text:
Critical Thinking Skills

Course Title: Critical Thinking

Lecture Topic: Critical Thinking Skills

Instructor: Dr. Crown

Institution: University of Texas - Pan American

It is imperative to develop a child's critical thinking skills. By developing a child's critical thinking, they become better able to respond to problems presented to them. Through this challenge, one will be better able to analyze the information presented to them and develop an independent solution with reason.

Backwards Design
Course Objectives
 * Primary Objectives: By the next class period students will be able to:
 * Understand the benefits of playing a game with a plan in mind
 * More effectively participate in critical thinking games
 * Sub Objectives: The objectives will require that students be able to:
 * Express their ideas without reserve
 * Willingly desire to triumph in critical thinking games
 * Difficulties
 * Students may have difficulty at first in understanding the strategy presented to them.
 * Real-World Contexts
 * Good critical thinking skills benefit one by allowing them to see problems differently and think things through so that they may form a solution.

Model of Knowledge
 * Concept Map
 * Creating a strategy
 * Forming ideas
 * Grouping characteristics
 * Communication skills
 * Expressing ideas
 * Accept the possibility of defeat

 * Content Priorities
 * Enduring Understanding
 * Understand how to solve higher level critical thinking skills problems
 * Important to Do and Know
 * Formulate ideas independently
 * Worth Being Familiar with
 * Describe a persons physical attributes when presented with a photograph

Assessment of Learning
 * Formative Assessment
 * In Class (groups)
 * Students will play the "Guess Who" game
 * Summative Assessment
 * Students will play "20 Questions"

Legacy Cycle
OBJECTIVE

By the next class period, the students will be able to: The objectives will require that students be able to:
 * Understand the benefits of playing a game with a plan in mind
 * More effectively participate in critical thinking games
 * Express their ideas without reserve
 * Willingly desire to triumph in critical thinking games

THE CHALLENGE

How can one play the “Guess Who?” game and be the first one to guess the person their opponent has chosen? GENERATE IDEAS

The students will be asked to generate questions on their own that would be appropriate when playing the game. Appropriate questions include, but are not limited to...

 * Is your person wearing a hat?
 * Does your person have glasses?
 * Are they wearing earrings?
 * Do they have any accessories?
 * Do they have a moustache?
 * Does your person have facial hair?

Note: Of the 24 faces on the game, 5 are wearing a hat, 4 have glasses, 5 wear earrings, 11 have accessories, 5 have a moustache, and 10 have facial hair.

MULTIPLE PERSPECTIVES

Once the student has generated questions that they would potentially ask an opponent while playing this game, they will be lectured on the importance of asking effective questions and how to they can do so on their own.

Brief Example: In order to competitively play the game, one should try to eliminate as many people as possible early on. One should ask a question that can eliminate many people regardless of the answer, such as whether or not the person has any accessories. Accessories include hats, glasses, and earrings and eleven people in the game have some type of accessory. As the game progresses, more specific questions should be asked. When there are only three people left, one should take a guess at who the person is because your chances of winning more quickly are far greater if you guess than if you continue asking questions.

RESEARCH & REVISE

Students play the game with the questions they have come up with.

TEST YOUR METTLE

Students will play the game “20 Questions.”

The type of questions asked by the student will indicate their understanding of the previous challenge. A student who has mastered the objectives of this challenge should be able to win the game with a reasonable number of questions.

GO PUBLIC

Students discuss the games, the strategies used, and how they could win more quickly in the future.

title: Critical Thinking Skills


text:
Votian/Vowel Harmony

Rules
E.g. levvettī  vs. ve̮te̮ttī .
 * Every back vowel has it's counterpart among front vowels.
 * Originally a word and it's suffixes could have either back vowels or front vowels only and never both of them.
 * In practical terms, we might say that, if a word stem has any back vowel, then every suffix added to it may have back vowels only and vice versa e.g. levvettägō vs. ve̮te̮ttagō.
 * i is an exception, because it's counterpart occurres only in very recent Russian loanwords.

Exceptions

 *  CERTAIN SUFFIXES DO NOT FOLLOW VOWEL HARMONY RULES.
 * 1) ö is found in the first syllable only, excluding some Ingrian and Finnish loanwords and derivation suffixes . Thus the following suffixes have no front vowel alternative:
 * 2) pesi-ko  ('Did he wash?')
 * 3) elkō jättägō  ('Let him not leave (it)!')
 * 4) tüttär-ikko  ('girl')
 * 5) pette-likko  ('cheatful')
 * 6) petä-zikko  ('pine forest')
 * 7) pǟ-tō  ('headless')
 * 8) Votian Imperative endings have back and front alternatives only in Lüganuse (and Kodavere) dialects
 * 9) sȫ-kā  ('Eat!')
 * 10) The following suffixes have no front vowel alternative either:
 * 11) leivǟ-kā  ('with bread')
 * 12) vere-kaz  ('bloody')
 * 13) päivü-kke̮in  ('sun')
 * 14) venä-лain  ('a Russian')
 * 15) ȫ-nikka  ('the one who spends a night (in a dorm etc.)')
 * 16) tšülǟ-ssā  ('to the village (edge)')
 * 17) viďďe-ttomā  ('the fifth's' <= genitive of viďďe-tō)

 *  CERTAIN ONOMATOPOETIC WORDS DO NOT FOLLOW VOWEL HARMONY RULES.
 * E.g. rǟkkumā  ('shout')

 *  CERTAIN LOANWORDS DO NOT FOLLOW VOWEL HARMONY RULES.
 * E.g. rǟtua mȫ ('in lines' ~ Russian: ряд)

 * SOME OLD COMPOUND WORDS DO NOT FOLLOW VOWEL HARMONY RULES.
 * E.g. kasta  ('this' (partitive of ka-ze))
 * E.g. kaneita  ('these ~ them' (partitive of ka-ne))

 * SOME OLD COMPOUND WORDS REPRESENT REGRESSIVE VOWEL HARMONY.
 * E.g.  ähüppǟlē  ('onto an oven' < *ahjon pǟllen)

Vaiga and Alutaguse dialects

 * Vowel harmony has almost disappeared in Vaiga and Alutaguse dialects (excluding Lüganuse and Kodavere) (influenced by Mid Estonian dialect).
 * 1) Front vowels were finally preserved only in the second syllables before they were completely replaced with their back counterparts  e.g. käsku  ('order, demand' in Lüganuse dialect < *käskü ) or süö-Du  ('eaten' in Lüganuse dialect < *süö-Dü ).
 * 2) Nevertheless  was replaced with e like in  Mid Estonian dialect).
 * 3) e may have substituted ä in some words  e.g. lüpseDä ('to milk (a cow)' in Lüganuse dialect < lüpsäDä).
 * 4) ä may have falsely substituted a following a syllable, which includes e or i, even though the stem could have back vowels  e.g. ammasteGä  ('with teeth' in Lüganuse dialect), e̮liväD ('they were').
 * 5) ä may have substituted even e of the second syllable, if the first syllable includes ä or ü  e.g. üläs ('upwards' in Lüganuse dialect < üles) or pǟlä  ('onto' in Lüganuse dialect < *pǟlle ).
 * 6) ü may have been substituted by i  in the second syllable of a stem, if the first syllable includes a short ü e.g. tüli   ('quarrel' in Lüganuse dialect) or püssiD  ('guns' in Lüganuse dialect < *püssüD ).
 * In Lüganuse dialect only the a | ä opposition remained active e.g. jättäGä ('Leave (it)!') vs. tuoGa ('Bring (it)!') or tüöGä ('with work') vs. maaGa ('with earth').
 * The u | ü opposition has left only rudiments e.g. küsütti ('it was asked') or kinniDettüD ('fixed').
 * There are traces of late o | ö opposition like in Eastern Vaivara dialects e.g. örsöttämä ('to boast').

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

title: Votian/Vowel Harmony


text: File:Orange ESAI.jpg

title: File:Orange ESAI.jpg


text:
ELMSmaster

Environmental legislation and Management Systems

Unit Co-Ordiantor Jonathan Wooldridge

<<< THIS IS A PILOT TEST, THE INFORMATION PROVIDED ON THIS PAGE IS TO PUSH YOU IN THE RIGHT DIRECTION >>>>

Notice the blue areas are hyperlinks to other areas

You may wish to include your own links, follow the wikiversity help system for doing this,

or ring me JONATHAN WOOLDRIDGE on 023 9284 2945

THIS PAGE IS FOR PORTSMOUTH UNIVERSITY STUDENTS ONLY
You have the opportunity to discuss issues, obstacles and conflicts by logging onto the online service provided by (PALTALK). This requires you to download some free software that has already been tried and tested.

Online conferencing and online tutorials are now AVAILABLE !

Use the room to make friends and network with each other at times were acadmic debates are not taking place. You will know when this time is because the room will be password protected.

If the password has been set, it will be (portsmouth)

Academic debate using paltalk.

This link will take you directly to the PALTALK online Universities room

PALTTALK IS Free video chat, instant messaging and chat rooms.

Our room is available in the area called online Universities.

Procedures
1. Download the software paltalk

2. Use this free service

3. Log in and find the room

4. talk to each other

5. JayJitsu is your online fascillitator

6. Where you see an @ symbol infront of a name, this is an administrator.

7. If you enjoy this type of learning I will make you an admin and give you a H@T (The HAT sign)

Question 1

A campaign for an International court for the environment ‘ICE

Question 2

Suggest ways that organisations could support NGO’s in addressing local environmental concerns.

WRITE YOUR PALTALK NICNAME (USERNAME) BELOW AND A SUITABLE TIME FOR YOU TO BE ONLINE, I SUGGEST INITIALLY TO LOG ON EVERYNIGHT BETWEEN 6 AND 7 GMT.

SET UP YOUR ONLINE STUDY GROUP
Remember when you edit this page, to scroll down and save changes.

JAYJITSU Will be online all day at the University and at home during the pilot test.

NAME 2, TIME ?

NAME 3, TIME ?

NAEM 4, TIME ?

etc

TOWARDS AN INTERNATIONAL COURT FOR THE ENVIRONMENT
Points for discussion. (FEEL FREE TO ADD COMMENTS TO THIS PAGE)

* What are current problems related to this topic in the world? Please identify at least two.

* What has caused these problems to exist in the world? Please identify at least two causes for each problem.

* What has the government done in attempting to resolve those problems?

* What is the position of your Country on those problems?

* What is the possible position of other countries in your committee on those problems? Consider at least two other countries.

* How could an International Court for the Environment a proposition to the United Nations resolve those problems? Making sure that your solution(s) are consistent with your country’s position

AFTER USING THE ONLINE DEBATE OR DOING YOUR OWN RESEARCH, RETURN TO THIS PAGE AND MAKE YOU ADDITIONS.

'''IF YOU ARE THE FIRST THEN IT WILL BE UP TO YOU TO SET THE STANDARD ! '''

HAVE FUN !!!!!!!

SPEND AS LONG AS YOU WANT ON IT, AND AIM TO GET A BETTER UNDERSTANDING OF ISSUES, OBSTACLES and CONFLICTS SO THAT YOU MAKE A GOOD JOB OF YOUR ASSIGNMENT.

Guidance on how to generate a position paper.
Edit this document as many times as you wish, put in relevant details and challenge each other.

define your public policy question (a public concern)

* Is it a real issue, with genuine controversy and uncertainty? * Can you distinctly identify two positions? * Are you personally interested in advocating one of these positions? * Is the issue narrow enough to be manageable? * Analysing an Issue and Developing an Argument

Provide an overview of the most current scientific understanding of the issue in question;

* Who is your audience? * What do they believe? * Where do they stand on the issue? * How are their interests involved? * What evidence is likely to be effective with them? * In determining your viewpoint, ask yourself the following: * Is your topic interesting? * Can you manage the material within the specifications set by the instructor? * Does your topic assert something specific and propose a plan of action? * Do you have enough material to support your opinion?

