began to see lines of correlation to Sir Thomas More's Utopia, and some changes as well. I looked into the life of Che Guevara, the argentinian revolutionary that played a key role in the independence fight for Cuba in the 1960s, and his view of society.

I am glad that I have done this as my "I've Always Wanted to Project" as it has opened my eyes to some broader and bigger ideas that i will now use to answer other questions that I face. At this moment i do face a question in fact, in both Plato's Republic, and Sir Thomas More's Utopia, are the citizens within these great pure societies working to stay in their land? Or fighting to get our of their land? Do people run to, or away from these societies?

 * Project Review (50%)
 * 1)What went well: I was able to read the book i set out to read, and to some extent understand the ideas presented within it. I am using these ideas to make my own new ideas, and to answer questions that may come up.  I have always been an over thinker, and I do much better when I have a direction to go in with my thoughts.  What went best in my project is that I now have some kind of direction.

 * 2)What went poorly: At times, reading all these ideas began to confuse me.  The subject at some points reached such a level that it was impossible to talk about all of the ideas to any one person.  The spectrum of my thought became so broad that i was unable to organize what i have done.  As to the answer of how to fix this?  I have no clue.  I believe it is just something natural that happens when anyone approaches such large ideas in philosophy.

 * 3)Future strategies: It is great to me that I am reading, and expanding on my idea, but i would very much like to start creating my own.  These ideas are all great, but it makes me curious where I could take these thoughts, and what i can create with them.  As Ghandi was able to use civil disobedience, i will use what i have learned.

title: User:CainanMartens


text:
Java Programming/Classes

Programs in Java are composed of Classes. A class is an object with a specified set of fields, methods, static functions organized for modular use.

Access
Objects in Java have four access levels:
 * The default is that a class is visible only within a package.
 * A public class or field is visible globally.
 * A protected class or field is visible only to the current class and its subclasses.
 * A private class or field is only accessible to that class.

Creating objects
An object within Java is an instance of a class. To create an object, you use the new operator:

An object declaration, as shown above, is a reference to an existing object. If the reference changes, it doesn't directly change or destroy the object it is pointing to.

Constructors
A constructor is a function that executes on creation of a given class. It is responsible for initializing variables to the starting state, if required.

Constructors are usually declared as public. If they are protected or private, they cannot be directly created outside the class unless you provide a factory method, or allow developers to use a different constructor.

Inheriting from classes
Java classes can inherit features from a parent class by using the extends keyword. A class can only inherit from one parent class. As a classical example, you may see the class Employee:

In another file:

If a child class uses a constructor, it can choose any constructor in the parent class by using the super keyword. This must be done within the first statement of the constructor.

Child classes have full access to the parent's public and protected fields and methods. Anything private is exclusive to the parent class and cannot be removed directly.

Abstract classes
Discussed later are abstract classes:

Abstract classes are declared similarly to regular classes, but unlike normal classes, cannot be instantiated directly. They are only created through subclasses that implement all abstract methods.

Multiple classes in a file
Under normal java programming, classes are normally located within a file of their own. For example, the Employee class should be found in Employee.java, and the manager class should be found in Manager.java. In rare cases, you may have a reason to include both classes into a single file.

There are two ways to do so. The first involves listing the classes one after another:

In this style, only the first class file may be declared public. All following classes must use default access (where only classes in the same package may access it.)

Nested classes have one class contained entirely in another, and may either be static or inner. A static class is not associated with the outer class instance, while an inner class maintains this association.

In this context, the inner class is declared private, but it can still be accessed by the Outer class. Ouside the Outer class, it is not accessible.

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

title: Java Programming/Classes


text:
User:MajoryGhalami

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

Perform Environmental Cleanup of Everett's Delta View Neighborhood
 * Research Component

Everett Washington's American Smelting Company/Adopt a Highway Program
 * week 1

Select section of Delta Neighborhood to adopt for clean-up/ discover methods of "adoption"
 * week 2

Contact Parks and Recreation for guidelines and legalities, research histories of clean-up organizations
 * week 3

Walk the area, photograph the area for "before" images, and organize my strategy for clean-up
 * week 4

Solicite contributions for litter containers/tools and protective garments
 * week 5

Make and post fliers informing neighbors of my "adoption"
 * week 6

Schedule sections for clean-up and gather information regarding recycling and disposal, research history of recycling organizations
 * week 7

Begin clean-up and segregation of collected materials, research individuals,groups and organizations formed that clean up large areas such as the Mississippi River
 * week 8

End clean-up, go over the areas for any missed items and inform organizations of discoveries such as road kill and larger items like tires. Photograph collected litter,count unique items,weigh similar items for weight totals/catalog #'s and then dispose/recycle. Compile personal experience/findings, data and research material in a respectable format for presentation

Midterm Assignment 1: Taste & Aesthetics
The Schubert Sonata sculpture was the only one I was able to see in person due to the weather. Thinking back on it now it was a disturbing sight. I think my opinions of it might be impure since I was in a rather foul mood beforehand. But I stepped underneath its outreaching appendages and surveyed its entire being. I might just be adverse to its color scheme and overall shape. It looks like a tree branch and something resembling scraps from a junk yard. It hadn't improved my mood.

Its supposed to symbolize undulating melodic notes to the gentle breezes. I suppose its brownish hue is in honor of some bass quality of sound and perhaps a ripling sensation of notes. The entire structure looks ready to topple any second, its center of balance so like a dish atop the end of some stick. Trying to respresnt music, but all I see is a hulk of stiff cold brown that, in no way, seems able to gently sway in the breeze. Its like a spinning top spinning slower and more unsteady by the second that when buffeted against by Seattle's gales would would sooner have its top heavy bits at its feet.

The work is dead to me. I don't think I feel anything for it. It feels like a mockery of sound. I think that's all I can say about it. I think I just dislike brown. It could have once been silver who knows but as it is... just not working.

After reading its description and what the symbology behind its shape represented I began to understand where it was coming from or going to. Although my eyes still find it repulsive I feel a tinge of respect for what its attempting to represent. After 18 years it remains standing.

Final Presentation

 * Topic (10%)

<<Delta Neighborhood Cleanup, goal: To contribute to the overall cleanup efforts of the Delta Neighborhood located on the northeastern tip of Everett Washington. My contribution was to do a cleanup of a portion of lands exterior to the perimeters of private property within a four block radius of my apartment (sidewalks, gutters, alleys, vacant lots, parks, and any other uninhabited surface).

This project was initiated when I noticed that the city had installed a large sign "The DELTA Neighborhood" outside of my apartment. A few days after that, a construction crew began installing a tree lined median that started a few blocks south of the sign and continued north through the northeastern tip of Everett. My family informed me that many years ago our neighborhood was the site of a historic smelter that was torn down in the early 1900's, the land quarantined as contaminated throughout the remainder of the century, cleaned up, and sold to a private developer who then built modern residential appartments and "old folks housing".

This activity caused homeowners within the neighborhood to upgrade the exteriors of their dwellings in order to compete with the area's rising property values. Some homes within the neighborhood are multi-family dwellings and the upkeep of their lands has not been as consistent as those with single families. So, every few houses there may be an occurance of litter, abandoned personal items, unkept lawns, etc. This situation kept the neighborhood with an overall ragedy look. My goal was to contribute to the elimination of this problem. I decided to pick up and dispose of waste materials being overlooked by the city.

 * Research (20%)

<>

 * 1) Internet site:

Public Participation Plan http://www.ecy.wa.gov/programs/tcp/sites/asarco/asarco_archive/psp_purch_cd/Everett%20Smelter/Exhibit%20E%20Public%20Participation%20Plan.pdf

 * 2) Book: Des Chenes, Elizabeth, ed. Garbage and Recycling. Christine Nasso. Print.
 * 3) Scholarly Journal:
 * 4) Other (interview, TV show,etc):book - Pregracke, Chad, and Jeff Barrow. From the Bottom Up One Man's Crusade to Clean America's Rivers. Washington D.C.: National Geographic, 2007. Print.

 * Your accomplishment (20%)

<> I succeeded in my clean-up of the Delta Neighborhood. I knew I'd be unable to remove every single peice of litter but the bits taunting me I made quick work of. Despite the cold and my lack of excersize I was able to do much more than I had first thought. Once the large obnoxious garbage was cleared finding enough to fill the gaps in the bags was rather easy as soon as I looked harder.

 * Project Review (50%)

 * 1)What went well - Found plenty of litter to gather and unexpected items like a Pocky stick box that is now a staple of litter pick-up in my eyes. Got a few statements of appreciation from passersby and property owners. Few even exchanged words with me regarding their own efforts to help keep the neighborhood up. I hadn't expected to receive so much gratitude. All in all I collected 5 garbage bags worth. Booyaka!

 * 2)What went poorly - I couldn't go too deep in the lawns of private poperty. Even though big objects were easy to see I fear I missed quite a bunch of buried trash and things hidden by leaves or too deep within thorny bushes. I regret that the animals living in those untouched areas must continue to suffer. I neglected a couple steps in my planner, those being the intentions to gain disposal information from Adopt a Highway and such organizations, as well as adopting anything as was my first intention. Due to procrastination I ended up disposing the bags in the local bin, without sorting the individual items, which on an environmental level negates the entire point of performing a clean-up. And I have yet to contact those that remove bird carcases and diapers in alleyways. I wonder which came first.  The last step of weighing and cataloging the garbage was ignored.

 * 3)Future strategies - I would like to perform the clean-up sooner than at the last minute. Early collaboration with a clean-up

organization would have prevented me from resorting to a land fill bin. I would like to involve the community in a large scale effort.

Self-Assessment
About Gen Ed; I have found that I have gathered some skills or am at least conscious or their application sometimes. I find myself catching the fallacies of the random speaker here and there. And due to the particular ones I found on its focusing assignment tend to hear the Allness factor most often. You suddenly favor blue thus you notice blue cars every which way you go.

Honestly I can not remember much else about the class from the top of my head. And I do not have my notes with me. But I am sure that after reviewing them the true spell this class has woven will be unveiled. I am sure I gathered much more than fallacies despite not trusting her brain to remember details exactly and enscribing everything, even the names of friends known for years, onto parchment. My brain betrayed me just the other day causing me to misinterpret the due date of my 2D-Design assignment. Confound it all!

