text:
Instructional design/Generate PBL Problems/1.2 Problems should challenge students

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Video
This is a video of an art history teacher who fails to motivate her students. Please watch this video from 6:45, pay more attention on the section of 9:24 – 10:24 and think about the reason why this teacher fails to motivate her students.(To watch the video: press Shift and click the PLAY button):

Reflection
In this video, the teacher fails to draw her students’ attentions because she doesnot think about her students’ prior knowledge; she starts the class by presenting the materials that she assumed her students don’t know. The result is apparent that her students donot buy it, and they even suggests the teacher that they could have an independence study by their own. Even though it is not a PBL, the principle behind this video is the same as using PBL teaching methods. As instructional designers, we should generate a problem that would challenge students within their knowledge scope. The image below shows a metaphor for this principle. (Picture 1 to picture 5) In picture 1, all the apples can be seen as problems. The difficulty levels of the problems vary, just like the heights of the apples. Some are lower, and some are higher. In picture 2, the student’s height is her prior knowledge towards a certain topic. In picture 3, the student does not take too much effort to reach the apple. This is the kind of problems that cannot challenge students. Students can easily come up with solutions towards such kind of problems, so they cannot be motivated. In picture 4, the student uses a ladder to reach the apple. This is the type of problems that challenge students within their knowledge scope. In picture 5, the apple is too high for the student to reach. This type of problems contain too many challenge factors that students won’t be able to solve.

Therefore, teachers should create problems that students have had certain prior knowledge to start working on. If the problem relies too much on prior knowledge, that will make students feel not being challenged enough; if it relies too little on their prior knowledge, it will make students feel frustrated.

Tips for instructional designers and instructor to generate challenging problems.
 * Gain information

-Truth Statements: Ask students to write a 5 sentence of “truth statement" about their past learning experience, and then ask students to exchange their experience in a group of 2, finally introducing their partners’ experience to the whole class. Remember to collect those statements so that you could have a copy of their prior knowledge. -Opening Letter: At the start of a class, write a letter to students explaining what you want them to know, understand and be able to do in the upcoming unit and then ask them for a return letter about their concerns. This is a reverse way to know what students are not good at.

 * Provide additional information

-Just like in picture 4. remember to provide students with necessary new knowledge (the ladder) so that they could solve

Quiz
{Which understanding is CORRECT? -Generate easy problems so that students could gain confidence in solving those problems. -Generate difficult problems to prove that “I” am the instructor of this class, “I” am knowledgeable. +Generate challenging problems based on students’ existing knowledge. -Generate problems based my (instructors’) ability.
 * type="[]"}

{Dr. Everman is generating problems for her third year musical Composition majored students, they have certain knowledge to compose different types of music; they don’t have enough knowledge outside of musical field (such as psychology, nursing, etc.), in your opinion, which of the following problems might be TOO challenging for his students? -Redesign the series of music for a newly upgraded 4 star Hotel & Restaurant. -Create Theme song for a popular TV series. -Design a 30 minutes stage musical for a local Elementary school for their coming Spring Musical Festival. +Design Music therapy for a health center’s patients who are suffering depression.
 * type="[]"}
 * Music therapy require students to have knowledge in psychology and nursinging. Those third year students don't have such knowledge. Even they were provided with additional knowledge in psychology and nursinging, it would take too much time for them to digest such new information.

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text:
Instructional design/Generate PBL Problems/1.3 Real-life problems

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Comparison
Assume you were a high school student again, which way do you prefer to learn geometry?

Reflection
More possibly, you prefer the way on the right, why? Because working on a design contract competition gives you the opportunity to apply your geometry knowledge into a REAL LIFE PROBLEM. Students are more engaged in solving real life problems because this learning experience:
 * activates students’ prior knowledge and skills
 * has students see the relevance of the knowledge to their life
 * leads to a deep understanding of concepts
 * allows students to apply their new learned knowledge right away into a real world context

Examples
To enhance students’ motivation, PBL utilizes real life problems. Below are several more examples of real life problems (statements in the parenthesis are corresponding non-examples)
 * 1) Have students make personal financial plans (instead of having them just memorize various financial management terms and principles).
 * 2) Have students tell directions or locate places by constellations (instead of having them merely recognize constellations on a sky map).
 * 3) Have students write reviews on new released movies and post their works online (instead of just talking about theories of film appreciation).