Examine the key trends within the issue and, where applicable, cross-links with other issues, and the significance of those trends;

Describe the efforts of governments, industry, and others in addressing the issue of concern;

Include any indicators that track key trends in the issue being addressed, making use of relevant existing national environmental indicators.

The following has been included to jog your memory about the ELMS question.

Question 1

A campaign for an International court for the environment ‘ICE’ has been gaining momentum around the globe, with the overall aim of suggesting a mechanism for the enforcement of appropriate International law and the development of International legal standards designed to prevent further destruction of our natural environment.

Discuss the ICE proposal and critically evaluate the recommendations.

THINK : To critically evaluate you may wish to make use of the questions used above for developing a position paper.

BUZZ WORDS : Problems with Policy implementation, Greening supply chains, Reducing the burden of legislation, Using ISO 14001, Aspects and impacts considerations, accountability, best practice, pro active rather than reactive considerations, transparency, reducing unecessary complexity.

Question 2

Suggest ways that organisations could support NGO’s in addressing local environmental concerns.

BUZZ WORDS : Corporate Social Responsibility, Governance, Forming alliances, Partnerships, Skills Sharing,consensus.

DONT FORGET TO REFER TO YOUR UNIT : Systems thinking, Developing management plans.

Useful links

Net Regs

Statutory Instruments

The Environmental Law Foundation

European Summaries of Legislation

Journals

Health and Safety Journals

Online dissertations

title: ELMSmaster


text:
Privacy

Privacy and Learning Environments
Digital Learning Environments can produce data about the learner, that interacts with the Digital Learning Environment. Furthermore the students may share the results of learning tasks with the teacher and the teacher analyses the learning results to provide individual feedback to the student. Privacy by design principles for digital learning environments assure that the data is shared and used in digital environment that is equivalent to physical non-digital environment of interaction between teacher and student or group of learners/students that collaboratively work on a joint learning task (e.g. on students device, the classroom, the school).
 * (OER1) Assume you have an set Open Source learning environment and several Open Educational Resources for specific subject in school (e.g. Biology, Chemistry, Social Sciences, Mathematics, ...) the software for the learning environment is executed with Open Source interpreter that is aware of the local IT infrastructure for individual work and sharing of results between students and teacher.
 * (OER2) Open Educational Resources can be adapted to the regional and local aspects (e.g. Real World Lab close to the school, college or university, that students can visit. These adaption made available for the classes and seminars and maybe shared beyond with other schools that visit the same location with the students. Integration in Open Source learning environment and the local client-server infrastructure in performed transparently via compilation for the local infrastructure.
 * (Digital Signature and Cryptography) Discuss the role of digital signature and cryptography for the privacy in digital learning environments that connect to remote IT services used in digital learning environments.
 * (JSON as Exchange Format for Learner Data) The data in the learning environment generated by student might be used just offline on the students device to adapt the learning environment to the students needs. If the data is not shared beyond the students device, then privacy is respected by default by the learning environment. As an example we store the generated learning data as JSON data that can be stored locally on a USB thumb drive to take home by the student, similar to Octave/Maxima file that is improved as homework. Combine JSON with Digital Signature and Cryptography and identify benefits and challenges for the application.
 * (Scaling Network Size for Sharing) Now we assume we have LAN (Local Area Network) for the classroom that is disconnected internet or even from the LAN for the whole school. Now the student wants to share the results on a digital white board. Furthermore we store the learning results as JSON. The digital white board has RESTful API the student can submit the learning data for a presentation she/he does in front of the classroom. On the digital whiteboard the results generated by the student is rendered in the same with OpenSource infrastructure as on client device. Define and identify the relevant aspects for the IT infrastructure to work within the classroom. Define and apply Open Source compilation or interpretation of the source to a given learning environment, so that is transparently integrated in the school environment.
 * (IT Fallback Method and Privacy) Privacy by design principle assure that data kept locally on the client's device if no client-server interaction is available. At the same time the offline use on the learning environment on the client is at the same time a fallback method for a lesson plan if network connection fails.

Learning Tasks

 * (Digital Learning Environment) Collect the IT requirements and constraints for an Open Source infrastructure at your school, college or university. What are the challenges for the implementation of privacy of data generated by students. Discuss this in the context of Learner Analytics and Privacy.

Fall 2009 Course Content

 * Privacy Outline Fall 2009
 * Privacy Cases Fall 2009
 * Privacy Lecture Fall 2009
 * Privacy Case Discussion Fall 2009

Other Resources
Reporting an alcoholic patient Randy Cohan, The Ethicist, New York Times, September 6, 2009. Listen to Letter #2.-- Taylor Raftery 7:06, 11th of September 2009

title: Privacy


text:
Talk:Environmental Legislation and Management Systems

Exclusivity
A line THIS PAGE IS FOR PORTSMOUTH UNIVERSITY STUDENTS ONLY was changed (by me) to THIS PAGE IS INTENDED FOR PORTSMOUTH UNIVERSITY STUDENTS ONLY. The INTENSION can be stated, but neither the MediaWiki platform nor the Support staff can enforce exclusion. OK? --CQ 12:37, 8 September 2009 (UTC)


text:
User:Gwatts88

This is my 3rd writings into my profile in the year of 2009- and what a few months it has been!

Going from the stress of the old house to the opportunities of the new place; right now I am creating a documentary for the NHS on mental health stigma and involvement. I am also on 2 national advisory panels for mental health, and have a second film in the works off my own back.

But some more about me: I suffer (or at least my label at the moment) from the mental illness bipolar disorder; defined by exaggerated highs and suicidal lows. I have become more open about it in the last few years, in the hope that others will be willing to stand up and have their voice heard.

I forever hold schools (particularly my old grammar school and the whole grammar school system) in contempt for acting as a catalyst to whatever problems I've had to deal with now. These schools are so bothered about being the top in the county league tables, they're ignoring wellbeing. I'm speaking for a huge silent minority of students that survived that school in saying they failed us in their snobbery and greed for grades. The school has also turned out a teenage counselling service rolling out across the county- which is absolutely disgusting.

My mission in life is to earn enough to live on, and to stand up for all the young people being abused by a system focused on exams rather than learning how to live.

title: User:Gwatts88


text:
User talk:Gwatts88

 Hello Gwatts88, 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! --mikeu talk 13:39, 8 September 2009 (UTC)

title: User talk:Gwatts88


text: Talk:Earth Stewardship/M-ICE

title: Talk:Earth Stewardship/M-ICE


text:
User:CQ/Hypoxic

Watershed Forum

Mississippi Watershed Taskforce at Bioneers

title: User:CQ/Hypoxic


text:
User:Egm6321.f09/Report table

 Please keep this table and the wiki code tidy. Use exactly the same format that I created. Remember to log in before you check in your team's HW report. Egm6321.f09 12:59, 15 September 2009 (UTC) Lecture plan, TA user page

 All versions:  Fall 2010, Fall 2009

(a) : The deadline for any report is in general on a Wed, unless extended by formal announcement (e.g., to accommodate the travel schedule of students, etc.), or upon a reasonable request.

(b) : Deadline for HW1 was extended from Wed, 9 Sep 09, to Wed, 16 Sep 09.

(c) : 21:00 UTC = 17:00 EDT = 5:00 pm EDT = 4:00 pm EST. From the first Sunday of November, the Eastern time changed back to the EST, and we used 22:00 UTC = 5:00 pm EST.

EGM 6322 Report table EAS 4200C HW report table EML 4500 HW report table

title: User:Egm6321.f09/Report table


text:
User:Thatguygomer

This is my user page. Once I read up on the rules and policies and style guides, etc, I'll update this page, and then start working on the page that prompted me to create an account.

title: User:Thatguygomer


text: File:Literacy in the information age diagram by Christopher J. Devers.jpg


text: Template:Attribution

title: Template:Attribution


text:
User:Egm6321.f09.TA

Office hours: TR (9:35 - 10:25) in MAE - A224 (on campus) Off campus (EDGE, REEF) hours = M,T,R (6:00 - 7:00) via Skype, email anytime On special occasions, appointments can be made outside the above official office hours. Back to Egm6321 Lecture plan Report table

Homework statements

Exam 1 grading New questions and answers - Questions may be publicly posted here.

The best method for asking homework questions is to use email. This will ensure the most prompt response. --Egm6321.f09.TA 21:36, 11 October 2009 (UTC)

Class: You may want to send e-mail to the TA to ask questions. But if your questions involved equations, then it is better to write down these equations (using different writing tools); one of these writing tools and method to communicate equations to the TA is to type your equations and questions here, then inform the TA via e-mail, and provide the TA with the link to this wiki page. Egm6321.f09 14:51, 13 October 2009 (UTC)

hello I have two questions the first is in regards to HW3 problem 4:

I understand why $$f_1$$ is $$\Phi_y$$ and that this gives $$\Phi_yx$$ when differentiated WRT x, but for $$f_0$$ I get $$\Phi_{xy}+\Phi_{yy}P$$ which does not satisfy the anwer

 Be careful, what you did was not correct. You need to think about the total derivative of $$\displaystyle f_1$$ wrt $$\displaystyle x$$, i.e., $$\displaystyle \frac{d f_1}{dx}$$, and not the partial derivative $$\displaystyle \frac{\partial f_1}{\partial x}$$. Once you understand this difference, you should be able to answer this question and other related questions. Egm6321.f09 23:19, 6 October 2009 (UTC)

Second in regards to HW 3 Problem 5 I cannot seem to get the relations to work out I am getting the following values for the $$f_0,f_1,f_2$$: $$f_0=\frac{dF}{dy}=\frac{d(\Phi_{x}+\Phi_{y}y'+\Phi_{y'}y'')}{dy}$$

$$f_0=\Phi_{xy}+\Phi_{yy}P+\Phi_{py}y''$$

$$f_1=\frac{dF}{dp}=\frac{d(\Phi_{x}+\Phi_{y}y'+\Phi_{y'}y'')}{dp}$$

$$f_1=\Phi_{xp}+\Phi_{yp}P+\Phi_{y}+\Phi_{pp}y''$$

$$f_2=\frac{dF}{dy}=\frac{d(\Phi_{x}+\Phi_{y}y'+\Phi_{y'}y)}{dy''}$$

$$f_2=\Phi_{p}$$

am I on the right track here? --Egm6321.f09.team7.benedict 03:38, 6 October 2009 (UTC)

Hi i received a notice from the professor stating,

"WARNING: Please move your work to the user namespace, and request a deletion of all of your wiki page under the main namespace by inserting the delete or delete my page template at the top of the page so wikiversity custodian could delete them. Remember to log in when you perform these operations so you are not mistaken to be vandals. Failure to do the above immediately will result in a lower HW grade. Eml4500.f08 09:28, 25 September 2008 (UTC)"

i am new to using wiki media and i would like to know what a user namespace and main namespace means.

Egm6321.f09.Team06.sada 20:34, 22 September 2009 (UTC)

 Look at the signature "Eml4500.f08 09:28, 25 September 2008 (UTC)"; that was not me this semester; that was me in Fall 2008 !! Someone used my message in Fall 2008 for a different class to convey the message to you, which is a valid message. You want to put your work in the user namespace. Talk to your teammates first, or any other student in the class; someone should be able to explain to you. You can also rewatch my lecture about using mediawiki. If you still cannot get help or figure out from my lecture, the TA would be the next step. You need to provide a link to your work that was not in the user namespace. Without that link, it is not possible to know what you did that was wrong. Egm6321.f09 23:19, 6 October 2009 (UTC)

title: User:Egm6321.f09.TA


text:
User:Egm6321.f09.Team17

user:egm6321.f09.team17/HW1

user:egm6321.f09.Team17/HW1b

title: User:Egm6321.f09.Team17


text:
User:Egm6321.f09.team17/HW1

this is HW1 of Team17.

title: User:Egm6321.f09.team17/HW1


text:
User:Egm6321.f09.team17

Assignment Descriptions

Homework #1: user:egm6321.f09.team4/HW1

Homework #2: user:egm6321.f09.team4/HW2

title: User:Egm6321.f09.team17


text:
User:Egm6321.f09.Team17/HW1

testing.

title: User:Egm6321.f09.Team17/HW1


text:
User:Egm6321.f09.Team17/HW1b

testing.

newer version.

title: User:Egm6321.f09.Team17/HW1b


text:
Draft:Original research/Measurements

Measurements and instrumentation are parts of a course in experimental methods where students will learn how to accurately
 * 1) design a measuring system,
 * 2) collect necessary data,
 * 3) process and
 * 4) interpret the collected data, and
 * 5) present the results.