I really enjoyed your teaching methods and liked your sense of humor. As far as helping the students realize the points they'd try to verbalize and form in their minds, you have a strong mind-reading ability. I'd like to add, without intending to offend, that the first imppresion of you was a look alike of Jim Carry, or that he is YOUR look alike. One of you shares the other's voice.

I suppose that is it. Thankyou for your time Steven. I would like to partake in sounding a consertina one day.

Do enjoy your break!

Final presentation; I think I did well despite my procrastination. I had ended up doing the actual clean-up on sunday. And I did not find much interest in the other sources I'd found or much use. I was mainly looking for something to stick on the page for that part. Sources have never been easy for me to find. Though I regret I was too nervous to remember the finer points of my research. I was planning on presenting with the enthusiasm others say I have for environmental topics, but that rant was left out.

I feel there was alot of gibberish being said and alot of not what I wanted being said. Rather dissapointing for I usually handle presentations with confidence not stutters and umms every other word. But my grade will reflect the effort I put into it. You get what you work hard for. But thankyou for putting up with that rather uninformative drabble. I hope I managed to convey something to you and the class.

As far as how the presention went in good terms, I lasted for almost 10 minutes. I thought I had too little information, turns out I didn't have enough time. I think my projection was adequate. Drama class taught me one thing.

I am not too sure what else to put here. I can't say that I won't procrastinate next time. I hadn't even learned my lesson when it caused me to repeat a class during summer. But I digress, I am glad about the overall product, not pleased about some parts and leaning towards mostly dissapointment. But I think going up there at all is better than not being ready and alotting to present the next week or skip the assignment alltogether. I am proud that I did complete it for the most part.

I am, deffinately, not using my ironwill care of the planet next time as a motivator to clean my neighborhood. Hypocricy till the end with me. I can not ask you to forgive me. I will likely disobey your advise again. But I hope, next time, I remember that cleaning up the environment is not fun and being in front of the desecration of my world only makes me angry and in even more of an incoherant frame of mind to do something about it.

But I do surprise myself: one day I might catch on.

title: User:MajoryGhalami


text:
User:KenH~enwikiversity

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

<>
 * Research Component

<>
 * week 1

Search where to buy a basic camera and find material I needed.
 * week 2

Read though the study Guide, and search information about the film develop.
 * week 3

Practice for first time taking photo in my room.
 * week 4

Sec week taking photo around Seattle or everything I have surround me.
 * week 5

Third week taking photo around Seattle or everything I have surround me.
 * week 6

Choose the best photo I have and develop it.
 * week 7

To put everything in order.
 * week 8

It's time to get ready for the presentation

Midterm Assignment 1: Taste & Aesthetics
Last Tuesday I went to the Olympic Sculpture Park. I found out the park has really good environment. I couldn’t see a lot of sculpture there maybe because of distance is too far from another sculptures. It’s really comfortable when I waking inside of park and I started to see more Sculptures around the park. However, I started to interpret every detail of a Sculpture. Most of Sculpture has huge volume, and I was trying to find out the art work which I don’t think is art work. I almost spent 15-20 mines on the researching. Finally, I found out the one i felt like doesn’t an art work. He used a frame with wood made for the construction by the way I noted down the information of the artiest. After I got home, I did a little bit research about it. I found out this Sculpture called Bunyon's Chess, and born in 1965 made by Mark di Suvero,At the moment, I don’t really understand that why it’s called Bunyon’s chess and how its going to do with the chess. I kind of clear up why that is when I read though the information. This sculpture like broad brushstrokes drawn in space, a vocabulary that was radically new in sculpture at the time it was made. Created specifically for outdoor presentation in Seattle. Moreover, I think that many sculpture looks weird and strange when you first time see them but if you do some reaseach about it, you may understand the significance of the art.

Midterm Assignment 2: Manipulation
http://www.youtube.com/watch?v=nN2dZHbPUsg&feature=related

Final Presentation

 * TOPIC (10%)

<< BASIC PHOTO>>

 * Research (20%)

<>

 * Your accomplishment (20%)

<< I love it I got some of good photos around Seattle >>

 * Project Review (50%)
 * 1)Everything went very well, I took some good photos in Larsen lake and Downtown Seattle.
 * 2)Its really hard to take photos with raining day.

title: User:KenH~enwikiversity


text:
User talk:Emil.fabic

 Hello Emil.fabic, 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
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 * 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! --Mu301Bot 07:17, 6 October 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 6 October 2009 (UTC)

title: User talk:Emil.fabic


text:
User talk:Tinystu

 Hello Tinystu, 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! --Mu301Bot 07:18, 6 October 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:18, 6 October 2009 (UTC)

title: User talk:Tinystu


text:
User talk:Budisantoso ms

 Hello Budisantoso ms, 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! --Mu301Bot 07:18, 6 October 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:18, 6 October 2009 (UTC)

title: User talk:Budisantoso ms


text:
User talk:Donlaporn

 Hello Donlaporn, 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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 * 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! --Mu301Bot 07:19, 6 October 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:19, 6 October 2009 (UTC)

Twitter faceoff
1. Facebook and Twitter are same because both of them are social network. Many people use them to contact with their friends. Moreover, many famous people and organizations use them in order to talk with their fans.

2.Facebook should worry about twitter because twitter is quicker response than facebook.

operating system
'Different types of operating systems: 1. Microsoft Windows plays a very big role in the market of personal computers by 91%. Also, there are nine main versions of Microsoft Windows, which are Windows’95, Windows’98, Windows’ 2000, Windows NT, Windows ME, Windows XP, Windows CE, Windows VISTA, and Windows 7. 2. Linux is usually used to install in embedded systems, mobile phones, some kinds of watches, desktop computers, laptop computers, netbooks, and supercomputers. Nowadays, Linux has been used to be an operating system in netbooks with the two kinds of devices, which are ASUS Eee PC and Acer Aspire One. Brazil, Russia, China, India, Spain, France, and Germany has been using Linux for various kinds of purposes. For example, Linux has been developed to be used in educational organizations and other official organizations. 3. Mac OS X has been developed and owned by Apple Inc. Mac OS X became the second most famous operating system in 2009 in terms of the usages of the Internet connection. Also, Mac OS X includes many different languages. For example, English, Japanese, French, German, Spanish, Portuguese, and Italian are available. There are four main types of operating systems, which are “Real-time Operating Systems”, “Single-User/Single-Tasking Operating Systems”, “Single-User/Multitasking Operating Systems”, and “Multi-User/Multitasking Operating Systems”. •	The first type of operating system is “Real-time Operating Systems” or “RTOS”. RTOS is also known as Embedded Operating Systems. A real-time operating system runs real-time application. Also, a real-time operating system support only single-tasking. A real-time application is an application that responses to the input extremely fast. BeOS, ChorusOS, eCos, FreeRTOS, ITRON, LynxOS, MicroC/OS-II, Nucleus, Nut/OS, OS-9, OSE, OSEK/VDX, OSEKtime, pSOS, QNX, RMX, RSX-11, RT-11, RTOS-UH, VRTX, VxWorks, Windows CE, RTLinux, and RTAI are examples of Real-time Operating Systems. Real-time applications are used in medical diagnostics equipment, life-support systems, machinery, scientific instruments, and industrial systems. •	The second type of operating system is “Single-User/Single-Tasking Operating Systems”. This type of operating system allows users to run a single task at a time. Printing a document, writing a file to disk, editing a file, and downloading a file from a network server are examples of task for a computer user. A small and simple operating system can manage only a time. MS-DOS is an example of single-user/single tasking operating systems. This type of operating system is usually found in the Palm handheld computers. •	The third type of operating system is “Single-User/Multitasking Operating Systems”. This type of operating system allows users to run many tasks at a time. Microsoft Windows and the Macintosh Operating System are the examples of this type of operating system. This type of operating system is usually found in personal computers. Also, it can be used in various kinds of work. •	The forth type of operating system is “Multi-User/Multitasking Operating Systems”. This type of operating system allows users to run on a terminal server. Each user’s applications run within their user session on the server separate from all other user sessions. A terminal client is the software that makes a user session possible. UNIX, VMS, and MVS are examples of multi-user/multi-tasking operating systems. MVS is used in mainframe operating systems. What operating systems should install on your netbook? The operating system that should install for netbook is Windows 7

title: User talk:Donlaporn


text:
User talk:Tangnida

Enjoying having you in class as well Icns141 13:06, 18 October 2009 (UTC)

title: User talk:Tangnida


text:
User talk:Malika~enwikiversity

 Hello Malika, 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! --Mu301Bot 07:19, 6 October 2009 (UTC)

Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:19, 6 October 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 Malika. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Malika~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 23:37, 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) 06:15, 19 April 2015 (UTC)

title: User talk:Malika~enwikiversity


text:
Power Generation/Hydro Power/Part6

it is imp part of the power plant

title: Power Generation/Hydro Power/Part6


text: File:PEW 5-10-2009.pdf

title: File:PEW 5-10-2009.pdf


text: File:PEW 28-9-2009.pdf

title: File:PEW 28-9-2009.pdf


text:
User talk:Segicollege

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 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.

title: User talk:Segicollege


text:
User talk:MaartenO

 Hello MaartenO, 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! --Gbaor 14:35, 6 October 2009 (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.

title: User talk:MaartenO


text:
User:Egm6321.f09.Team1.andy/HW3

= Problem 9: Finding solution to Homogeneous L2-ODE-VC =

Given
A Homogeneous L2-ODE-VC is given by
 * {| style="width:100%" border="0" align="left"

x^2y_{xx} - 2xy_{x} + 2y = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

where

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

\begin{align} & x = e^t \\ \Rightarrow & \frac{dy}{dx} = \frac{dy}{dt}\frac{dt}{dx} \\ \Rightarrow & \frac{dy}{dx} = e^{-t}\frac{dy}{dt} \\ \Rightarrow & y_x = e^{-t}y_t \end{align} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * $$\displaystyle (Eq. 2)
 * }

and so,

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

\begin{align} \Rightarrow & y_{xx} = e^{-2t}(y_{tt} - y_t) \end{align} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