This experimental process will be practically applied in the laboratory exercises throughout the semester.

By the end of the course students are expected to understand the fundamentals of measuring systems including the particular limitations and capabilities of a number of specific measuring devices (pressure transducers, strain gages, thermocouples, etc.) and equipment (oscilloscope, data acquisition card, etc.).

In addition students are expected to understand the experimental process applied in the laboratory experiments such that they are able to successfully design and conduct an experiment and interpret and present the results.

Laboratories

 * Analytical astronomy laboratory
 * Cratering laboratory
 * Distance to the Moon
 * Electric orbits laboratory
 * Electron beam heating laboratory
 * Empiricisms laboratory
 * Galaxies laboratory
 * Intergalactic medium laboratory
 * Locating the Sun
 * Meteorites laboratory
 * Neutrinos from the Sun
 * Observational astronomy
 * Standard candles laboratory
 * Vega spectrum laboratory
 * Vertical precession
 * X-ray classification of a star
 * X-ray trigonometric laboratory

Lectures

 * Astronomical observatories
 * Backgrounds
 * Radiation bands
 * Radiation continua
 * Radiation emissions
 * Laboratory
 * Radiation detectors
 * Radiation intensities
 * Satellites for radiation astronomy
 * Spectroscopy
 * Telescopes for radiation astronomy

Problem sets

 * Angular momentum and energy
 * Column densities
 * Cosmic circuits
 * Energy phantoms
 * Furlongs per fortnight
 * Planck's equation
 * Radiation astronomy/Problem set
 * Radiation dosage
 * Radiation mathematics/Problem set
 * Spectrographs
 * Star jumping
 * Synchrotron radiation/Problem set
 * Telescopes and cameras
 * Unknown coordinate systems
 * Unusual units
 * Vectors and coordinates

Hypotheses

 * 1) Accurate measurements can be made with simple, inexpensive devices and instruments.

title: Draft:Original research/Measurements


text:
User talk:Egm6321.f09.Team17.smith1

 Hello Egm6321.f09.Team17.smith1, 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! --mikeu talk 21:35, 8 September 2009 (UTC)

edit on another account
You edit this account, but it do not exist ! Can you explain the reason ? Crochet.david 19:42, 14 September 2009 (UTC)
 * Can you done the explain ? Crochet.david 14:05, 15 September 2009 (UTC)

title: User talk:Egm6321.f09.Team17.smith1


text:
User talk:Gosox5555

 Hello Gosox5555, 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.
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --mikeu talk 22:38, 8 September 2009 (UTC)

title: User talk:Gosox5555


text:
User talk:Thatguygomer

 Hello Thatguygomer, 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.
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! --mikeu talk 22:43, 8 September 2009 (UTC)

title: User talk:Thatguygomer


text:
User talk:Jmaustin

 Hello Jmaustin, 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! --mikeu talk 22:45, 8 September 2009 (UTC)

title: User talk:Jmaustin


text:
User:Egm6321.f09.team3

User:Egm6321.f09.team3/HW1

User:Egm6321.f09.team3/HW2

User:Egm6321.f09.team3/HW3

User:Egm6321.f09.team3/HW4

User:Egm6321.f09.team3/HW5

User:Egm6321.f09.team3/HW6

User:Egm6321.f09.team3/HW7

title: User:Egm6321.f09.team3


text:
User:Egm6321.f09.team3/HW1

=Homework #1 PEA1 Fall 2009 Team 3=  Separate your problem statement from the solution. It is not always clear where the question ends and the solution begins.--Egm6321.f09.TA 02:48, 24 September 2009 (UTC)

Problem #1
Derive the 1st and 2nd order total time derivative for the function $$f$$ related to the Maglev, transrapid trains

Equation (1)
This equation is obtained as follows:

\dfrac{df}{dt} = \dfrac{\partial f}{\partial s} \dfrac{ds}{dt} + \dfrac{\partial f}{\partial t} \dfrac{dt}{dt} $$

With more details shown below:

\begin{align} \dfrac{d}{dt}\left[f\left(Y^{1}(t),t\right)\right] &= \dfrac{\partial}{\partial s}\left[f\left(Y^{1}(t),t\right)\right] \dfrac{d}{dt}\left[Y^{1}(t)\right] + \dfrac{\partial}{\partial t}\left[f\left(Y^{1}(t),t\right)\right]\\ &=\dfrac{\partial}{\partial s}\left[f\left(Y^{1}(t),t\right)\right] \dfrac{d}{dt}\left[Y^{1}(t)\right] + \dfrac{\partial} {\partial t}\left[f\left(Y^{1}(t),t\right)\right]\\ \end{align} $$  This equation is repeated. What is the progression from the first line to the second?--Egm6321.f09.TA 02:32, 24 September 2009 (UTC)

Equation (2):
Analogously we can follow the same procedure to obtain the $$2{nd}$$ order total derivative of $$f$$

\begin{align} \dfrac{d^2}{dt^2}\left[f\left(Y^{1}(t),t\right)\right] &= \dfrac{d}{dt}\left[\dfrac{\partial}{\partial s}\left(f\left(Y^{1}(t),t\right)\right) \dfrac{d}{dt}\left(Y^{1}(t)\right) + \dfrac{\partial}{\partial s} \left(f\left(Y^{1}(t),t\right)\right)\right]\\ &=\dfrac{\partial}{\partial s} \left[(\dfrac{\partial}{\partial s} \left(f\left(Y^{1}(t),t\right)\right) \dfrac{d}{dt}\left(Y^{1}(t)\right) +\dfrac{\partial}{\partial t}\left(f\left(Y^{1}(t),t\right)\right)\right] \dfrac{d}{dt}\left(Y^{1}(t)\right)+ \dfrac{\partial}{\partial t} \left[\dfrac{\partial}{\partial s}\left(f\left(Y^{1}(t),t\right)\right) \dfrac{d}{dt}\left(Y^{1}(t)\right) + \dfrac{\partial}{\partial t}\left(f\left(Y^{1}(t),t\right)\right)\right]\\ &=\dfrac{\partial^2}{\partial s^2}\left(f(Y^{1},t)\right) \left[\dfrac{d}{dt}\left(Y^{1}(t)\right)\right]^2 + \dfrac{\partial^2}{\partial s \partial t}\left(f\left(Y^{1},t\right)\right) \dfrac{d}{dt}\left(Y^{1}(t)\right) + \dfrac{\partial^2}{\partial t \partial s}\left(f\left(Y^{1},t\right)\right) \dfrac{d}{dt}\left(Y^{1}(t)\right) + \dfrac{\partial^2}{\partial t^2}\left(f(Y^{1},t)\right) + \dfrac{\partial}{\partial s}\left(f(Y^{1},t)\right) \dfrac{d}{dt}\left[\dfrac{d}{dt}\left(Y^{1}(t)\right)\right]\\ &=\dfrac{\partial^2}{\partial s^2}\left(f(Y^{1},t)\right)\left[\dfrac{d}{dt}\left(Y^{1}(t)\right)\right]^2 +2\cdot \dfrac{\partial^2}{\partial s \partial t}\left(f\left(Y^{1},t\right)\right) \dfrac{d}{dt}\left(Y^{1}(t)\right) + \dfrac{\partial^2}{\partial t^2}\left(f(Y^{1},t)\right) + \dfrac{\partial}{\partial s}\left(f(Y^{1},t)\right) + \dfrac{d^{2}}{dt^{2}}\left(Y^{1}(t)\right) \end{align} $$  Convert your result to match the notation from the problem statement in the lecture transparency. It is not clear that you have arrived at the final answer, although you have.--Egm6321.f09.TA 02:34, 24 September 2009 (UTC)

Problem #2
Derive the following equation using the integration factor knowledge:

 * $$ y(x) = \int^{x}q(z)dz = -Aexp^{-x} + \frac{x^{2}}{2} - x +B$$

To illustrate the use of integrating factor the following problem was posed:

 * $$y'' + y' = x\!$$

Let
 * $$ p(x) = y'(x)\! $$

which gives the necessary form to utilize the integrating factor method. The standard form is :

 * $$a_{1}p' + a_{0}p = b(x)\!$$

therefore our case yields the values $$ a_{0} = 1$$, $$b(x) = x$$. From this result we can say that

\begin{align} N(N_{x} - M_{y}) &=-f(x)\\ N(N_{x} - M_{p}) &=-f(x)\\ 1(0 - a_{0}) & = -f(x)\\ -a_{0} &= -f(x) \end{align} $$  $$f(x)=-\frac{1}{N}(N_{x}-M_{y})$$This makes a big difference in other problems. --Egm6321.f09.TA 02:42, 24 September 2009 (UTC)

The integration factor then becomes:

 * $$ h(x)=exp\int f(s)ds = exp(x)$$

 $$\exp$$ should have an argument, otherwise you have written $$e^{1}$$--Egm6321.f09.TA 02:42, 24 September 2009 (UTC)

Using the equation derived in class:

 * $$p(x) =\dfrac{1}{h(x)}\int h(s)b(s)ds$$

Now plugging the expression for $$h(x)$$ and $$b(s)$$ in the equation above

\begin{align} p(x) &=\dfrac{1}{exp(x)}\int exp(s)sds\\ &=\dfrac{1}{exp(x)}\left[exp(x) x - exp(x) +A\right]\\ &=x-1 + A \cdot exp(-x) \end{align} $$

Integrating once we can obtain $$ y(x)$$:

\begin{align} y(x) &= \int p(x)\\ & = \int \left[A \cdot exp(-s) + s -1\right]ds\\ &= -A \cdot exp(-x) + \frac{x^{2}}{2} -x + B \end{align} $$

Therefore we obtain the equation derived on class:

 * $$y(x)=-A \cdot exp(-x) + \frac{x^{2}}{2} -x + B$$

Problem #3
Show that the following $$1^{st}$$ order ODE is non-linear:

 * $$\left(2x^{2} +\sqrt{y}\right) + \left(x^{5}y^{3}\right)y' = 0$$

To identify the above expression is non-linear we will test the linearity with the differential operator. The differential operator for the above equation is the follwoing:following:

 * $$D(\cdot) = \left(2x^{2} +\sqrt{(\cdot)}\right) + \left(x^{5}(\cdot)^{3}\right)\dfrac{(\cdot)}{dx}$$

 Close, write the differential operator like this: $$D(\cdot) = \left(2x^{2} +\sqrt{(\cdot)}\right) + \left(x^{5}(\cdot)^{3}\right)\dfrac{d}{dx}(\cdot)$$--Egm6321.f09.TA 02:46, 24 September 2009 (UTC)

For the ODE to be linear it must follow the following condition:

 * $$D\left(\alpha u + \beta v \right) = D\left(\alpha u \right) + D\left(\beta v \right)$$

Let's find each of the conditions stated above:

\begin{align} D\left(\alpha u + \beta v \right) &= \left[2x^{2} + \sqrt{\left(\alpha u + \beta v \right)}\right] + \left[x^{5}\left(\alpha u + \beta v \right)^{3}\right] \dfrac {d}{dx}\left(\alpha u + \beta v \right)\\ D\left(\alpha u \right) + D\left(\beta v \right) &= \left[2x^{2} + \sqrt{\left(\alpha u \right)}\right] + \left[x^{5}\left(\alpha u \right)^{3}\right] \dfrac{d(\alpha u )} {dx} + \left[2x^{2} + \sqrt{\left(\beta v\right)}\right] + \left[x^{5}\left(\beta v\right)^{3}\right] \dfrac {d(\beta v)} {dx} \end{align} $$

Since the above conditions do not equal to each other, then we conclude that:

 * $$\left(2x^{2} +\sqrt{y}\right) + \left(x^{5}y^{3}\right)y' = 0$$

is non-linear.

Problem #4
Show that the following ODE is $$1^{st}$$ order and non-linear:

 * $$ x^{2}y^{5} + 6(y')^{2} = 0\!$$

To identify the above expression is non-linear we will test the linearity with the differential operator. The differential operator for the above equation is the follwoing:

 * $$D\left(\cdot\right) = x^{2}(\cdot)^{5} + 6 \left(\dfrac{d(\cdot)}{dx}\right)^{2} $$

For the ODE to be linear it must follow the following condition:

 * $$D\left(\alpha u + \beta v \right) = D\left(\alpha u \right) + D\left(\beta v \right)$$

Let's find each of the conditions stated above:

\begin{align} D\left(\alpha u + \beta v \right) &= x^{2} \left(\alpha u + \beta v \right)^{5} + 6\left[ \dfrac {d}{dx} \left(\alpha u + \beta v \right)\right]^2\\ D\left(\alpha u \right) + D\left(\beta v \right) &= x^{2} \left(\alpha u \right)^{5} + 6\left[ \dfrac {d( \alpha u )} {dx}\right]^{2} + x^{2} (\beta v )^{5} + 6\left[ \frac {d ( \beta v )} {dx}\right]^2 \end{align} $$

Since the above conditions do not equal to each other and that since the highest order of the derivative is first order, then we conclude that:

 * $$ x^{2}y^{5} + 6(y')^{2} = 0\!$$

is a $$1^{st}$$ order and non-linear ODE.

 Good write up. Nice work.--Egm6321.f09.TA 02:48, 24 September 2009 (UTC)

Part (I)
For the following $$\phi(x,y)$$ find $$M$$, $$N$$, and $$F(x,y,y')$$

 * $$ \phi = 6x^4 + 2y^{3/2}\!$$

$$M$$ and $$N$$ represent derivative expressions of $$\phi$$ the equations for their solutions are as follows:

 * $$ M = \phi_x = 24x^3\! $$

 * $$ N = \phi_y = 3y^{1/2}\! $$

With the results above we can find $$ M_y$$ and $$ N_x $$

 * $$ M_y = 0\!$$

 * $$ N_x = 0\!$$

Since, $$ M_y = N_x $$ it proves that the equation exact.

$$ F(x, y, y') = M + N \cdot y' = 24x^3 + 3y^{/frac{1}{2}} \cdot y' = 0 \! $$  Forward slashes for HTML, back slashes for math. Your /frac should be \frac --Egm6321.f09.TA 02:50, 24 September 2009 (UTC)

Part (II)
Create 3 exact non-linear $$1^{st}$$ ODEs:

#1

\begin{align} \phi_1 &= 2x^3y^4 + 4x^2y^5 \!\\ M = \phi_x &= 6x^2y^4 + 8xy^5 \!\\ N = \phi_y &= 8x^3y^3 + 20x^2y^4\! \\ M_y &= 24x^2y^3 + 40xy^4\! \\ N_x &= 24x^2y^3 + 40xy^4\! \end{align} $$

therefore the equation is exact!

 * $$ F1(x, y, y') = M + N y' = (6x^2y^4 + 8xy^5) + (8x^3y^3 + 20x^2y^4) y' = 0 \!$$

#2

\begin{align} \phi_2 &= 12x^{\frac{7}{4}}y^4 + 5x^2y^{\frac{9}{2}}\!\\ M = \phi_x &= 21x^{\frac{3}{4}}y^4 + 10xy^{\frac{9}{2}}\!\\ N = \phi_y &= 48x^{\frac{7}{4}}y^3 + 22.5x^2y^{\frac{7}{2}}\!\\ M_y &= 84x^{\frac{3}{4}}y^4 + 45xy^{\frac{7}{2}}\!\\ N_x &= 84x^{\frac{3}{4}}y^3 + 45xy^{\frac{7}{2}}\! \end{align} $$

therefore the equation is exact!

 * $$ F2(x, y, y') = M + N y' = \left(21x^{\frac{3}{4}}y^4 + 10xy^{\frac{9}{2}}\right) + \left(48x^{\frac{7}{4}}y^3 + 22.5x^2y^{\frac{7}{2}}\right) y' = 0 \!$$

#3

\begin{align} \phi_3 &= 4x^{-3}y^7 + 7x^6y^{\frac{1}{2}}\\ M = \phi_x &= -12x^{-4}y^7 + 42x^5y^{\frac{1}{2}} \\ N = \phi_y &= 28x^{-3}y^6 + 3.5x^6y^{-\frac{1}{2}} \\ M_y &= -84x^{-4}y^6 + 21x^5y^{-\frac{1}{2}}\\ N_x &= -84x^{-4}y^6 + 21x^5y^{-\frac{1}{2}} \end{align} $$

therefore the equation is exact!

 * $$ F3(x, y, y') = M + N y' = \left(-12x^{-4}y^7 + 42x^5y^{\frac{1}{2}}\right) + \left(28x^{-3}y^6 + 3.5x^6y^{-\frac{1}{2}}\right) y' = 0 $$

Contributing Team Members
Angela Diggs Egm6321.f09.team3.diggs 01:13, 16 September 2009 (UTC)

Barrett Mooney Egm6321.f09.team3.mooney 01:24, 16 September 2009 (UTC)

Catherine Snow EGM6321.f09.Team3.cgs 01:43, 16 September 2009 (UTC)

Francisco Kuljevan--Egm6321.f09.team3.Kuljevan.Francisco 07:03, 16 September 2009 (UTC)

title: User:Egm6321.f09.team3/HW1


text:
Collaborative Tools: Using Mind Meister for Student Collaboration

 * {| cellpadding="4" cellspacing="0" width="450px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Subject: English-Language Arts/Humanities and Electives
 * }

 * {| cellpadding="4" cellspacing="0" width="450px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Sub-Subject: Collaboration/Earth Charter Principles
 * }

 * {| cellpadding="4" cellspacing="0" width="450px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Length/Duration: 2 class periods (1 hour each)/On-going
 * }

 * {| cellpadding="4" cellspacing="0" width="450px"

 * bgcolor="#b4b4b4" style="border: 0px #cccccc solid;" |Technologies Used: Mindmeister, Wikispaces
 * }
 * }

{| cellpadding="5" cellspacing="5" style="width: 90%; background-color: inherit; margin-left: auto; margin-right: auto"
 * style="width: 60%; background-color: #e4e3c8; border: 2px solid #969696; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Background
According to Dewey (1902), the modern child has traditionally been taught in ways which each content and concepts are taught separately. When this is the case, there are no personal connections for the child to reference. Learning is seen as separate and scattered. It is this pedagogical model that I seek to reform in this lesson. Concept mapping is not a new idea. However, in schools it is often done on paper or poster board and lost with time. Mindmeisteris a collaborative concept mapping tool that will not only allow multiple users to work together, but it will live on in cyberspace for as long as the owner of the map wishes it to remain.

Clay Shirky (2009) speaks on social media and its effects on communication. The internet has evolved into a platform for the consumers of media to become generators of their own media message. Using Mindmeister to track ideas as they evolve in the classroom allows for students to be the generator of their own messages and track their learning process. This allows for students to make the connections from one concept to another and track how each new thought was generated from the thought that preceded it.

While it is important to have a medium for students to engage in collaboration, the content and message of the collaborative process is equally important. The content focus of this lesson is "peace". When we take a powerful concept such as "peace" we can build on its historical, political, and social implications. We can draw on many cultures to explore this concept from multiple points of view.

Finally, the use of on-line collaborative tools, such as Mindmeister allows for collaborators to be invited from around the world. On-line tools are a platform for globalized education. Globalized education opportunities are one of the many goals of the The Earth Charter Initiative. The Earth Charter principle 1.3 describes the goal of building a democratic society that is just, participatory, sustainable, and peaceful. Through content choices and on-line collaboration, we can lead the pursuit of these ideas.
 * }

{| cellpadding="5" cellspacing="5" style="width: 90%; background-color: #c9e4c8: inherit; margin-left: auto; margin-right: auto"
 * style="width: 60%; background-color: #c9e4c8; border: 2px solid #969696; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |

Objective:
This lesson is designed to integrate technology and the principles of The Earth Charter. Specifically, this lesson will introduce students to MindMeister, a collaborative mind mapping tool. Students will collaboratively define "peace" and embed digital resources that support their thinking. This collaborative mind map will be utilize as a tracking tool for gathering research and evidence. Students will then use this body of evidence to extend their thinking about "peace" by creating a 3-5 minute video or design a Wikispace to promote peace.

Engage:
Direct students to the Wikipedia page: September 11 attacks. Have students read the page and ask students to consider how people may have felt at this time. Next, have students write just one word or a short phrase to explain their thinking about September 11 on paper, wad it into a ball, and throw it in the middle of the room. Next, have each student select a paper ball and share the word or phrase written on the paper ball. Discuss how individual words and short phrases can be powerful.

Explore:
Have students login to MindMeister and begin collaboration on mind mapping "peace" with one or more collaborators. Collaborative mind mapping should not be done individually. Remind students to utilize powerful words and phrases to define "peace". You may want to provide students the following questions to consider as they begin responding to some of the following questions in the mind map: 1. What does peace look like? 2. What does peace feel like? 3. What is the opposite of peace and how does this happen? 4. How can you help promote peace in your life?

In addition to writing words and phrases, encourage students to add links to other websites, videos, or attach documents to expand their thinking about "peace".

Sample Collaborative Map

Explain:
Have students choose one branch of the peace mind map, beginning with the root node, and present how one node connects to the next.

Elaborate:
Provide students with choices to elaborate on their learning about "peace". For example, you could have students create or design their own mind map on MindMeister on another principle from The Earth Charter or students could search for other collaborative maps about peace and compare it to their collaborative map.

Evaluate:
This is a collaborative project and should evaluated as such. A sample rubric is available from Rubistar.

 * }

{| cellpadding="5" cellspacing="5" style="width: 90%; background-color: #cdd6ee: inherit; margin-left: auto; margin-right: auto"
 * style="width: 60%; background-color: #cdd6ee; border: 2px solid #969696; vertical-align: top; -moz-border-radius-topleft: 8px; -moz-border-radius-bottomleft: 8px; -moz-border-radius-topright: 8px; -moz-border-radius-bottomright: 8px;" rowspan="2" |


text:
New Testament (Greek)

What's the big idea?
These pages are intended for people who know some modern Greek, enough to read and write simple texts, and who are interested in reading the New Testament in the original Koine Greek. Parts of the New Testament are surprisingly approachable for folks at an intermediate level on up. You can decide how many or which of the questions you want to answer, how much to write, whether to do the additional readings, and whether to go investigate on your own, according to your time, interest and energy.

Unlike sites that rely on traditional student-teacher models of learning, Wikiversity is built around the concept of learning communities. (Eh, at least some of the time.) So these pages aren't full of exercises with set answers. They are intended to help learners figure out strategies for reading comprehension that work best for them, while having a little fun at the same time.

These pages take a short text from one of the Gospels as a starting point.

Using the Wiki
Users of these pages are encouraged to annotate them on their discussion pages: see the "discussion" tab at the top of each page you view. Please also add new references or other items to make the existing pages more useful: click the "edit" tab at the top of a page be taken to a form that allows you to add or change content. You are also encouraged to start the next set of pages: Η Καινή Διαθήκη 2!

If you have never used a Wiki before, here are some short instructions on how to navigate pages and add content to a page.