Find
To show that,

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

y_{xxx} = e^{-3t}(y_{ttt} - 3y_{tt} + 2y_t) $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

and

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

y_{xxxx} = e^{-4t}(y_{tttt} - 6y_{ttt} + 11y_{tt} - 6y_t) $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Solution
Part 1:

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

\begin{align} y_{xxx} & = \frac{d}{dx} (y_{xx}) \\ & \Rightarrow \frac{dt}{dx} \frac{d}{dt} (y_{xx}) \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

From Equations (2) and (3),

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

\begin{align} y_{xxx} & = \frac{dt}{dx} \frac{d}{dt} \left[e^{-2t}(y_{tt} - y_t) \right] \\ & \Rightarrow e^{-t} \left[-2e^{-2t}(y_{tt} - y_t) + e^{-2t}(y_{ttt} - y_{tt}) \right] \\ & \Rightarrow e^{-3t} \left[-2y_{tt} + 2y_t + y_{ttt} - y_{tt} \right] \\ \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

and the solution,

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

$$\displaystyle \Rightarrow y_{xxx} = e^{-3t}(y_{ttt} - 3y_{tt} + 2y_t) $$ $$
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * $$\displaystyle (Eq. 4)
 * }
 * }

Part 2:

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

\begin{align} y_{xxxx} & = \frac{d}{dx} (y_{xxx}) \\ & \Rightarrow \frac{dt}{dx} \frac{d}{dt} (y_{xxx}) \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

From Equation (4),

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

\begin{align} y_{xxxx} & = \frac{dt}{dx} \frac{d}{dt} \left[e^{-3t}(y_{ttt} - 3y_{tt} + 2y_t) \right] \\ & \Rightarrow e^{-t} \left[-3e^{-3t}(y_{ttt} - 3y_{tt} + 2y_t) + e^{-3t}(y_{tttt} - 3y_{ttt} + 2y_{tt}) \right] \\ & \Rightarrow e^{-4t} \left[-3y_{ttt} + 9y_{tt} - 6y_t + y_{tttt} - 3y_{ttt} + 2y_{tt} \right]  \\ \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

and the solution,

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

$$\displaystyle y_{xxxx} = e^{-4t}(y_{tttt} - 6y_{ttt} + 11y_{tt} - 6y_t) $$ $$
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * $$\displaystyle
 * }
 * }

= Problem 10: Finding solution to Homogeneous L2-ODE-VC =

Given
A Homogeneous L2-ODE-VC is given by
 * {| style="width:100%" border="0" align="left"

x^2y'' - 2xy' + 2y = 0 $$ $$ where
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

y' = \frac{dy}{dx} $$ y'' = \frac{d^2y}{dx^2} $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Find
Find the solution for equation (1) directly by the method of trial solution,

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

y = e^{rx} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

Compare the solution with,

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

y = C_1 x + C_2 x^2 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

with boundary conditions,
 * {| style="width:100%" border="0" align="left"

y(1) = 3 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

y(2) = 4 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }

Solution
= Problem 12: Reduction of Order Method =

Given
To solve the Homogeneous L2-ODE-VC,

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

y'' + a_1(x)y' + a_0(x)y = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

which has one solution as

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

y = u_1(x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

where the complete solution is given by,
 * {| style="width:100%" border="0" align="left"

y = k_1u_1(x) + k_2u_2(x) $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Find
To develop reduction of order method using the following algebraic expressions,

Part 1: $$\displaystyle y(x)=U(x)\pm u_1 (x)$$ Part 2: $$y(x)=\frac{U(x)}{u_1 (x)}$$ Part 3: $$y(x)=\frac{u_1 (x)}{U(x)}$$

Solution
Part 1:

Using the first algebraic expression,

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

y(x)=U(x)\pm u_1 (x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

On differentiating the Equation (3), we get the following first derivative,

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

y'(x)=U'(x)\pm u_1'(x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }

Second derivative,

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

y(x)=U(x)\pm u_1''(x) $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 5)
 * }
 * }

Using Equations (3), (4) and (5) in Equation (1),

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

y + a_1(x)y' + a_0(x)y = \left[U(x)\pm u_1''(x) \right] + \left[U'(x)\pm u_1'(x) \right] a_1(x) +  \left[U(x)\pm u_1(x) \right] a_0(x)  = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

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

\begin{align} \Rightarrow y + a_1(x)y' + a_0(x)y = & \left[U(x) + U'(x)a_1(x) + U(x)a_0(x)\right] \pm \underbrace{\left[u_1''(x) + u_1'(x)a_1(x) + u_1(x)a_0(x) \right]}_{=0\ as\ per\ Eq(2)} \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

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

\begin{align} \Rightarrow y + a_1(x)y' + a_0(x)y = & \left[U(x) + U'(x)a_1(x) + U(x)a_0(x)\right] = 0 \end{align} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

In the above equation, the dependent variable U(x) is present and not missing. The Reduction of Order Method is possible only when dependent variable is missing.

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

So, assumption that $$\displaystyle y(x)=U(x)\pm u_1 (x)$$ as full homogeneous solution for Equation (1) is incorrect.
 * style="width:70%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }
 * }

Part 2:

Using the second algebraic expression,

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

y(x)=\frac{U(x)}{u_1 (x)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * }
 * }

On differentiating the Equation (6), we get the following first derivative,

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

y'=\frac{U'u_1 - Uu_1'}{u_1^2} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)
 * }
 * }

Second derivative,

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

y =\frac{1}{u_1^2}(U'u_1' + Uu_1 - Uu_1'' - U'u_1') - \frac{u_1'}{u_1^3}(U'u_1 - Uu_1') $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)
 * }
 * }

Using Equations (6), (7) and (8) in Equation (1),

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

y + a_1(x)y' + a_0(x)y = \frac{U}{u_1}a_0 + \left[\frac{U'}{u_1} - \frac{U'u_1'}{u_1^2}\right] a_1+ \left[\frac{U}{u_1} - \frac{Uu_1''}{u_1^2} - \frac{U'u_1'}{u_1^2} + \frac{Uu_1'^2}{u_1^3}\right]  = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

In the above equation, the dependent variable U(x) is present and not missing. The Reduction of Order Method is possible only when dependent variable is missing.

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

So, assumption that $$\displaystyle y(x)=\frac{U(x)}{u_1 (x)}$$ as full homogeneous solution for Equation (1) is incorrect.
 * style="width:70%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }
 * }

Part 3:

Using the third algebraic expression,

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

y(x)=\frac{u_1(x)}{U(x)} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }

It is obvious from the above Part 2 section, if we let $$U(x) = u_1(x)$$ and $$ u1(x) = U(x)$$, then the same argument holds that Equation (9) cannot be used as a full homogeneous solution for Equation (1). Following is the derivation, anyways.

On differentiating the Equation (9), we get the following first derivative,

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

y'=\frac{u_1'U - u_1U'}{U^2} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 10)
 * }
 * }

Second derivative,

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

y =\frac{1}{U^2}(u_1'U' + u_1U - u_1U'' - u_1'U') - \frac{U'}{U^3}(u_1'U - u_1U') $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 11)
 * }
 * }

using Equations (9), (10) and (11) in Equation (1),

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

y + a_1(x)y' + a_0(x)y = \frac{u_1}{U}a_0 + \left[\frac{u_1'}{U} - \frac{u_1'U'}{U^2}\right] a_1+ \left[\frac{u_1}{U} - \frac{u_1U''}{U^2} - \frac{u_1'U'}{U^2} + \frac{u_1U'^2}{U^3}\right]  = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

In the above equation, the dependent variable U(x) is present and not missing. The Reduction of Order Method is possible only when dependent variable is missing.

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

So, assumption that $$\displaystyle y(x)=\frac{u_1(x)}{U (x)}$$ as full homogeneous solution for Equation (1) is incorrect.
 * style="width:70%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }
 * }

= Problem 13: Using given trial solutions to solve function =

Given
Given the following homegenious L2_ODE_VC
 * {| style="width:100%" border="0" align="left"

(1-x^2) y''-2xy'+2y=0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 1)
 * }
 * }

The two test trial solutions are
 * {| style="width:100%" border="0" align="left"

y=ax^b $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 2)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

y=e^{rx} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 3)
 * }
 * }

Find
Find $$u_1(x)$$ and $$u_2(x)$$ of Eq. 1 using two given trial solutions. Compare it with the solution, given by reduction of order method 2,

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

u_1=x $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 4)
 * }
 * }

and

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

u_2=\frac{x}{2}log_e\left(\frac{1+x}{1-x}\right) - 1 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 5)
 * }
 * }

Solution
Part 1:

With the trial solution,

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

y=ax^b $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

The derivatives are,

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

y'=abx^{(b-1)} $$  $$  y''=ab(b-1)x^{(b-2)} $$  $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 6)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 7)

 * }

Substituting Equations (2), (6), and (7) in Equation (1),

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

\Rightarrow (1-x^2)ab(b-1)x^{(b-2)} - 2xabx^{(b-1)} + 2ax^b = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

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

\Rightarrow ab(b-1)x^{(b-2)}-ab(b-1)x^b - 2abx^b + 2ax^b = 0 $$  \Rightarrow ab(b-1)x^{(b-2)}-\left[ab(b-1) + 2ab - 2a \right]x^b = 0 $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 8)

 * }

In Equation (8), equating co-efficients of $$ x^{(b-2)}$$ ,

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

\Rightarrow ab(b-1) = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Since a and b both cannot be zero, one value of $$ b=1$$.

In Equation (8), equating co-efficients of $$ x^b$$ ,

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

\Rightarrow ab(b-1) + 2ab - 2a = 0 $$  \Rightarrow a(b^2+b-2) = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle

 * }

Again $$ a$$ cannot be zero, so $$ b =1,-2$$.