Contents

 * Εισαγωγή
 * Το κείμενο
 * Μερικές ερωτήσεις
 * Δεύτερη ανάγνωση
 * Γράψτε κι εσείς
 * Ακόμα έχετε όρεξη;
 * Χρήσιμοι σύνδεσμοι
 * Αξιολόγηση
 * Απόλυτα άσχετο

title: New Testament (Greek)


text:
Wikiversity:Threaded discussions with NavFrames with subst/20090624123430

20090909041046 --210.75.252.157 04:10, 9 September 2009 (UTC)
 * Comment: good idea
 * reply[]

What links here


text:
New Testament (Greek)/Εισαγωγή

Τι κάνουμε;
Για όσους μαθαίνουν την νεοελληνική γλώσσα κια ενδιαφέρονται για την κατανόηση του πρωτότυπου κειμένου της Καινής Διαθήκης, ας διασκεδάσουμε λίγο με μία ιστοριούλα από το Ευαγγέλιο Κατά Μάρκον. Σκοπός αυτών των σελίδων είναι να καταλάβετε καλύτερα τι σας βοηθά στην κατανόηση όταν διαβάζετε ένα γραπτό κείμενο. Επίσης μπορείτε να συνειδητοποιήσετε μερικά χρήσιμα εργαλεία που σας είναι ήδη διαθέσιμα.

Πώς το κάνουμε;
Θα διαβάσετε το κείμενο δύο φορές. Την πρώτη φορά, δεν είναι αναγκαίο να καταλάβετε κάθε λεπτομέρεια. Βγάλτε απλώς το γενικό νόημα του κειμένου. Ένας τρόπος για να καταφέρετε αυτό είναι να μην δώσετε πολλή προσοχή στις άγνωστες λέξεις ή τα ίσως περίεργα γραμματικά στοιχεία. Έχετε άλλες ιδέες στο νου για το πώς να αντιμετωπίσετε το κείμενο; Δοκιμάστε τες και ύστερα γράψτε τις εντυπώσεις σας!

Στις ακόλουθες σελίδες θα έχετε την ευκαιρία να κρατήσετε σημειώσεις, να θέσετε τις δικές σας ερωτήσεις, και να προτείνετε άλλα θέματα για έρευνα. Επιπλέον, αν θέλετε μπορείτε να επεξεργαστείτε τις σελίδες τις ίδιες και να προσθέσετε ιδέες, ερωτήσεις, και οτιδήποτε άλλο σας φαίνεται χρήσιμο για τον επόμενο αναγνώστη. Ας αρχίσουμε!

- |Γυρίστε πίσω στην αρχή.

title: New Testament (Greek)/Εισαγωγή


text:
New Testament (Greek)/Κείμενο

Ορίστε το απόσπασμα από το Ευαγγέλιο Κατά Μάρκον:

Πηγή:Κατά_Μάρκον (Mark 1:1-8)

Μπορείτε να ακούσετε το ίδιο κείμενο εδώ (αρχείο mp3).

- |Γυρίστε πίσω στην αρχή.

title: New Testament (Greek)/Κείμενο


text:
New Testament (Greek)/Μερικές ερωτήσεις

 * Τι κάνατε για να βγάλετε νόημα από το κείμενο; Πώς διαβάσατε το κείμενο, με ποια διαδικασία;
 * Αναγνωρίσατε την ιστορία; Αν ναι, με ποιον τρόπο, και πώς σας βοήθησε αυτό;
 * Υπάρχουν συγκεκριμένες λέξεις ή φράσεις που σας βοήθησαν να καταλάβετε τη γενική ιδέα; Ποιες είναι μερικές από αυτές;
 * Όταν διαβάσετε ένα δύσκολο κείμενο περισσότερες από μία φορές, μάλλον καταλαβαίνετε καλύτερα το νόημα. Γιατί; Τι κάνετε κατά τη δεύτερη ανάγνωση που σας βοηθά;
 * Τι προτιμήσατε να παρακολουθήσετε, το γραπτό κείμενο ή το προφορικό; Για ποιο λόγο;  Γενικά προτιμάτε να ακούτε ή να διαβάζετε άγνωστες λέξεις και φράσεις στα ελληνικά;  Ποια είναι η προτίμησή σας όσον αφορά καινούργιες αγγλικές λέξεις και φράσεις;

-

title: New Testament (Greek)/Μερικές ερωτήσεις


text:
New Testament (Greek)/Δεύτερη ανάγνωση

Τώρα μπορείτε να ξαναδιαβάσετε το κείμενο και να προσέχετε τις άγνωστες λέξεις και άλλες λεπτομέρειες. Εκτός αν το θέλετε, δεν χρειάζεται να ψάξετε τις λέξεις στο λεξικό, ούτε να έχετε πλήρη κατανόηση της γραμματικής. Κοιτάξτε τις παρακάτω ερωτήσεις και διαβάστε το κείμενο έχοντας αυτές στο νου.
 * Ξέρετε την ιστορία στα αγγλικά; Αν ναι, σας βοήθησε αυτό στα δύσκολα σημεία;  Σημειώστε 1-2 από τα μέρη που σας εμπόδισαν  και εξηγήστε πώς τα ξεπεράσατε.

 * Ποιες λέξεις φαίνονται να είναι ίδιες ή παρόμοιες με λέξεις της νεοελληνικής που ξέρετε; Σημειώστε μερικές από αυτές.
 * Αναγνωρίζετε όλες τις μορφές των παραπάνω λέξεων στο κείμενο; Αν κάτι σας προβληματίζει ιδιαίτερα, μπορείτε να το ερευνήσετε στην ιστοσελίδα Perseus. Δείτε τους χρήσιμους συνδέσμους για πληροφορίες σχετικά με το Perseus.

 * Είχατε ακουστά την έκφραση "φωνή βοώντος εν τη ερήμω"; Ξέρετε την αντίστοιχη αγγλική έκφραση; Πότε λέγεται και τι σημαίνει;  Τι φαντάζεστε να σημαίνει η ελληνική έκφραση;  Λέγεται στις ίδιες περιπτώσεις όπως η αγγλική;  Μπορείτε να κάνετε αναζήτηση στο Google για να βρείτε μερικά παραδείγματα χρήσης της έκφρασης.

-

title: New Testament (Greek)/Δεύτερη ανάγνωση


text: File:Greek New Testament Scrivener.png

title: File:Greek New Testament Scrivener.png


text:
New Testament (Greek)/Γράψτε κι εσείς

Δοκιμάστε να γράψετε μερικές προτάσεις από το κείμενο σε απλά ελληνικά. Ή μπορείτε να ξαναγράψετε την ιστορία ή ένα μέρος του με απλά λόγια. Ή αν προτιμάτε, μπορείτε να γράψετε μια άλλη ιστορία ή παραβολή από την Καινή Διαθήκη.

Πώς διαφέρει η γραμματική των δικών σας προτάσεων από τις προτάσεις στο κείμενο; Τι σας έκανε ιδιαίτερη εντύπωση;

Αν ενδιαφέρεστε, μπορείτε να μάθετε περισσότερο για τις γραμματικές διαφορές ανάμεσα στην ελληνιστική κοινή και την νεοελληνική εδώ: (στα τμήματα "Basic Morphology" και "Basic Syntax").

-

title: New Testament (Greek)/Γράψτε κι εσείς


text:
New Testament (Greek)/Ακόμα έχετε όρεξη;

Είδαμε πώς γράφει την ιστορία ο Μάρκος. Τι λέει ο Ματθαίος; Μπορείτε να διαβάσετε τη δική του παραλλαγή εδώ: Κατά Ματθαίον

 * Πώς διαφέρει η δική του μεταχείριση της γλώσσας από αυτή του Μάρκου; Ποιες είναι οι γενικές εντυπώσεις σας;
 * Ήταν πιο εύκολο το κείμενο, πιο δύσκολο, ίδιο; Αναγνωρίσατε περισσότερες λέξεις σε ένα από τα δύο κείμενα;
 * Ποια είναι η γνώμη σας για το ύφος και το λεξιλόγιο που χρησιμοποιεί ο κάθε συγγραφέας;

Ένα μέρος του κειμένου διατηρείται σε πάπυρο [http://www.csad.ox.ac.uk/POxy/papyri/vol64/300dpi/4401back300.jpg P.Oxy. LXIV 4401]. Από τις προτάσεις

μπορείτε να διακρίνετε στην εικόνα μερικές λέξεις;

-


text:
New Testament (Greek)/Χρήσιμοι σύνδεσμοι

Παρακάτω παρουσιάζεται ένας κατάλογος μερικών χρήσιμων ιστοτόπων για την έρευνα πληροφοριών σχετικά με τα Ευαγγέλια.

 * Η ολόκληρη Βίβλος στα ελληνικά, μαζί με πολλά άλλα ελληνικά κείμενα, παρουσιάζονται εδώ. Μπορείτε επίσης να δείτε τα μενού στα αγγλικά.
 * Η Βίβλος στα ελληνικά, σε αρχεία mp3, είναι διαθέσιμη σε αυτή τη διεύθυνση:.
 * Μια αγγλική μετάφραση της Βίβλου βρίσκεται εδώ. Προσέξτε, μπορεί το ελληνικό πρωτότυπο να διαφέρει λίγο από το κείμενο που μελετούμε εμείς.
 * Ο ιστότοπος Perseus έχει μια έκδοση του κειμένου μας στα ελληνικά, με αναφορές σε λεξικά και μορφολογικά εργαλεία. Πατήστε μια λέξη και θα ανοίξει ένα παραθυράκι με τη λέξη και συνδέσμους προς διάφορα λεξικά.  Μπορείτε για παράδειγμα να πατήσετε τη λέξη «εὐαγγελίου». Στο παραθυράκι θα δείτε μορφολογικές πληροφορίες για τη λέξη: "noun sg neut gen" (singular neuter genitive case), και τα λεξικά (LSJ, Middle Liddell, κλπ).  Αν πατήσετε για παράδειγμα το LSJ, θα δείτε ορισμούς για τη λέξη «εὐαγγέλιον» από το λεξικό Liddell-Scott-Jones.  Για άλλα ελληνικά κείμενα μπορείτε να μπείτε στην αρχική σελίδα της ελληνικής συλλογής.
 * Ένας άλλος ιστοχώρος παρουσιάζει τη Βίβλο στα ελληνικά με λεξικό, μορφολογικές πληροφορίες και αγγλική μετάφραση εδώ (λεξικό εδώ).
 * Λεξικά, γραμματικές κι άλλα βιβλία για την ελληνιστική κοινή βρίσκονται εδώ. Αυτά τα βιβλία είναι παλιά (εκδόθηκαν πριν από το 1920) αλλά μπορεί να είναι χρήσιμα παρ' όλα αυτά.
 * Υπάρχουν στο Διαδίκτυο πολλές μελέτες σχετικά με την κατανόηση γραπτού λόγου. Μια καλή εισαγωγή στο θέμα βρίσκεται εδώ: εδώ.

Και κάτι ακόμα...

 * Σύγχρονες λέξεις από παλιά κείμενα

- |Γυρίστε πίσω στην αρχή.


text:
New Testament (Greek)/Αξιολόγηση

Τι θα θέλατε να αλλάξετε σε αυτές τις σελίδες αν είχατε την ευκαιρία; Εδώ μπορείτε να σημειώσετε τις ιδέες σας για αλλαγές, διορθώσεις και ανάπτυξη του υλικού. Αν έχετε θάρρος, μπορείτε να αλλάξετε τις σελίδες εσείς. Δείτε την καρτέλα «edit» πάνω πάνω σε κάθε σελίδα. Αν κάνετε μια μεγάλη αλλαγή, καλό θα ήταν να γράψετε μια εξήγηση στη σελίδα συζήτησής της (δείτε την καρτέλα «discussion» πάνω πάνω σε κάθε σελίδα). Ποια πράγματα θα θέλατε να αλλάξετε; Για παράδειγμα:

 * Σε ποια σημεία έλειπαν εξηγήσεις ή δεν σας ήταν επαρκείς;
 * Σας έρχονται στο νου άλλες ερωτήσεις ή άλλες πηγές πληροφοριών που θα θέλατε να προστεθούν;
 * Βρήκατε λανθασμένες πληροφορίες, ορθογραφικά/συντακτικά λάθη, ή άλλα παρόμοια προβλήματα;
 * Τι θα αλλάζατε στη δομή ή στη ροή των κειμένων και ερωτήσεων για να διευκολυνθεί η κατανόηση άλλων αναγνωστών;
 * Υπήρχαν πληροφορίες που ήταν περιττές ή σας μπέρδεψαν αντί για να σας ρίξουν φως στο θέμα;

Ποια πράγματα σας άρεσαν ιδιαίτερα; Για παράδειγμα:

 * Υπήρχε κάποια πηγή που σας ήταν ειδικά χρήσιμη;
 * Κέντρισαν το ενδιαφέρον σας αυτές οι σελίδες; Αν ναι, πώς;
 * Σας έβαλε σε σκέψεις καμία από τις ερωτήσεις; Αν ναι, ποια, και ποιο ήταν το αποτέλεσμα;

Θέλετε να δημιουργηθούν παρόμοια θέματα στο μέλλον; Αν ναι, έχετε συγκεκριμένες προτάσεις στο νου;

Αν έπρεπε να δώσετε βαθμό στις σελίδες αυτές (με οποιαδήποτε κλίμακα θέλετε), τι θα βάζατε και γιατί;

-

title: New Testament (Greek)/Αξιολόγηση


text:
New Testament (Greek)/Απόλυτα άσχετο

Φορέσατε ποτέ σας παλτό από καμηλόμαλλο; (Εγώ πάντως όχι.)

- |Γυρίστε πίσω στην αρχή.

title: New Testament (Greek)/Απόλυτα άσχετο


text:
New Testament (Greek)/Λεξιλόγιο

Ορίστε το πρώτο μέρος του κειμένου μας με συνδέσμους προς μερικές λέξεις της σύγχρονης γλώσσας.

Οι σύνδεσμοι οδηγούν προς το Βικιλεξικό (Wiktionary), ένα πολυγλωσσικό λεξικό που απευθύνεται σε ελληνόφωνους. (Βρίσκεται υπό κατασκευή και συντάσσεται από μη ειδικούς ανθρώπους. Όπως κάθε wiki, μπορεί να περιέχει ανακρίβειες.)

- |Γυρίστε πίσω στην αρχή.

title: New Testament (Greek)/Λεξιλόγιο


text:
Talk:New Testament (Greek)

So, amusingly enough these pages are written as part of online coursework (see for details, text in Greek). Of course that doesn't preclude them from being edited mercilessly :-D If you want to ask me questions about them or the course, you can leave a message on my talk page... but I'm not here very often. Best to join the irc channel #wikiversity-el, or even better #wiktionary-el on the server irc.freenode.net. Happy trails! -- Απεργός 05:50, 9 September 2009 (UTC)

title: Talk:New Testament (Greek)


text:
New Testament (Greek)/Μερικές ερωτήσεις/Ideas

Εδώ μπορείτε να συζητήσετε το κείμενο, τις ερωτήσεις, τα σχόλια των συμμαθητών σας, κλπ. Μπορείτε επίσης να θέσετε τις δικές σας ερωτήσεις και να προσφέρετε βοήθεια σε άλλους. -


text:
New Testament (Greek)/Δεύτερη ανάγνωση/Ideas

Εδώ μπορείτε να συζητήσετε το κείμενο, τις ερωτήσεις, τα σχόλια των συμμαθητών σας, κλπ. Μπορείτε επίσης να θέσετε τις δικές σας ερωτήσεις και να προσφέρετε βοήθεια σε άλλους. -


text:
New Testament (Greek)/Γράψτε κι εσείς/Ideas

Εδώ μπορείτε να συζητήσετε το κείμενο, τις ερωτήσεις, τα σχόλια των συμμαθητών σας, κλπ. Μπορείτε επίσης να θέσετε τις δικές σας ερωτήσεις και να προσφέρετε βοήθεια σε άλλους. -


text:
New Testament (Greek)/Ακόμα έχετε όρεξη;/Ideas

Εδώ μπορείτε να συζητήσετε το κείμενο, τις ερωτήσεις, τα σχόλια των συμμαθητών σας, κλπ. Μπορείτε επίσης να θέσετε τις δικές σας ερωτήσεις και να προσφέρετε βοήθεια σε άλλους. -


text:
New Testament (Greek)/Αξιολόγηση/Ideas

Εδώ μπορείτε να συζητήσετε το κείμενο, τις ερωτήσεις, τα σχόλια των συμμαθητών σας, κλπ. Μπορείτε επίσης να θέσετε τις δικές σας ερωτήσεις και να προσφέρετε βοήθεια σε άλλους. -

title: New Testament (Greek)/Αξιολόγηση/Ideas


text:
Template:New Section Comments

Comments by ~
--

title: Template:New Section Comments


text:
Template talk:New Section Comments

This template is intended for use to preload editing a new section of a course notes page or a discussion page. (Some people who use the Wikiversity learning resources may be new to wiki notation, and this gives them an easy way to write their message.)

title: Template talk:New Section Comments


text:
User:Akshaysarode21

Akshaysarode21 (b. 21 April 1988, Mumbai, India). I am doing my Masters in Computer Science (MCA) from IGNOU University. My Blog

title: User:Akshaysarode21


text:
User:Egm6321.f09.team5

Team 5 Members
Guillermo Varela       g.varela.me@gmail.com Gary Risher            gary.risher@eglin.af.mil Zhichao Gong             gzc6064@gmail.com Alan Bear                nbear01@ufl.edu

User Tests
Test --Egm6321.f09.team5.GV 06:26, 9 September 2009 (UTC)

Test Egm6321.f09.team5.bear 15:58, 9 September 2009 (UTC)

Test --Egm6321.f09.team5.risher 09:14, 14 September 2009 (UTC)

Test --Egm6321.f09.team5.Jason(Zhichao Gong) 00:17, 23 September 2009 (UTC)

HW links
These are the new HW links in the manner instructed by the Professor.

User:Egm6321.f09.team5/HW1 User:Egm6321.f09.team5/HW2 User:Egm6321.f09.team5/HW3 User:Egm6321.f09.team5/HW4 User:Egm6321.f09.team5/HW5 User:Egm6321.f09.team5/HW6 User:Egm6321.f09.team5/HW7

title: User:Egm6321.f09.team5


text:
Talk:Flexible learning

Flexible Learning Strategy & Tactics
I added some 'Samuel Smiles' about learning plans. The difficulty most of us 'mature students' encounter is 'grasshopper minds' - we simply know too many diverse things but not enough about the study area! Maybe somebody expert in psychology of learning could develop this theme, maybe on another page?Timpo 07:29, 9 September 2009 (UTC)

title: Talk:Flexible learning


text:
User:She0910004/Lyceumphil.edu.ph/manila

lyceum university of the Philippines, Manila


text:
Studygroups

Greetings University of Portsmouth Students.
To arrange your own study groups then add your paltalk nickname to the list below, and a date and time.

If you want a tutorial AFTER the drafts have come in, then arrange a time and date in a similar fashion and I will organise 2 dates for you all.

WARNING : DO NOT OPEN LINKS OR ACCEPT FILES FROM PEOPLE YOU DON'T KNOW

UPDATE YOUR ONLINE PROFILE, AND PUT (EDAM D/L) IN THERE.

BELOW IS THE LIST YOU NEED TO UPDATE USING THE UPDATE BUTTON ABOVE WHEN YOU HAVE DONE THIS, YOU NEED TO SAVE ANY CHANGES BY LOOKING TOWARDS THE BOTTOM OF THIS PAGE AND CLICKING THE BUTTON.

YOU NEED TO PUT AN EXACT DATE
ELMS STUDENTS GROUP CHAT ONLY

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Contact the Academic Skills Unit on http://www.port.ac.uk/departments/studentsupport/ask/

They cover a wide range of skills areas, including:

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Academic debate using paltalk.

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PALTTALK IS Free video chat, instant messaging and chat rooms.

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7. If you enjoy this type of learning I will make you an admin and give you a H@T (The HAT sign)

title: Studygroups


text:
User:Xadrex

I am a UK Forensic Psychologist with 20 years exeperience of working with offenders. I specialise in working with people with learning disabilities. I believe that everyone has the right to learn and that materials should be free to all. Hopefully Wikiversity is a first step towards this goal.

title: User:Xadrex


text:
Votian/Present Tense

Morphemes

 * The very same morphemes of the first and second person are used in all moods and tenses.

Pronunciation

 * 1) Final -n is omitted everywhere in Eastern Votic dialect including the first person of singular. It causes lengthening of the preceding vowel pronounced and sometimes gemination of a short consonant preceding the vowel e.g. tuл̆лē̮ ('I come' < *tule-n), luğgē̮ ('I read' < *luge-n).
 * 2) All the other dialects both in Ingria and Estonia pronounce it n e.g. elän ('I live.').
 * 3) The morpheme -mmak of the first person of plural is pronounced as -mmaG or -mmäG in Eastern Votic dialect depending in vowel harmony e.g. sāmmaG ('We get (it).') vs. mǖmmäG ('We sell.').
 * 4) All the other dialects both in Ingria and Estonia pronounce it -mma or -mmä depending in vowel harmony e.g. sāmma ('We get (it).') vs. mǖmmä ('We sell.').
 * 5) In Jõgõperä dialect it may be sometimes pronounced as -mme̮ or -mme depending in prosody e.g. nüttä sǖmme i jūmme̮  ('Now we('ll) eat and drink.').
 * 6) In Western Votic dialects it may sometimes drop it's final vowel and sound simply -m̄ depending in prosody e.g. kē̮s ̮tue̮m̄ tağgāz? ('When we('ll) come back.' in Mati dialect).
 * 7) In Alutaguse dialects the geminated mm has weakened after an unstressed syllable.
 * 8) In Lüganuse dialect it is pronounced m̆m then e.g. eläm̆mä ('We live.').
 * 9) In Jõhvi, Iisaku and Western Vaivara dialect it is degeminated to m in every position, if the preceding syllable does not carry a secondary stress e.g. luGesimma ('We read (in past).') vs. annama ('We give (something).' in [[Iisaku dialect]).
 * 10) In old Lüganuse dialect the morpheme -mmak of the first person of plural was pronounced maije or mäije after a secondary stress e.g. ve̮ttamaije  ('We take (something).').
 * 11) This ending may be composed of  -mma and the first person's pronoun of plural meije e.g. ve̮ttamaije  < *ve̮ttama meije (even though usually a subject does not follow a verb) or it may be influenced by  maije infinitive.
 * 12) The morpheme -t of the second person of singular is pronounced as -D both in Ingria and Estonia e.g. eläD ('You live.').
 * 13) It may be sometimes pronounced -t or -d caused by sandhi e.g. ve̮ttaizid ̮enellēz ('You might take it (for yourself).') or e̮sit ̮kaunī tšiutō ('You bought a beautiful shirt.'). (Unfortunately the examples above are not in present tense of indicative.)
 * 14) The morpheme -ttak of the second person of plural is pronounced as -ttaG or -ttäG in Eastern Votic dialect depending in vowel harmony e.g. sāttaG ('You get (it).') vs. mǖttäG ('You sell.').
 * 15) All the other dialects both in Ingria and Estonia pronounce it -tta or -ttä depending in vowel harmony e.g. sātta ('You get (it).') vs. mǖttä ('You sell.').
 * 16) In Jõgõperä dialect it may be sometimes pronounced as -tte̮ or -tte depending in prosody e.g. nüttä sǖtte i jūtte̮  ('Now you('ll) eat and drink.').
 * 17) In Western Votic dialects it may sometimes drop it's final vowel and sound simply -t̄ depending in prosody e.g. minē peräs̄ sūttuzit̄ ke̮vassi ('Why did you get (very) angry?'). (Unfortunately the example above is not in present tense of indicative.)
 * 18) In Alutaguse dialects the geminated tt has weakened after an unstressed syllable. It is pronounced t̆t then e.g. lähät̆tä ('You go.').
 * 19) The morpheme -p of the third person of singular is pronounced as -B both in Ingria and Estonia e.g. eläB ('He lives.').
 * 20) In Alutaguse dialects it may sound -p or -p̆ also e.g. se̮isap̆  ('It stands.').
 * 21) The morpheme -vat of the third person of plural is pronounced as -vaD or -väD depending in vowel harmony e.g. sāvaD ('They get (it).') vs. eläväD ('They live.').
 * 22) In Alutaguse dialects even the third person of plural is falsely in the same grade as all the other persons (influenced by  Mid Estonian dialect) e.g. piäväD instead of pitäväD ('They must.'), even though this morpheme can never close the preceding syllable.
 * 23) In Alutaguse dialects the morpheme may be pronounced -väD even with back vowel stems e.g. e̮liväD ('They were.').
 * 24) In Lüganuse dialect the first v of this suffix may be degeminated after a secondary stress e.g. kelisevvad ('(The bells) ring.').
 * 25) This morpheme is recently substituted by indefinite voice both in Ingria and in Alutaguse dialects e.g. nämä tuллassa ('They come.') (probably influenced by  Russian language, where the 3. person of plural serves similar role to Finnic indefinite voice e.g. говорят ('They speak.' or 'Someone speaks.').).