Therefore,

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

\Rightarrow u_1(x) = ax $$ \Rightarrow u_2(x) = \frac{a}{x^2} $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle

 * }

So, the trial solution,

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

\Rightarrow y = k_1u_1(x) + k_2u_2(x) $$  \Rightarrow y = K_1x + K_2\frac{1}{x^2} $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Using the boundary conditions,

 * {| style="width:30%" border="0" align="left"

y(\frac{\pi}{2\sqrt{2}}) = 1 $$  $$\displaystyle and $$ $$\displaystyle y(\frac{\pi}{\sqrt{2}}) = 2 $$  We arrive at,
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

 * {| style="width:30%" border="0" align="left"

K_1 = \frac{2\sqrt{2}}{\pi} $$  $$\displaystyle and $$ $$\displaystyle K_2 = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

The trial solution becomes,
 * {| style="width:100%" border="0" align="left"

\Rightarrow y = \frac{2\sqrt{2}}{\pi}x $$  $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 9)
 * }
 * }

Therefore,

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

u_1 = \frac{2\sqrt{2}}{\pi}x;\ and\ u_2 = 0 $$
 * $$\displaystyle
 * $$\displaystyle

 * }

Part 2:

With the trial solution,

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

y=e^{rx} $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

The derivatives are,

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

y'=re^{rx} $$  $$  y''=r^2e^{rx} $$  $$
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 10)
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 11)

 * }

Substituting Equations (3), (8), and (9) in Equation (1),

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

\Rightarrow \left[(1-x^2)r^2 - 2xr + 2\right]e^{rx} = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

$$ e^{rx}$$ cannot be zero.

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

\Rightarrow -x^2r^2-2xr + r^2 +2 = 0 $$  \Rightarrow -x^2[r^2]-x[2r] + r^2 +2 = 0 $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle

 * }

We do not have any terms on the right hand side to equate with co-efficients of $$ x^2$$ and $$ x$$, so equating the constant co-efficients,

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

\Rightarrow r^2 +2 = 0 $$  \Rightarrow r = \pm \sqrt2i $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle

 * }

The trial solution becomes,

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

\Rightarrow y = e^{\sqrt2ix} $$ \Rightarrow y = K_1 cos(\sqrt2x) + K_2 sin(\sqrt2x) $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Using the boundary conditions,

 * {| style="width:30%" border="0" align="left"

y(\frac{\pi}{2\sqrt{2}}) = 1 $$  $$\displaystyle and $$ $$\displaystyle y(\frac{\pi}{\sqrt{2}}) = 2 $$  We arrive at,
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

 * {| style="width:30%" border="0" align="left"

K_1 = -2 $$  $$\displaystyle and $$ $$\displaystyle K_2 = 1 $$  The trial solution then becomes,
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

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

\Rightarrow y = -2 cos(\sqrt2x) + sin(\sqrt2x) $$ $$ and so,
 * $$\displaystyle
 * $$\displaystyle
 *
$$\displaystyle (Eq. 12)
 * }
 * }
 * {| style="width:100%" border="0" align="left"

u_1 = -2 cos(\sqrt2x);\ and\ u_2 = sin(\sqrt2x) $$
 * $$\displaystyle
 * $$\displaystyle
 * }
 * }

Plotting solutions y1,y2,y3 respectively, from Equations (9), (12) and solution from equations (4),(5).

title: User:Egm6321.f09.Team1.andy/HW3


title: File:HW3-8.jpg


text:
User:Rileykey

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

Write a song on guitar preferably a blues style song
 * Research Component

I will research guitar history as well as the history and theory of the blues guitar style.
 * week 1

Begin song writing
 * week 2

Continue song writing/ revising and perfecting progress on song
 * week 3

Continue song writing/ perfecting
 * week 4

Start research as well as finishing up song and perfecting
 * week 5

Practice/ clean up song, continue research
 * week 6

practice/ continue research
 * week 7

practice/ create presentation materials and prep for presentation
 * week 8

practice/ finnish up presentation materials, present

Midterm Assignment 1: Taste & Aesthetics
The art piece is named Typewriter Eraser, Scale X by Claes Oldenburg and Cossje Van Bruggen. I did not like this piece because it seems so out of place compared to all of the other pieces. I did not even know what it was at first, goes to show how technology has advanced I am sure I would have known what it was if computers did not exist. It looks like an oversized makeup tool that is rolling super fast into the street! After researching the artists a little bit I learned that Claes is known for making very large sculptures of widely used things such as: a large scale lipstick on caterpillar tracks, a large clothes pin, a screw, a huge spoon with a cherry on it, a baseball bat, a large pick axe, and many more. Claes also went to The Art Institute Of Chicago; I thought that was pretty cool. Cossje got a masters degree in art history from the University of Groningen, then later joined up with Claes and moved to New York with him. Claes was born in Stockholm, Sweden in 1929 and Cossje was born in Groningen, Netherlands in 1942 and she died this year. (seattleartmusium.org) When I figured out what the Typewriter Eraser sculpture was I decided that I liked it a little more, but I still feel that it is out of place. I do like their other work though because they turned widely used objects into meaningful public art for everyone to view. My favorite piece is the giant stamp that says “free” on it.

Midterm Assignment 2: Manipulation

 * DUBIOUS AUTHORITY:
 * 1) The gecko talking about car insurance for the Gieco insurance company
 * 2) Smoky the bear talking about preventing forest fires.
 * http://www.youtube.com/watch?v=4GJlP6yPC0w&feature=PlayList&p=9C313A025D852309&index=0

 * ALLNESS:
 * 1) All cows love becoming food for humans!
 * 2) No one thinks before they speak.
 * http://www.toothpastefordinner.com/102208/everyone-likes-cats.gif

Midterm Assignment 3: Always Wanted To Progress Report (100 words or so)
> I have started writing the song on my guitar but have not made much progress on researching much about it. What i plan to do is begin vigorously researching and writing starting next week and i am sure that i will be able to produce a quality product. My research will begin this coming week, i will be able to complete this i am sure. I will most likely be paying a visit to the Experience Music Project in the near future, i hear they have a spectacular guitar section. Following the researching will be intensive song writing sessions! I currently have a bunch of pieces of a song that i am trying to put together, it should all work out awesomely.

Final Presentation

 * Topic (10%)

<>

 * Research (20%)

<>

 * 1) Internet site: T-Bone Walker first to amplify blues and bring it to a group style/ more sophisticated sounding. Charlie Christian was the first guitar player to make it clear that guitar was in fact not just a rhythm keeping back up instrument but in fact a lead instrument.

http://guitar.about.com/od/education/a/history_guitar.htm BLUES! In the 20's and 30's the slide was brought to the plate. Most blues back then was rarely ever played the same way twice, pretty much all improv. In the 40's blues started becoming a lot more organized and is thought to be the influence of modern day rock and roll and rhythm. After the electric guitar was invented, right around the end of world war 2 the Mississippi style blues was born (harmonica) witch later moved up to Chicago. B.B. King and Freddie King were also gaining popularity at the time because of their unique style of playing. during the 60's blues started to gain a lot more popularity inspiring people such as Janis, Jimi, and, Johnny Winter. http://www.bluesforpeace.com/blues-guitar-history.htm Guitars used to be strung with gut strings as oposed to metal! http://www.yeoldeguitar.com/history.html

JIMI- http://api.ning.com/files/8Rn-WjtUWcU2GSbUmwl7FrdPT5pNtV3Yhz*wrB1rVof0vi5iaGhq0AU-03owvODFKnAz3t51Jxc22lBi8u7JB8DlTDkznczr/Jimi_Hendrix_Wallpaper_1_by_JohnnySlowhand.jpg

B.B. King- http://midiblog.net/pics/b/b/-/bb-king-3-high.jpg

Eric Clapton- http://www.pit-schmidt.de/eric_clapton/covers/eric_clapton.jpg

Freddie King- http://www.bobtjeblues.com/files/images/Freddie-King.jpg

 * 2) Book:
 * 3) Scholarly Journal:
 * 4) Other (interview, TV show,etc): It is unknown where the guitar originated but it is thought to have come from ancient Egypt, Greece, or maybe even Central Asia. The frying pan guitar.  The first electric guitars were known as the frying pan guitar.

Experience Music Project

 * Your accomplishment (20%)

<> I came very close and if not that i did reach my goal, i did compose several pieces to a song and put them together. But it is not as complete as i wanted it to be.

 * Project Review (50%)
 * 1)Coming up with the idea and planning out what i was going to do to attain the goal went very well, and partly writing the song.
 * 2)I procrastinated a little bit too much on this project that was the biggest problem. I also had trouble following my planned out schedule
 * 3)Get started sooner (do not procrastinate), get more motivated, work on not getting distracted so much.

Self-Assessment
I could have done a lot better if i did not procrastinate as much as i did. But i still feel that i did a pretty good job all together.

title: User:Rileykey


text:
User:SkylarHolcomb

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

<< crafting an overarching plot line for a novel and writing a few chapters of the aforementioned novel>>
 * Research Component

<>
 * week 1

-write 1 chapter

-hammer out first quarter of plot

-acquire copy of thoreau's "civil disobedience"
 * week 2

-write 1 chapter

-hammer out first quarter of plot

-read "civil disobedience"
 * week 3

-write 1 chapter

-hammer out second quarter of plot

-acquire copy of "letter from birmingham jail"
 * week 4

-write half a chapter

-hammer out second quarter of plot

-read "letter from birmingham jail"
 * week 5

-write half a chapter

-hammer out third quarter of plot

-acquire copy of "one flew over the cuckoo's nest"
 * week 6

-write 1 chapter

-hammer out third quarter of plot

-read "one flew over the cuckoo's nest"
 * week 7

-write 1 chapter

-hammer out fourth quarter of plot

-research various texts involving themes pertaining to social commentary
 * week 8

-write 1 chapter

-hammer out fourth quarter of plot

-research various texts involving themes pertaining to social commentary

Midterm Assignment 1: Taste & Aesthetics
–                       Upon my trip to the sculpture park, there was one piece of "art" that really stood out to me. It was Anthony Caro's "riviera". At first glance I assumed that the sculpture was merely large pieces of metal haphazardly welded together in some chaotic fashion. Later visits would serve only to confirm my suspicions. Researching the man forced me to at least begrudgingly admire him. He has a nice work ethic I suppose. I was a little shocked to find out that many consider him a huge influence on modern sculpture and that he was knighted in the late eighties. So after learning of the respect this man earns the world over I returned to the sculpture park to see how I felt, desperately attempting to convince myself that perhaps he was a genius, or at least talented. I mean, I don't know how to weld. So, he had that much on me. A second viewing brought nothing but affirmation.The man's genius must be like his sculptures, perplexing, uninteresting and not worth your time. –

Midterm Assignment 3: Always Wanted To Progress Report (100 words or so)
In regards to my always wanted to assignment I would have to say that the progress i'm making is largely non-existant. My project was to write a few chapters of my book and to research social commentary. My lack of progress on the assignment is due to my lack of inspiration. Writing a book fueled by random bursts of idea of creative thought isn't necessarily the way to go. It leaves a very unreliable and random work schedule to attend to. The fact that I work in such a way only goes to show how undiciplined of a writer I am. So the plan is to take long walks into the night and to wander the seedy parts of the city until I found something to complain about in beautiful literature.