Morphophonology

 * In all dialects both in Ingria and Estonia personal endings never follow any consonant stem e.g. imperative plural pes-kā ('Wash!') vs. the second person of singular peze-B ('(Someone) washes.') or imperative plural page̮t-kā ('Escape!') vs. the first person of plural pake̮ne̮-mma ('We run away.').
 * Thus these forms are always in the same grade as the singular of the second person imperative and in a grade opposite to any other suffixal imperative form caused by consonant gradation in stems e.g. jättägō ('Let him leave (it)!') vs. jätäD ('You leave (it).') or page̮t-kā ('Escape!') vs. pake̮n-e̮-D ('You escape.').
 * The only exception is the third person of plural, which according to consonant gradation principles may occur only in the strong grade e.g. tetševäD ('They do (it).') and pake̮ne̮-vaD ('They run away.'), because this morpheme can never close the preceding syllable.
 * In Alutaguse dialects even the third person of plural is falsely in the same grade as all the other persons (influenced by Mid Estonian dialect) e.g. piäväD instead of pitäväD ('They must.'), even though this morpheme can never close the preceding syllable.

=== Phonological history ===
 * The morpheme of the first person of singular has underwent a sound change *-m > -n in Proto-Finnic stage.
 * Thus it is the first component of the morpheme -mmak of the first person of plural.
 * Analogically the morpheme -t of the second person of singular is the first component of the morpheme -ttak of the second person of plural.
 * The very same original components of the first and second person are found in possessive suffixes and personal pronouns.
 * The plural -mmak < *-ma? and -ttak < *-ta? were geminated by a present tense marker -k, which has probably preceded them. Later it has supposedly melt into the following m and t e.g. sāmma ('We get (it).') < *sā+k+ma?. In some Finnish and Karelian dialects these personal endings are not geminated in the past tense, where the marker -k was absent. Though in most of Finnic dialects (including the Votian ones) they are geminated in all moods and tenses.
 * The vowel of -mmak and -ttak is e in Standard Finnish, Standard Estonian and their western dialects. In Southern Vepsian dialects it's counterpart is ai and in South Estonian dialects it is i, but that is probably a late feature, because it has not went through the obligatory Finnic Sound changes, caused by similar plural and past tense marker.
 * The final k of -mmak and -ttak does not occur in Hevaha Ingrian and those Eastern Finnish dialects, where the final k usually has been preserved and Eastern Votic dialect, where it may be found, has sometimes added k to words, where it was originally absent e.g. sūre̮piG  ('bigger' comparative), sūre̮ssiG  ('to (become) big' translative). The final consonant of those morphemes is n in Hevaha Ingrian and some Finnish dialects. E. Itkonen has proposed based on Saami data, that these various vowels and final consonants may originally come both from dual (> -men, -ten) and plural (> -mak, -tak) sets, which may have been mixed up in the Finnic branch.
 * The morpheme of the third person of singular has underwent following sound changes *-pa > *-pi > -p like the comparative  marker and was originally a suffix of present participle.
 * The morpheme of the third person of plural is derived from the same suffix of present participle with a plural nominative marker t.

=== Other Finnic dialects ===

The first person of singular
 * Standard Finnish : lue-n ('I read.')
 * Vesjegonski Karelian dialects : luve-n ('I read.')
 * Vepsian dialects : luge-n ('I read.')
 * Ingrian dialects : lue-n ('I read.')
 * Standard Estonian : loe-n ('I read.')
 * South Estonian dialects : loè- ('I read.')
 * Livonian dialects : lugù-B ('I read.')

The first person of plural
 * Standard Finnish : lue-mme ('We read.')
 * Finnish dialects : -mmen, -mmon, -mma
 * Vesjegonski Karelian dialects : luve-mma ('We read.')
 * Vepsian dialects : luge-mai ('We read.')
 * Ingrian dialects : lue-(m)man ('We read.')
 * Standard Estonian : loe-me ('We read.')
 * South Estonian dialects : an̆na-miʔ ('We give.')
 * Livonian dialects : lu ̉ggə̑-m ('We read.')

The second person of singular
 * Standard Finnish : lue-t ('You read.')
 * Vesjegonski Karelian dialects : luve-t ('You read.')
 * Vepsian dialects : luge-d ('You read.')
 * Ingrian dialects : lue-D ('You read.')
 * Standard Estonian : loe-d ('You read.')
 * South Estonian dialects : loe-t̀ ('You read.')
 * Livonian dialects : lugù-D ('You read.')

The second person of plural
 * Standard Finnish : lue-tte ('You read.')
 * Finnish dialects : -tten, -tton, -tta
 * Vesjegonski Karelian dialects : luve-tta ('You read.')
 * Vepsian dialects : luge-tai ('You read.')
 * Ingrian dialects : lue-tta ('You read.')
 * Standard Estonian : loe-te ('You read.')
 * South Estonian dialects : anna-tti ('You give.')
 * Livonian dialects : lu ̉ggə̑-t̀ ('You read.')

The third person of singular
 * Standard Finnish : luke-e ('She reads.')
 * Vesjegonski Karelian dialects : lugo-u ('She reads.')
 * Vepsian dialects : lugo-b ('She reads.')
 * Ingrian dialects : lukk-ō ('She reads.')
 * Standard Estonian : loe-b ('She reads.')
 * South Estonian dialects : luGè̮- ('She reads.')
 * Livonian dialects : lugù-B ('She reads.')

The third person of plural
 * Standard Finnish : luke-vat ('They read.')
 * Karelian dialects use indefinite voice instead : lugie-tah ('They read.').
 * Vepsian dialects : lugo-ba(d) ('They read.')
 * Ingrian dialects : lukk-ōD ('They read.') due to the consonant gradation in suffixes
 * Standard Estonian : loe-vad ('They read.')
 * South Estonian dialects : luge̮-vaʔ ('They read.')
 * Livonian dialects : lu ̉ggə̑-bə̑D ('They read.')

title: Votian/Present Tense


text:
User:Egm6321.f09.team3.Kuljevan.Francisco

=Page of Francisco Kuljevan/ Principles of Engineering Analysis I=

User:Egm6321.f09.team3.Kuljevan.Francisco/HW1

User:Egm6321.f09.team3.Kuljevan.Francisco/HW2

User:Egm6321.f09.team3.Kuljevan.Francisco/HW3

User:Egm6321.f09.team3.Kuljevan.Francisco/HW4


text:
Open education

Open education is a broad term which can refer to learning programs which have one or more of the following features:
 * use open educational resources
 * allow anyone to participate at no cost

Open education can be one of the outputs of open academia.

Wikipedia

 * Open education
 * Open educational resources
 * Open learning
 * Massive open online course
 * Outline of open educational resources
 * Open educational practices
 * Open research
 * Open University

Videos

 * Intro to Open Education

Discussion questions and essay ideas

 * Can research be considered an aspect of open education?
 * How can open education help there to be more prosperity and abundance on Earth?
 * How can open education most advantageously interface and interact with traditional accredited educational institutions?
 * In what ways can open education make progress towards eliminating poverty?

title: Open education


text:
User:Egm6321.f09.Team1

Homework 1

Homework 2

Homework 3

Homework 4

Homework 5

Homework 6

Homework 7

title: User:Egm6321.f09.Team1


text: File:Wikiversity learning path button.svg


text:
User:Egm6321.f09.Team1/HW1

 See my comments or TA's comments below. Nice organization of wiki page. Egm6321.f09 20:49, 19 September 2009 (UTC)

= Problem 1 - Maglev First and Second Derivative Derivations =

Given
The equation of motion for a Maglev train can be modeled by the function :

 Nice contribution Maglev train. Egm6321.f09 12:47, 22 September 2009 (UTC)

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

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

 * }
 * }

Find
Derive the first and second time derivatives for the given equation shown by Equation 1 and 2 respectively.

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

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

 * }
 * }

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

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

$$ $$
 * $$\displaystyle (Eq. 2)

 * }
 * }

Solution
 Solving for Equation 1

Taking the time derivative:

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

For ease, a dummy variable
 * {| style="width:100%" border="0" align="left"

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

is used and substuted into the previous equation. The chain rule is now applied:
 * {| style="width:100%" border="0" align="left"

\frac{d}{dt} f \left(s,t\right) = \frac{\partial f}{\partial s} \frac{\partial s}{\partial t}+ \frac{\partial f}{\partial t} \underbrace{\frac{\partial t}{\partial t}}_{=1} $$ $$
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

Note that
 * $$\frac{\partial s}{\partial t}=\dot Y^1(t)$$

Equation 3 can be rewriten to the form:

 * {| style="width:60%" border="0"

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

Solving for Equation 2

Note that

\frac{d^2 }{dt^2} f= \frac{d}{dt}\left(\frac{d}{dt}f\right) $$ Substituting in Eq. 1 yields

\frac{d^2}{dt^2} f\left(Y^1(t),t\right) = \frac{d}{dt}\left(\frac{\partial f}{\partial s} \frac{\partial s}{\partial t}+ \frac{\partial f}{\partial t} \right) $$ Now, we can apply the chain rule so that

\frac{d^2}{dt^2} f\left(Y^1(t),t\right) =\frac{\partial^2 f}{\partial s^2} \left(\frac{\partial s}{\partial t}\right)^2 + \frac{\partial^2 f}{\partial s \partial t} \frac{\partial s}{\partial t} \frac{\partial t}{\partial t} + \frac{\partial f}{\partial s} \underbrace{\frac{\partial^2 s}{\partial s \partial t}}_{=0}\frac{\partial s}{\partial t} + \frac{\partial f}{\partial s} \frac{\partial^2 s}{\partial t^2}\frac{\partial t}{\partial t} + \frac{\partial^2 f}{\partial s\partial t}\frac{\partial s}{\partial t} + \frac{\partial^2 f}{\partial t^2} \frac{\partial t}{\partial t} $$ Collecting terms in the above equation

\frac{d^2}{dt^2} f\left(Y^1(t),t\right) =\frac{\partial^2 f}{\partial s^2} \left(\frac{\partial s}{\partial t}\right)^2 + 2\frac{\partial^2 f}{\partial s \partial t} \frac{\partial s}{\partial t} + \frac{\partial f}{\partial s} \frac{\partial^2 s}{\partial t^2} +  \frac{\partial^2 f}{\partial t^2} $$ To compare with the given notation, the derivates in the equations above are replaced with subscripts. For example, dX/dy would be simply X,y. The following equation shows this transformation.