Final Presentation

 * Topic (10%)

< >

 * Research (20%)

<>

 * 1) Internet site:
 * 2) Book:Cohen, Samuel. "Letter from Birmingham jail." 50 Essays A Portable Anthology. Boston: Bedford/St. Martin's, 2006. 220-37. Print.
 * 3) Scholarly Journal:
 * 4) Other (interview, TV show,etc):

 * Your accomplishment (20%)

<> I got sort of nearly pretty close to reaching my goal. I did in fact manage to squeeze out some inspired writings over the course of the quarter, but not nearly enough and not at the rate in which I challenged myself to perform. In fact, it was drastically lower. But I do have a solid foot in the door on my novel.

 * Project Review (50%)
 * 1)What went well

I was able to write an awesome schedule that would have been doubly awesome had I followed it. But I did manage to read portions of the writings that I determined to be my research. And I'm quite satisfied with the writing that I did accomplish.
 * 2)What went poorly

What went poorly, was my assumption that I could induce sudden creativity and inspiration at will. Learning this half way through the quarter was a good lesson in disciplined writing versus undisciplined.
 * 3)Future strategies

To counter act my undisciplined writing style, I plan to just vomit words on the page when I don't feel particularly inspired. Later I will return, read them again and make suitable adjustments. This will help to increase my overall productivity.

Self-Assessment
I've thoroughly enjoyed my time in Gen ed. My initial impression, boosted by the sheer curiosity of such an odd and vague title for a class, was that it would be overtly easy and a waste of time. but as fate and destiny conspired to prove me false, I learned quite a bit. The breakdown of education and the discussion of various theories pertaining to it was fascinating. Being forced to think about what I know, how I know it, why it was taught to me, and what was decided irrelevant to my education, was a tad liberating. And the "i've always wanted to" assignment was a nice refreshing change of pace. It also taught me a few things about the way I approach such a non linear concept of homework. Plus there was a live concertina performance on the last day. i learned that something called the concertina existed, and made noise. I attempted to be successful in this class. Deciding not to go with the first impression of an ensuing relative ease, and deciding to treat it as a serious and valuable part of my college education was certainly a intelligent decision.

title: User:SkylarHolcomb


text:
ICT Literacy

Resources for learning how to use computers and the Internet:

 * Commonwealth Computer Navigator's Certificate
 * Libraries and transliteracy

Introduction
ICT Literacy covers the skills using ICT, awareness about available methods, technologies and services and Risk Literacy to operate as an informed decision maker.

Learning Task

 * (ICT Literacy) Explain the role of ICT Literacy for being an informed decision maker in the ICT driven environment. Distinguish between technology induced vulnerabilty of ICT infrastructure and human risk literacy that could create vulnerability to an ICT infrastructure. Explain those two domains are connected according to training and education.
 * (Risk Management and Risk Literacy) Analyze the Risk Management module and apply the underlying structure to ICT Literacy.
 * Identify the skill, knowledge, tools and expertise in the area of ICT that help individuals to detect Fake News and Fake Science.
 * (Devices and Knowledge) Ubiquitous mobile devices and application for different services beyond communication are used by many by the mobile device owners. Identify ICT literacy skills that are associated mainly with mobile devices and smartphones. What are skills that can be associated to any device that processes digital data (e.g. a photocopier that stores the copied data on a harddrive and the users do not know, that their copy is stored on the harddrive).

title: ICT Literacy


text:
User:Gene.arboit

fr:Utilisateur:Gene.arboit

title: User:Gene.arboit


text:
User:AndrewReynolds

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

I have always wanted to create a full mixed party mixtape/album.
 * Research Component

I will research mixtapes, mashups and DJs. My focus will be on techniques used, other DJs who have made full mixtapes, and the history of mashups/remixes. Another topic of this research I am going to get into is the legality of sampling when creating mashups/mixtapes. This is a hot issue in the music industry right now.
 * week 1

I will begin gathering ideas/songs for my mixtape. Gather study topics and resources.
 * week 2

I would like to have 15 minutes completed of mixtape. Document progresses and start researching.
 * week 3

I should be at about 22.5 minutes in the mix. Listen to other works as much as possible this week and maintain inspiration.
 * week 4

I should be at 30 minutes or more (about halfway done). Render and distribute to some friends for critiquing.
 * week 5

I should be at about 37.5 minutes. Begin working on cover, and CD front. Have all resources, spend time at the library.
 * week 6

I would like to have 15-20 completed of the mix. This week I will have all my sources gathered and will put them in MLA format.
 * week 7

Keep moving forward with the mix as best as I can. Start working on presentation part of it and begin to prepare what I will be showing the class. Continue researching the art of mashups and mixing along with the history behind it.
 * week 8

Finish up what I have done, make any edits needed, complete cover and make copies. Complete presentation. celebrate.

Midterm Assignment 1: Taste & Aesthetics
I decided that one of my least favorite was a sculpture called [“Schubert Sonata”] by artist [Mark di Suvero]. It is painted and unpainted steel created in 1992. I learned a lot about Mark and his works. I honestly didn’t think I was going to find many more sculptures or art he has done, but I was very wrong. Apparently, Mark is known and accepted as one of the world’s top modern sculptors. When looking for examples of his other works, I was able to find similar sculptures all around the world. He’s got works in many of the nation’s well known locations and museums. Although many were very similar in style, I learned quite a bit about it. I picked this one because my High School (Mt Spokane HS) had 5 statues in the courtyard, and I was very frustrated back then that the school district had spent so much money on these (what I thought were stupid at the time) statues instead of on programs in school. I couldn’t find out the artist who did those sculptures, but I did look at other metal works (such as the horse sculptures at Vantage which I have seen all so many times) and after looking at all the varieties, I did find them a bit more interesting. After doing this research, I do appreciate the sculpture quite a bit more. Mark uses the shapes to draw on shadows that they cast, and uses materials that are common place in construction. I do think it’s very cool that he can take something so common and make it into something we can recognize and appreciate as art. One thing I did learn is that this is not his only statue at Seattle’s Sculpture Park. Yes, Paul “Bunyon’s Chess” is also his (The one we were not allowed to choose). And even after this research I do not like that one. It is interesting that we can develop a liking for something (or even a deeper dislike) by educating ourselves on it. I don’t think that it’s us not being able to control our brain, but a demonstration of how we create harsh opinions so quickly with just “surface information”. All in all I have developed a better liking for this sculpture thanks to learning about it, the artist, and his other works. Seeing it after the research was most definitely different the second time.

Midterm Assignment 2: Manipulation
 False Dilemma  This ad I found is an example of false dilemma. It attempts to make you believe that your only options here are to either be miserable and take your time looking for an apartment, or use their web site and start living. There could actually be many other options. Also they are implying that you are "living" once you have an apartment. This many also be a slight bit of oversimplification.

 Truth By Humor  This video from Jack Link's is a great example of truth by humor. In no way does the activity or things mentioned in the ad actually have to do with jerky. It depicts something that's very funny to watch, then presents their product along with it, making you feel an immediate association with it.

Midterm Assignment 3: Always Wanted To Progress Report (100 words or so)
My "I Have Always Wanted To" project is going well, however I think I may have looked beyond my reach for this quarter. So far, the section of my mashup mixtape I have sounds good, but I don't think I will reach 60 minutes by week 9. I have found some good resources and am looking forward to completing as much as I can. I will be modifying my topic to reach toward being half way done with the mix itself (bout 30 minutes or so). I would still like to come up with a cover for the CD case and be ready to let the class listen to part of what I have during the presentation.

Final Presentation

 * Topic (10%)

My final topic for the, “I’ve always wanted to” project was to get a solid foundation created for a full length mash-up album.

 * Research (20%)

I researched various aspects of mash-ups, the legality surrounding it, the “big players” and contributors to the genre, and its development as an art form. I am bias toward the “fair use” side of the legal argument, but one way or another it’s definitely a hot topic that I will continue to educate myself on. I look forward to continuing my research as I see this project to its end result. :1) Internet site: Levine, Robert. "Steal This Hook? D.J. Skirts Copyright Law." Nytimes.com. 6 Apr. 2008. Web. 15 Nov. 2009. . :2) Book: Miller, Paul D., ed. Sound Unbound. Cambridge: The MIT, 2008. Print. :3) Scholarly Journal: CROSLEY, HILLARY. "Mashing Up ‘Purple Rain’." Billboard 118.26 (2006): 34-34. Wilson Web. Web. 1 Dec. 2009. :4) Other (Documentary): Good Copy Bad Copy. Prod. Rosforth. Dir. Andreas Johnson, Ralf Christiansen, and Henrik Moltke. Perf. Girl Talk. Goodcopybadcopy.Net. 2007. Web. 1 Dec. 2009. .

 * Your accomplishment (20%)

It’s hard for me to determine if I have completed my goal or not. My original guidelines stated that I wanted to have the full 60 minute album mixed by the end of the quarter. Throughout that time I realized that was not a realistic goal and modified it to 30 minutes completed. I also started to focus on other aspects of the album other than the music itself; such as a title, album cover, and a vision of what I want the music to reflect. I’m glad that I didn’t just focus on the quantity (time alone) of the mix and really got down to focus on the quality of it and what I wanted it to be. I had many peer evaluations of the project as it progressed and changed things accordingly. So all that being said, I’m not sure of the cumulative length of the pieces I have created, thus I don’t know if I have achieved my original quantitative goal. I can say for certain that I have come a long way on this project that I have always wanted to do and have a genuine drive to finish it. I am also very satisfied with what I have accomplished so far. Success.

 * Project Review (50%)

I believe that I really underestimated the time it will take to put this together. Many times I sat down and mixed for hours on end to complete anywhere from nothing I liked to only a couple minutes I felt good about. There were also times where I would just work on my current material thus not adding any new time (part of my original goal). I believe my biggest downfall in this project was my original expectation and idea of what could be accomplished and when I would do it. Now that I have spent time doing this, I have a better idea of goals I could set. :3)Future strategies Since I plan to complete this album, I will be putting my future strategies to action. Instead of setting goals like, “I want to have 42 minutes completed by Tuesday” I will be setting goals like, “I want to find something that inspires me today and spend 1 hour trying new things.”  Also I want to have a more diverse group evaluate my progress beyond my girlfriend and very close friends.  Since I have realized that quantitative goals are less productive that I thought, I am not sure how long this album will take to complete.  But I will keep the momentum going that I have created this quarter.

Self-Assessment
This class was very enjoyable and educational for me. Learning more about critical thinking versus information literacy is a valuable topic for college. The day we “dove into” the criteria for critical thinking and created a list on the board of what it meant to us was greatly helpful. I rather enjoyed the assignments in this class. The Sculpture park assignment is something that can be applied to just about anything. It’s not often we take something we don’t like and research it to see if it changes our viewpoint. This is something that I will do in the future to give myself a more educated opinion on things instead of accepting initial judgment. I have taken college logic before so I previously knew about logical fallacies; however this was a great thing to go over. I really enjoyed it the first time around and think it’s an important topic to cover to better understand and evaluate our surroundings. As for the final project I am glad this gave me the push I needed to get this album going. “I’ve always wanted to” is a project that should be continued on for future classes. I really feel I have gotten a lot out of this class and am happy with what I contributed to it. I am glad I didn’t miss any classes and satisfied with my participation in discussions. I feel I did very well on the final project and presentation and look forward to seeing the project to its end in future months. Thanks for a great class!

title: User:AndrewReynolds


text:
User:Egm6321.f09.Team6/HW3

 Please place edit links for each problem so that I can leave feedback without scrolling through an entire assignment worth of code. --Egm6321.f09.TA 04:28, 15 October 2009 (UTC)  In Problem #1: You have errors in two of your partials which is why you were not able to make your ODE exact. --Egm6321.f09.TA 04:28, 15 October 2009 (UTC)

Problems 1-3:

Problem 2: Your integrating factor is correct. The evaluated integral from wolfram is ok - you could have left the solution in terms of the integral. Egm6321.f09.TA 01:31, 28 October 2009 (UTC)

Problem 3: Your expressions are not functions of the arguments you claim. Egm6321.f09.TA 02:09, 28 October 2009 (UTC)

Problem 4:
Statement:

For the case N1-ODE $$F(x,y,y')=0=\frac{d\Phi}{dx}(x,y)$$ show that

$$f_0-\frac{df_1}{dx}=0\Leftrightarrow\Phi{xy}=\Phi{yx}$$

Specifically, find $$f_0$$ and $$f_1$$ in terms of $$\Phi$$.

Solution:

We know the first condition for exactness is $$F=\frac{d\Phi}{dx}(x,y)=\Phi_x+\Phi_yy'$$

We also know the second condition for exactness is $$f_i=\frac{\delta F}{\delta y^{(i)}}$$   for i=1,2,...,n

 Why the use of $$\delta$$ notation for partials? --Egm6321.f09.TA 14:35, 15 October 2009 (UTC) Thus, $$f_o=\frac{\delta F}{\delta y}$$ $$=\frac{\delta}{\delta y}(\Phi_x+\Phi_yy')$$ $$=\Phi_{xy}$$

 $$f_0=\phi_{xy}+\phi_{yy}y'$$. You are missing terms.--Egm6321.f09.TA 14:35, 15 October 2009 (UTC) and $$f_1=\frac{\delta F}{\delta y'}$$ $$=\frac{\delta}{\delta y'}(\Phi_x+\Phi_yy')$$ $$=\Phi_y$$

Therefore, $$\Phi_{xy}-\frac{d}{dx}\Phi_y=0$$ $$\Phi_{xy}-\Phi_{yx}=0$$ $$\Phi_{xy}=\Phi_{yx}$$  $$\frac{d}{dx}\phi_y=\phi_{xy}+\phi_{yy}y'$$. --Egm6321.f09.TA 14:35, 15 October 2009 (UTC)

Problem 5:
Statement:

For the case N2-ODE, show: $$\frac{d}{dx}(\Phi_y)=f_0$$

$$f_1=\frac{df_2}{dx}+\Phi_y$$

$$f_0-\frac{df_1}{dx}+\frac{d^2f_2}{dx^2}=0$$

Relate this last equation to the following: $$f_{xx}+2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y$$

$$f_{xp}+pf_{yp}+2f_y=g_{pp}$$

Solution:

We know the first condition for exactness is $$F=\frac{d\Phi}{dx}(x,y,y')=\Phi_x+\Phi_yy'+\Phi_{y'}y^{''}$$

We also know the second condition for exactness is $$f_i=\frac{\delta F}{\delta y^{(i)}}$$   for i=1,2,...,n

Thus, we can show: $$f_o=\frac{\delta F}{\delta y}=\frac{\delta}{\delta y}(\Phi_x+\Phi_yy'+\Phi_{y'}y^{''})$$

$$=\Phi_{xy}$$

$$=\Phi_{yx}$$

$$=\frac{d}{dx}(\Phi_y)$$

 This is not true. $$f_0=\frac{\partial F}{\partial y}=\frac{\partial}{\partial y}(\phi_x+\phi_yp+\phi_pp')=\phi_{xy}+\phi_{yy}p+\phi_{py}p'$$.

Furthermore, we can show: $$f_0-\frac{df_1}{dx}+\frac{d^2f_2}{dx^2}=0$$

$$\frac{df_1}{dx}=f_0+\frac{d^2f_2}{dx^2}$$

$$\int{\frac{df_1}{dx}dx}=\int{f_0dx}+\int{\frac{d^2f_2}{dx^2}dx}$$

$$f_1=\int{\frac{d}{dx}\Phi_ydx}+\int{\frac{d^2f_2}{dx^2}dx}$$

$$f_1=\Phi_y+\frac{df_2}{dx}$$

By substituting the found values above into $$f_0-\frac{df_1}{dx}+\frac{d^2f_2}{dx^2}=0$$

we get: $$\frac{d}{dx}\Phi_y-\frac{d}{dx}(\Phi_y+\frac{df_2}{dx})+\frac{d^2f_2}{dx^2}=0$$

$$\frac{d}{dx}\Phi_y-\frac{d}{dx}\Phi_y-\frac{d^2f_2}{dx^2}+\frac{d^2f_2}{dx^2}=0$$

$$0=0$$  You need to perform the partial differentiations as above to calculate $$f_0,f_1,f_2$$ and using the appropriate total derivatives, explicitly show that the relations hold. --Egm6321.f09.TA 01:56, 16 October 2009 (UTC)

Problem 6:
Statement:

For the following Legendre differential equation

$$F=(1-x^2)y^{''}-2xy'+n(n+1)y=0$$

verify exactness using two methods. Method 1: $$f_{xx}+2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y$$

$$f_{xp}+pf_{yp}+2f_y=g_{pp}$$

Method 2:

$$f_0-\frac{df_1}{dx}+\frac{d^2f_2}{dx^2}=0$$

If it is not exact, see whether it can be made exact using the integrating factor with $$h(x,y)=x^my^n$$

Solution:

We know $$f=(1-x^2)$$ and $$g=-2xy'+n(n+1)y$$

Thus: $$f_x=-2x$$ → $$f_{xx}=-2$$ → $$f_{xy}=0$$ → $$f_{xy'}=0$$ $$f_y=0$$ → $$f_{yy}=0$$ → $$f_{yy'}=0$$ $$g_x=-2y'$$ → $$g_{xy'}=-2$$ $$g_y=n(n+1)$$ → $$g_{yy'}=0$$ $$g_{y'}=-2x$$ → $$g_{y'y'}=0$$

Plugging the above into method 1 equations, we get: $$f_{xx}+2pf_{xy}+p^2f_{yy}=g_{xp}+pg_{yp}-g_y$$ $$-2+2p(0)+p^2(0)=-2+p(0)-n(n+1)$$ $$-2=-2-n(n+1)$$ NOT TRUE!

$$f_{xp}+pf_{yp}+2f_y=g_{pp}$$ $$0+p(0)+2(0)=0$$ $$0=0$$ TRUE!

Method 1 has only one equation satisfied; therefore, the method as a whole is not satisfied and exactness cannot be shown.

Next, we use method 2. We know:

$$f_0=\frac{\delta F}{\delta y}=n(n+1)$$

$$f_1=\frac{\delta F}{\delta y'}=-2x$$ → $$\frac{df_1}{dx}=-2$$

$$f_2=\frac{\delta F}{\delta y''}=(1-x^2)$$ → $$\frac{df_2}{dx}=-2x$$ → $$\frac{d^2f_2}{dx^2}=-2$$

Thus: $$n(n+1)-(-2)-2=0$$ $$n(n+1)=0$$ NOT TRUE!