\frac{d^2}{dt^2} f\left(Y^1(t),t\right) =f_{,ss} \left(\frac{\partial s}{\partial t}\right)^2 + 2f_{,st} \frac{\partial s}{\partial t} + f_{,s}\frac{\partial^2 s}{\partial t^2} + f_{,tt} $$ Finally, the dummy variable is replaced and the desired solution remains.
 * {| style="width:60%" border="0"

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

= Problem 2 - Method of Integrating Factor =

Given
A Linear 1st order ODE is given by

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

$$
 * $$\displaystyle y' + y = x$$
 * $$\displaystyle (Eq. 4)
 * $$\displaystyle (Eq. 4)

 * }
 * }

Find
Solve Eq. 4 for y(x) and show
 * {| style="width:100%" border="0" align="left"

 * $$\displaystyle y(x) = A e^{-x} + x - x$$
 * $$\displaystyle y(x) = A e^{-x} + x - x$$

 * }
 * }

Solution
To find the solution, we need to perform the exactness test which requires two steps:

1. Writing the ODE in the form of
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle M(x,y)+N(x,y)y'=0$$
 * $$\displaystyle M(x,y)+N(x,y)y'=0$$

$$
 * $$\displaystyle (Eq. 5)
 * style= |
 * }

2. Checking the condition given by
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$
 * $$\displaystyle \frac{\partial M}{\partial y}=\frac{\partial N}{\partial x}$$

$$
 * $$\displaystyle (Eq. 6)
 * style= |
 * }.

Checking Condition 1

Re-writing Eq. 4 in the form of Eq. 5 gives

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

 * style="width:100%" |
 * $$\displaystyle (y-x)+ y' = 0$$
 * $$\displaystyle (y-x)+ y' = 0$$

 * style= |
 * }

where $$\displaystyle M=(y-x)$$ and $$\displaystyle N=1$$. It is shown that condition 1 is met.

Checking Condition 2

Now, we have to test if $$\displaystyle M_y=N_x$$

 * $$\displaystyle M_y = 1$$ and $$\displaystyle N_x = 0$$

Therefore, Eq. 4 is not an exact differential equation and an integrating factor is needed to force the ODE to be exact. The definition of the integrating factor is

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

 * style="width:95%" |
 * $$\displaystyle h(x)=\exp \int^x f(x)dx$$
 * $$\displaystyle h(x)=\exp \int^x f(x)dx$$

 * style= |
 * }

where

 * $$\displaystyle f(x)=\frac{1}{N}\left[ M_p - N_x \right ]$$

Substiuting the values of M and N yield

 * $$\displaystyle f(x)== \frac{1}{1}\left[ 1 - 0 \right ] = 1 $$

Therefore the integrating factor is
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle h(x)= e^x$$
 * $$\displaystyle h(x)= e^x$$

 * style= |
 * }

Multiplying Eq. 4 by the integrating factor gives

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

 * style="width:95%" |
 * $$\displaystyle e^x y + e^x y' = xe^x$$
 * $$\displaystyle e^x y + e^x y' = xe^x$$

 * style= |
 * }

Now it can be seen that the left hand side is in the form of a derivative product. Recognizing this yields:

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

 * style="width:95%" |
 * $$\displaystyle (e^xy)' = xe^x$$
 * $$\displaystyle (e^xy)' = xe^x$$

 * style= |
 * }

Integrating both sides results

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

 * style="width:95%" |
 * $$\displaystyle (e^xy) = e^x(x-1)+A$$
 * $$\displaystyle (e^xy) = e^x(x-1)+A$$

Finally, dividing by e^x results in
 * style= |
 * }
 * {| style="width:60%" border="0"

$$\displaystyle y = Ae^{-x}+(x-1)$$
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style= |
 * }

= Problem 3 - Linearity Test of ODEs =

Given

\left( 2 x^2 + \sqrt{y} \right) + x^5 y^3 y' = 0 $$

Find
Show that the following first order ODE is non-linear

Solution
The definition of a linear function is that it obeys the cumulative and additive properties shown respectively. F is an arbitrary function while C is an arbitrary constant.

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

 * style="width:95%" |
 * $$\displaystyle F(Cx) = CF(x)$$
 * $$\displaystyle F(Cx) = CF(x)$$

 * style= |
 * }

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

 * style="width:95%" |
 * $$\displaystyle F(x+y) = F(x) + F(y)$$
 * $$\displaystyle F(x+y) = F(x) + F(y)$$

 * style= |
 * }

The given equation is defined as follows:

H(y)=\left( 2 x^2 + \sqrt{y} \right) + x^5 y^3 y' $$ Applying the cumlitive property
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle H(Cy) = CH(y)$$
 * $$\displaystyle H(Cy) = CH(y)$$

Therefore:
 * style= |
 * }
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle H(C y)=\left( 2 x^2 + \sqrt{C} \sqrt{y} \right) + x^5 C^3 y^3 y' $$
 * $$\displaystyle H(C y)=\left( 2 x^2 + \sqrt{C} \sqrt{y} \right) + x^5 C^3 y^3 y' $$

 * style= |
 * }

and

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

 * style="width:95%" |
 * $$\displaystyle C H(y) = C \left [\left( 2 x^2 + \sqrt{y} \right) + x^5 y^3 y'\right]$$
 * $$\displaystyle C H(y) = C \left [\left( 2 x^2 + \sqrt{y} \right) + x^5 y^3 y'\right]$$

 * style= |
 * }

Because these two equations are clearly not equal, this function in nonlinear.

= Problem 4 - Linearity Test of ODEs=

Given

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

 * style="width:95%" |
 * $$\displaystyle G(x,y,y') = x^2 y^5 + 6 (y')^2 = 0 $$
 * $$\displaystyle G(x,y,y') = x^2 y^5 + 6 (y')^2 = 0 $$

 * style= |
 * }

Find
Show that $$\displaystyle G(x,y,y') = 0$$ is a non-linear 1st order ODE.

Solution
The ODE is first order, since the highest order derivative of $$y$$ in the equation is 1st order.

To test for linearity, the same requirements have to be meet as in Problem 3. The differential operator for the ODE is
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle G(y) = x^2 y^5 + 6 (y')^2$$
 * $$\displaystyle G(y) = x^2 y^5 + 6 (y')^2$$

 * style= |
 * }

Unlike in Problem 3, the additive condition will be applied, that is for an arbitary function F
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle F(u+v) = F(u) + F(v)$$
 * $$\displaystyle F(u+v) = F(u) + F(v)$$

 * style= |
 * }

Applying this on the given function G results in
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle G(u+v) = x^2 (u+v) ^5 + 6 ((u+v)')^2$$
 * $$\displaystyle G(u+v) = x^2 (u+v) ^5 + 6 ((u+v)')^2$$

 * style= |
 * }

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

 * style="width:95%" |
 * $$\displaystyle G(u) + G(v) = x^2 u ^5 + 6 (u')^2 + x^2 v ^5 + 6 (v')^2$$
 * $$\displaystyle G(u) + G(v) = x^2 u ^5 + 6 (u')^2 + x^2 v ^5 + 6 (v')^2$$

 * style= |
 * }

Clearly, the two equations are not linear and the function G is nonlinear.

= Problem 5 - Exactness of a Nonlinear 1st Order ODE =

Given
The following functions:

1) $$\displaystyle \phi(x,y)=6 x^4 + 2 y ^{\frac{3}{2}}$$

2) $$\displaystyle \phi(x,y)=xy + x^2y^2$$

3) $$\displaystyle \phi(x,y)=e^{xy}+x$$

4) $$\displaystyle \phi(x,y)=y \sin(x)$$

Find
Create four exact non-linear ODEs.

Solution
A 1st Order ODE is given by the following equation

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

 * style="width:95%" |
 * $$\displaystyle M(x,y)+N(x,y)y'=0$$
 * $$\displaystyle M(x,y)+N(x,y)y'=0$$

 * style= |
 * }

The conditions under and exact 1st Order ODE are that 1) the equation must have the form of the one given above and 2) that

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

 * style="width:95%" |
 * $$\displaystyle \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x} $$
 * $$\displaystyle \frac{\partial M}{\partial y} = \frac{\partial N}{\partial x} $$

 * style= |
 * }

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

 * style="width:95%" |
 * $$\displaystyle M = \frac{\partial \phi}{\partial y}$$
 * $$\displaystyle M = \frac{\partial \phi}{\partial y}$$

and
 * style= |
 * }
 * {| style="width:100%" border="0"

 * style="width:95%" |
 * $$\displaystyle N = \frac{\partial \phi}{\partial x}$$
 * $$\displaystyle N = \frac{\partial \phi}{\partial x}$$

 * style= |
 * }

Substituting $$M$$ and $$N$$ for the given case into the given form yields a exact 1st order ODE.

Solution 1
 * $$\displaystyle \phi(x,y)=6 x^4 + 2 y ^{\frac{3}{2}}$$

 * $$\displaystyle M=24 x^3$$

 * $$\displaystyle N=3 y ^{\frac{1}{2}}$$

 * {| style="width:60%" border="0"

 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * $$\Rightarrow \displaystyle \left (24 x^3 \right) + \left( 3 y ^{\frac{1}{2}} \right) y'=0$$
 * $$\Rightarrow \displaystyle \left (24 x^3 \right) + \left( 3 y ^{\frac{1}{2}} \right) y'=0$$

 * style= |
 * }

Solution 2

 * $$\displaystyle \phi(x,y)=xy + x^2y^2$$

 * $$\displaystyle M=y + 2xy^2$$

 * $$\displaystyle N=x + 2yx^2$$

 * {| style="width:60%" border="0"

 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * $$\Rightarrow \displaystyle \left (y + 2xy^2 \right) + \left (x + 2yx^2 \right) y'=0$$
 * $$\Rightarrow \displaystyle \left (y + 2xy^2 \right) + \left (x + 2yx^2 \right) y'=0$$

 * style= |
 * }

Solution 3

 * $$\displaystyle \phi(x,y)=e^{xy}+x$$

 * $$\displaystyle M=ye^{xy}+1$$

 * $$\displaystyle N=xe^{xy}$$

 * {| style="width:60%" border="0"

 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * $$\Rightarrow \displaystyle \left (ye^{xy}+1 \right) + \left (xe^{xy} \right) y'=0$$
 * $$\Rightarrow \displaystyle \left (ye^{xy}+1 \right) + \left (xe^{xy} \right) y'=0$$

 * style= |
 * }

 On the other hand, choosing $$\displaystyle \phi$$ as shown above resulted in a L1-ODE-VC (linear), instead of a N1-ODE (nonlinear) as required. Egm6321.f09 12:43, 22 September 2009 (UTC)

Solution 4

 * $$\displaystyle \phi(x,y)=y \sin(x)$$

 * $$\displaystyle M=y \cos(x)$$

 * $$\displaystyle N=\sin(x)$$

 * {| style="width:60%" border="0"

 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * $$\Rightarrow \displaystyle \left [y \cos(x) \right] + \left [\sin(x) \right] y'=0$$
 * $$\Rightarrow \displaystyle \left [y \cos(x) \right] + \left [\sin(x) \right] y'=0$$

 * style= |
 * }

 On the other hand, choosing $$\displaystyle \phi$$ as shown above resulted in a L1-ODE-VC (linear), instead of a N1-ODE (nonlinear) as required. Egm6321.f09 20:49, 19 September 2009 (UTC)

=Contributing Team Members= Egm6321.f09.Team1.vasquez 15:29, 15 September 2009 (UTC)

Egm6321.f09.Team1.andy 17:54, 15 September 2009 (UTC)

Egm6321.f09.Team1.sallstrom 22:52, 15 September 2009 (UTC)

Egm6321.f09.Team1.AH 00:23, 16 September 2009 (UTC)

=Notes and references=

title: User:Egm6321.f09.Team1/HW1


text:
User:Egm6321.f09.team5.bear

Test Egm6321.f09.team5.bear 15:57, 9 September 2009 (UTC)

title: User:Egm6321.f09.team5.bear


title: Template:Note2


text:
Northern Arizona University/Environmental Ethics/Collaborative Projects

 * Climate Change


text:
Northern Arizona University/Environmental Ethics/Climate Change

 * ../Mitigation for Climate Change/
 * ../Adaptation to Climate Change/


text: File:Wikiversity learning path button2.svg