As the above equation is not true, method 2 cannot show exactness. We will need to use the integrating factor to show exactness. So, we must find $$x^my^n$$ such that:

$$F=x^my^n[(1-x^2)y''-2xy'+n(n+1)y]=0$$

For simplification, let's assume $$p=y'$$, and $$p'=y''$$. We know:

$$\Phi=h(x,y)+\int{f(x,y,p)dp}$$ $$=h(x,y)+\int{(1-x^2)dp}$$ $$=h(x,y)+(1-x^2)p$$ $$=h(x,y)+p-x^2p$$

and:

$$g=\Phi_x+\Phi_yp$$

Therefore:

$$2xp+n(n+1)y=(h_x-2xp)+(h_y+0)p$$ $$2xp+n(n+1)y=h_x-2xp+h_yp$$ $$4xp+n(n+1)y=h_x+h_yp$$

So: $$4xp=h_yp$$ $$4x=h_y$$ which leads to: $$h=4xy+k_x$$

Also: $$n(n+1)y=h_x$$ which leads to: $$h=n(n+1)xy+k_y$$

Therefore: $$4xy=n(n+1)xy$$ $$4=n(n+1)$$ $$4=n^2+n$$ $$n=1.56$$ or $$n=-2.56$$

That means $$h(x,y)=x^my^n$$ has two solutions for exactness: $$h(x,y)=1.56xy$$ or $$h(x,y)=-2.56xy$$

Problem 7:
Statement:

Show that: $$\forall u,v$$ functions of $$x$$, $$L(u+v)=L(u)+L(v)$$ and $$\forall \lambda\in\mathbb{R},L(\lambda u)=\lambda L(u)\forall$$ functions of $$ x$$

are equivalent to: $$L(\alpha u+\beta v)=\alpha L(u)+\beta L(v)$$

Solution:

We know that the linearity operator L(.) allows use of superposition. Thus: $$L(u+v)=L(u)+L(v)$$ $$L(\lambda u)=\lambda L(u)$$

Therefore, we can use the above two relations to show: $$L(\alpha u+\beta v)= L(\alpha u)+ L(\beta v)=\alpha L(u)+\beta L(v)$$

 clean and clear. good work. --Egm6321.f09.TA 04:05, 16 October 2009 (UTC)

Problem 8
Problem Statement: From, plot the shape function $$N_{j+1}^{2}(x)$$ (From TA website). Solution:

correct. Egm6321.f09.TA 03:09, 28 October 2009 (UTC)

Problem 9
Problem Statement: From (| p.16-2), show that $$y_{xxx}=e^{-3t}\left(y_{ttt}-3y_{tt}+2y_t\right)$$ $$y_{xxxx}=e^{-4t}\left(y_{tttt}-6y_{ttt}+11y_{tt}-6y_t\right)$$ (From TA website).

Solution: First, we differentiate the second partial derivative of y with respect to x, $$y_{xx}$$, by x again. This can be done by taking the derivative with respect to t and multiplying by $$e^{-t}$$. $$y_{xxx}=\frac{d}{dx}y_{xx}=\left(\frac{dt}{dx}\frac{d}{dt}\right)y_{xx}=e^{-t}\frac{d}{dt}y_{xx}$$ We use the product rule to solve for the derivative with respect to t. $$y_{xxx}=e^{-t}\left[-2e^{-2t}(y_{tt}-y_t)+e^{-2t}(y_{ttt}-y_{tt})\right]$$ By substitution, we find the equation given below. $$y_{xxx}=e^{-3t}\left(y_{ttt}-3y_{tt}+2y_t\right)$$ We can now solve for $$y_{xxxx}$$ using the same method. $$y_{xxxx}=\frac{d}{dx}y_{xxx}=\left(\frac{dt}{dx}\frac{d}{dt}\right)y_{xxx}=e^{-t}\frac{d}{dt}y_{xxx}$$ Again, we use the product rule to solve for the derivative with respect to t. $$y_{xxxx}=e^{-t}\left[-3e^{-3t}(y_{ttt}-3y_{tt}+2y_t)+e^{-3t}(y_{tttt}-3y_{ttt}+2y_{tt})\right]$$ Finally, by substitution, we find the equation given below. $$y_{xxxx}=e^{-4t}\left(y_{tttt}-6y_{ttt}+11y_{tt}-6y_t\right)$$

Box your results so it is clear that you have solved the problem. Everything runs together here. Good concise approach. Egm6321.f09.TA 03:28, 28 October 2009 (UTC)

Problem 10
Problem: From (| p.16-4) Solve equation 1 on p.16-1, $$ x^2y''-2xy'+2y=0 $$ using the method of trial solution $$ y=e^{rx}$$ directly for the boundary conditions $$\left\{ \begin{array}{rl} y(1)=&3\\ y(2)=&4\\ \end{array}\right.$$ Compare the solution with equation 10 on p.16-3. Use matlab to plot the solutions (From TA website). Solution: First, we solve for the derivatives of y.  $$y=e^{rx}$$ (10.1) $$y'=re^{rx}$$ (10.2) $$y''=r^2e^{rx}$$ (10.3) Next, we substitute these equations into the characteristic equation to get the following equation. $$x^2r^2e^{rx}-2xre^{rx}+2e^{rx}=0$$ (10.4) We can now divide by $$e^{rx}$$ to find the following equation. $$x^2r^2-2xr+2=0$$ (10.5) Letting x=1, we have $$r^2-2r+2=0\rightarrow r=1\pm i$$ (10.6) This yields the following general solution: $$y(x)=c_1e^xcos(logx)+c_2e^xsin(logx)$$ (10.7) Substituting in the boundary conditions. $$\left\{ \begin{array}{rl} y(1)=&3\\ y(2)=&4\\ \end{array}\right.$$ Now, we have: $$y(x)=3e^{-1}e^xcos(logx)+\frac{4-3e^1cos(log2)}{e^2sin(log2)}e^xsin(logx)$$ (10.8)

Comparing to Equation with Constant Coefficients: The original equation was converted to a linear second order ordinary differential equation using the transfer of variable method. The resulting equation is given as: $$y(x)=c_1x+c_2x^2$$ (10.9) Solving for $$c_1$$ and $$c_2$$ using the given boundary equations resulted in the following solution: $$y(x)=4x-x^2$$ (10.10)

Discussion:  It is already apparent that this solution is much simpler than the solution found using the original equation. It should be noted that by using the Transfer of Variables Method to convert a linear second order differential equation with variable coefficients to one with constant coefficients, the solution found using the Method of Undetermined coefficients can be made much simpler. A plot of the two functions was created using MATLAB. This plot is given below where Equation 10.8 is in blue and Equation 10.10 is in black.

MATLAB Code:  x=0.1:0.1:3; y1=zeros(1,30); for i=1:30; y1(:,i)=3*exp(-1)*exp(x(:,i))*cos(log(x(:,i)))+((4-3*exp(1)*cos(log(2)))/(exp(2)*sin(log(2))))*exp(x(:,i))*sin(log(x(:,i))); y2(:,i)=4*x(:,i)-(x(:,i))^2; end plot(x,y1) title('Two Solutions for L2.ODE') xlabel('x') ylabel('y(x)')

very good. Good job showing how you can 'force' a bad guess to approximate the true solution for a local area, but a more appropriate trial solution will yield a more elegant (and accurate) solution. Egm6321.f09.TA 03:53, 28 October 2009 (UTC)

 Acknowledgments: Francisco

Problem 11
From $$ u_1(x) z' + [a_1(x)u_1(x) + 2u_1'(x)]z = 0 $$ obtain Eq.2 (P.17.3) using the integrating factor method.

Solution:

$$u_{1}(x) Z'+\left[a_{1}u_{1}(x)+2u_{1}' (x) \right]Z=0 $$

$$h(x)\left[Z'+\left[a_{1}+\frac{2u_{1}' (x)}{u_{1}(x)} \right]Z=0 \right]$$

$$h(x)Z'+h(x)\left[a_{1}+\frac{2u_{1}' (x)}{u_{1}(x)} \right]Z=0 $$

$$\frac{d}{dx}\left[h(x)Z(x) \right]=h(x)Z'(x)+h'(x)Z$$

Let $$h'(x)= h(x)\left[a_{1}+\frac{2u_{1}' (x)}{u_{1}(x)} \right]$$

$$\frac{h'(x)}{h(x)}= \left[a_{1}+\frac{2u_{1}' (x)}{u_{1}(x)} \right]$$

Integrating this will give:

$$h(x)=B exp \left[\int_{}^{x}a_{1}(s)ds+ln\left|u_{1} \right|^{2} \right]$$

$$h(x)Z'+h(x)Z=0$$

$$\int_{}^{}h(x)*Z(x)=\int_{}^{}0$$

$$h(x)Z(x)=K$$

$$ B exp \left[\int_{}^{x}a_{1}(s)ds+ln\left|u_{1} \right|^{2} \right]Z(x)=K $$

$$Z(x)= C exp \left[-\int_{}^{x}a_{1}(s)ds-ln\left|u_{1} \right|^{2} \right]$$

$$Z(x)= \frac{C}{u_{1}^{2}} exp \left[-\int_{}^{x}a_{1}(s)ds \right]$$

very good. Egm6321.f09.TA 04:10, 28 October 2009 (UTC)

Problem 12
Develop reduction of order method 2 using different algebric ops.

a. $$ y(x)=U(x)\pm u_1 $$

b. $$ y(x) = U(x)/u_1(x) $$

c. $$ y(x) = u_1(x)/U(x) $$

Solution:

a. $$ y(x) = U(x) \pm u_1(x) $$

The first and second derivatives of y(x) are:

$$y'(x) = U' \pm u_1'$$

$$y(x) = U \pm u_1''$$

The desired form is $$ y'' + a_1y' + a_0y = 0 $$,

Substituting in the above equation,

$$ a_0y + a_1y' + y = a_0U \pm a_0u_1 + a_0U' \pm a_1u_a' + U \pm u_1'' $$

We get $$ 0 = a_0U \pm a_0u_1 + a_0U' \pm a_1u_a' + U \pm u_1 $$

In the above equation, the dependent variable U(x) is present and not missing. The Reduction of Order Method is possible only when dependent variable is missing.

b. $$ y(x) = U(x)/u_1(x) $$

The first and second derivatives of y(x) are:

$$y'(x) = U'/u_1 + U/u_1'$$

$$y(x) = U/u_1 + 2U'/u_1' + U/u_1''$$

The desired form is $$ y'' + a_1y' + a_0y = 0 $$,

Substituting in the above equation,

$$ a_0y + a_1y' + y = a_0 U/u_1 + a_1 U'/u_1 + a_1 U/u_1' + U/u_1 + 2U'/u_1' + U/u_1'' $$

We get $$ 0 = a_0 U/u_1 + a_1 U'/u_1 + a_1 U/u_1' + U/u_1 + 2U'/u_1' + U/u_1 $$

The above y(x) here is not valid because the equation above is not missing U(x). The Reduction of Order Method is possible only when dependent variable is missing.

c. $$ y(x) = u_1(x)/U(x) $$

The first and second derivatives of y(x) are:

$$y'(x) = u_1'/U + u_1/U'$$

$$y(x) = u_1/U + 2u_1'/U' + u_1/U''$$

The desired form is $$ y'' + a_1y' + a_0y = 0 $$,

Substituting in the above equation,

$$ a_0y + a_1y' + y = a_0 u_1/U + a_1 u_1'/U + a_1 u_1/U'+ u_1/U + 2u_1'/U' + u_1/U''$$

We get $$ 0 = a_0 u_1/U + a_1 u_1'/U + a_1 u_1/U'+ u_1/U + 2u_1'/U' + u_1/U $$

In the above equation, the dependent variable U(x) is present and not missing. The Reduction of Order Method is possible only when dependent variable is missing.

very good. Use some color, lines, or boxes to help separate the sections of your solution. Egm6321.f09.TA 04:18, 28 October 2009 (UTC)

Problem 13
Find $$ u_1 and u_2 $$ of $$ (1-x^2)y'' - 2xy' + 2y = 0 $$ using the 2 trial solutions:

i. $$ y = ax^b $$

ii. $$ y = e^{rx} $$

and compare the two solutions using the boundary conditions $$y(0) = 1$$ and $$y(1) = 2$$ and compare the solution using the reduction of order method 2. Plot the solutions using MATLAB.

Solution:

Part 1:

$$ (1-x^{2})y''-2xy'+2y=0 $$ (13.1)

With the trial solution,

$$ y=ax^{b} $$

$$ y'=bax^{b-1} $$

$$ y''=ab(b-1)x^{(b-2)} $$

Substituting into Equation 1

$$ (1-x^2)ab(b-1)x^{(b-2)} - 2xabx^{(b-1)} + 2ax^b = 0 $$

$$ ab(b-1)x^{(b-2)}-ab(b-1)x^b - 2abx^b + 2ax^b = 0 $$

$$ ab(b-1)x^{(b-2)}-[ab(b-1) + 2ab - 2a]x^b = 0 $$

$$ ab(b-1)x^{(b-2)}-ab(b-1)x^b - 2abx^b + 2ax^b = 0 $$

$$ ab(b-1)x^{(b-2)}-\left[ab(b-1) + 2ab - 2a \right]x^b = 0 $$   (13.2)

In Equation (2), equating co-efficients of $$ x^{(b-2)}$$,

$$ ab(b-1) = 0 $$

We know that a and b both cannot be zero, and one value of $$ b=1$$.

In Equation (2), equating co-efficients of $$ x^b$$ ,

$$ ab(b-1) + 2ab - 2a = 0 $$

$$ a(b^2+b-2) = 0 $$

Again $$ a$$ cannot be zero, so $$ b =1,-2$$.

Therefore,

$$ u_1(x) = ax $$

$$ u_2(x) = \frac{a}{x^2} $$

So, the trail solution

$$ y = c_1u_1(x) + c_2u_2(x) $$

$$ y = C_1x + C_2\frac{1}{x^2} $$

Using the boundary conditions,

$$ y(\frac{\pi}{2\sqrt{2}}) = 1 $$

$$ y(\frac{\pi}{\sqrt{2}}) = 2 $$

We arrive at,

$$\displaystyle C_1 = \frac{2\sqrt{2}}{\pi} $$

$$\displaystyle C_2 = 0 $$

The trial solution becomes,

$$\displaystyle \Rightarrow y = \frac{2\sqrt{2}}{\pi}x $$  (13.3)

Therefore,

$$\displaystyle u_1 = \frac{2\sqrt{2}}{\pi}x;\ and\ u_2 = 0 $$

Part 2:

$$ (1-x^{2})y''-2xy'+2y=0 $$ (Equation 1)

Find solution using the trial solution

$$ y=e^{rx} $$

$$ y'= re^{rx} $$

$$ y''= r^{2}e^{rx} $$

Substituting into Equation 1

$$ (1-x^{2}) r^{2}e^{rx} -2x re^{rx}  +2 e^{rx}  =0  $$

$$ r^{2}e^{rx}  - r^{2} x^{2} e^{rx}  -2rx e^{rx}  +2 e^{rx}=0 $$

Rearranging and dividing by $$ e^{rx} $$,

$$ -x^2r^2-2xr + r^2 +2 = 0 $$

$$ -x^2[r^2]-x[2r] + r^2 +2 = 0 $$

We do not have any terms on the right hand side to equate with co-efficients of $$ x^2$$ and $$ x$$, so equating the constant co-efficients,

Rearranging, $$ r^2 +2 = 0 $$

$$ r = \pm \sqrt2i $$

The trial solution becomes,

$$\displaystyle \Rightarrow y = e^{\sqrt2ix} $$

$$\displaystyle \Rightarrow y = C_1 cos(\sqrt2x) + C_2 sin(\sqrt2x) $$

Using the boundary conditions,

$$\displaystyle y(\frac{\pi}{2\sqrt{2}}) = 1 $$

$$\displaystyle y(\frac{\pi}{\sqrt{2}}) = 2 $$

We arrive at,

$$\displaystyle C_1 = -2 $$

$$\displaystyle C_2 = 1 $$

The trial solution then becomes,

$$\displaystyle \Rightarrow y = -2 cos(\sqrt2x) + sin(\sqrt2x) $$       (13.4)

and,

$$\displaystyle u_1 = -2 cos(\sqrt2x);\ and\ u_2 = sin(\sqrt2x) $$

Solution given by reduction of order method 2,

$$\displaystyle u_1=x $$

and

$$\displaystyle u_2=\frac{x}{2}log_e\left(\frac{1+x}{1-x}\right) - 1 $$

Matlab Plot: A MATLAB Plot of Equations 13.3 and 13.4 is given below where Eq. 13.3 is represented by a blue line and 13.4 is given in black.

Matlab Code: x=0:0.1:7; y1=zeros(1,71); for i=1:71; y1(:,i)=(2*sqrt(2)/pi)*x(:,i); y2(:,i)=-2*cos(sqrt(2)*x(:,i))+sin(sqrt(2)*x(:,i)); end plot(x,y1,x,y2) title('HW 3 - Problem 13') xlabel('x') ylabel('y(x)')

Why do the two solutions not agree? Egm6321.f09.TA 05:56, 28 October 2009 (UTC)

Contributing Members
Egm6321.f09.Team6.PaulMoore 23:12, 6 October 2009 (UTC) Egm6321.f09.Team06.sada 07:47, 7 October 2009 (UTC) Egm6321.f09.team6.breaux 15:39, 7 October 2009 (UTC) Egm6321.f09.Team6.dianafoster 17:59, 7 October 2009 (UTC)

title: User:Egm6321.f09.Team6/HW3


text:
User:Codyjones

=Freshman Seminar=

Always Wanted To Schedule

 * Topic

run to the top of oyster dome in vibram fivefingers
 * Research Component

i will research the history of barefoot running, the benefits, why normal running shoes can cause injury vs running barefoot, types of barefoot running shoes.
 * week 1

compile list of resources i will use, run at least 5 miles this week
 * week 2

read Born To Run, find an upcoming half marathon and look into registration, run at least 6 miles
 * week 3

go to some barefoot running sites, such as Birthday Shoes!!!
 * week 4

research leg mechanics when running barefoot compared to running in running shoes, need to run 4 times this week,( 4-5 miles per run one run being 6-7 miles)
 * week 5

run some more (4 times at 5 miles per time with one run being 8-9 miles)
 * week 6

go to fairhaven runners to see what they have to say about running in fivefingers, run 4 times this week at 6 miles per run, one run being 10-11 miles)
 * week 7

research nutrition for running, and how food affects the body while running, run 4 times this week 6 miles per run, one run being 12 miles)
 * week 8

week of ascent, get mentally prepared

Midterm Assignment 1: Taste & Aesthetics
Schubert Sonata is a sculpture by Mark di Suervo in the Olympic sculpture park in seattle. The sculpture was done in the honor of composers. it was on display in front of Benaroya Hall, home of the Seattle Symphony. It is a combination of painted steel and raw steel. It measures 22x10 feet, its relation to the area is that it blows in the wind and gently changes direction just as a fish in a current would do in the sound. at first i disliked this sculpture due to the fact that it is really confusing looking, and at the same time it didnt really look like a fish to me. Then i went into the research of how it was created and why the artist went through the troubles of making this sculpture. He mentioned how when you are welding metal, the light of the welder is extremely intense, and that the creation of the sculpture is happening while that light exists. Also and that once the light ceases to exist, creation ceases to exist, and that really made me appreciate the sculpture due to the fact that i have done artistic welding. After i took the time to research that sculpture and his reasoning for the creation of it, i started to semi like it, and that is as far as i have gotten in my quest to liking the sculpture Schubert Sonata.

Midterm Assignment 3: Always Wanted To Progress Report (100 words or so)
so far i have been running regularly, it is awesome to run almost barefoot. i have looked into foot mechanics lightly, and seen how we run differently in shoes versus barefoot. i have gotten in better shape. i found a medical journal on the internet? there seems to be a lot of support these days for barefoot running, i feel like it is going to be the next "cool" thing in running. i have trouble trying to comprise all of this information in a presentable fashion worthy of showing to the class.

Final Presentation

 * Topic (10%)

how barefooting (fivefingers) has changed my view of footwear and the use of running shoes
 * Research (20%)

 * 1) Internet site:http://www.birthdayshoes.com/, http://www.livingbarefoot.info/
 * 2) Book: born to run
 * 3) Scholarly Journal:http://www.sportsci.org/jour/0103/mw.htm
 * 4) Other (interview, TV show,etc):Fairhaven running employees

 * Your accomplishment (20%)

i have achieved my goal, although it was painful and hard to stay motivated
 * Project Review (50%)
 * 1)What went well: running felt great, strengthened my feet, legs and mind
 * 2)What went poorly: staying on track regardless of how i was feeling, weather
 * 3)Future strategies: being motivated and mentally in the game at all times regardless of how i feel in the moment

title: User:Codyjones