Quiz
{PBL uses real life problems because(there are more than one answers): +Students are more engaged in solving real life problems. +Students will achieve a deep understanding of concepts in solving real life problems. +Students can see close connections between the knowledge and themselves. +Students will learn how to apply their knowledge into the real world.
 * type="[]"}

{Which one below is a real life problem? -What is the wavelength range of ultraviolet? -What percent of mid-range ultraviolet can be blocked by the ozone layer? +How to effectively prevent skin cancer caused by UVB radiation? -How many subtypes of ultraviolet light have been identified by the draft ISO standard on determining solar irradiances (ISO-DIS-21348)?
 * type="[]"}
 * the correct selection is a problem that is related to everybody's life.

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


text:
Instructional design/Generate PBL Problems/2.1 Ill-structured problems

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Definition
What kind of problems can enhance students’ critical thinking skills? Compared to well-structured questions (have certain number of solutions and correct answers), ill-structured questions can better serve this mission. Ill-structured problems are complex and ill-defined. There are many ways to solve an ill-structured problem, and you cannot simply identify a “best answer” among many possible answers.

Examples
To bring up an ill-structured problem, ask how to effectively clean up the RiverX in X (a badly polluted area), instead of which is the most polluted river in X? The latter question is a well-structured problem, which only has one correct answer, and students can easily get the answer from a quick Google search. On the contrary, how to effectively clean up the RiverX in X (a badly polluted area) is ill-structured. To answer the question, students may need to collect water samples from that river, bring them into labs to test contaminants, interview people, search information online or in the library, and do other things till they can suggest possible solutions. Examples of Ill-structured problems about water pollution can also be (questions in the parenthesis are corresponding well-structured problems):

You may have noticed that well-structured questions usually ask about facts (“what”, “when”, “where” and “who”), which mainly relies on the memorization of information. Whereas, ill-structure questions ask about reasons and solutions (“why” and “how”), which requires analysis, reasoning, and making decisions based on acquired knowledge and information. Put it in a sentence: solving ill-structured questions make students to be critical thinkers.
 * 1) People in a small fishing village are recently catching a highly contagious digestive system disease. Can you identify the exact causes of
 * 2) A leather factory located at the upstream of a river badly threatens the lives of creatures in and alongside the river. But this factory is the back bone of the economy in that area. Is there any way that the area can keep this factory, but control its pollution? (Instead of asking “what are the chemical pollutants that a leather factory always produces?”)

Quiz
{Which understanding about ill-structured problems is INCORRECT? -Ill-structured problems are more complex and difficult, compared to well-structured problems. -An ill-structured problem usually has many possible solutions. +There is always only one correct way to solve an ill-structured problem. -Problems used in PBL should be ill-structure to help students build critical thinking skills.
 * type="[]"}
 * There are many possible ways to solve an ill-structured problem.

{Dr. Bowman is a psychology professor. He is enthusiastic about applying PBL into his Human Development class. Here are several questions he prepared for teaching the attachment theory (a psychological theory describing the strong emotional attachment infants build with their caregivers). As an instructional designer in the same university, can you help Dr. Bowman choose the appropriate question for PBL? -What is attachment? -How does attachment differ from the concept of “bonding?” -What are the three major categories of attachment, and what kind of parenting is theorized to lead to each? +How does attachment differ across cultures, and why?
 * type="[]"}

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text:
Instructional design/Generate PBL Problems/2.2 Require higher level thinking activities

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Bloom’s Taxonomy and critical thinking skills

In Bloom’s Taxonomy, higher level thinking activities are on the top of the pyramid, involving cognitive activities of analysis, synthesis and evaluation. To help students develop critical thinking skills, you need to make sure that the PBL problems you generate require students to be involved in the above cognitive activities. Here we use the river pollution questions from the previous part again. The question how to effectively clean up the RiverX in X? is suitable to be a PBL problem, because students have to analyze, synthesize and evaluate the current situation, available information, others’ opinions, and all possible solutions to eventually decide a best solution. Whereas question which is the most polluted river in X? is not eligible to be a PBL problem because it only requires lower level thinking activities-- the memorization of the knowledge/fact. Generally speaking most ill-structured problems require students to be involved in higher level thinking activities and enhance their critical thinking skills. In the contrary, well-structured questions just require lower level cognitive actives, and cannot help students develop critical thinking skills.

Tips of generating PBL problems which require higher level thinking activities Ask students to do one or a few of the following things while they are solving the problem:
 * analysis：analyze, appraise, compare, contrast, criticize, differentiate, discriminate, distinguish, examine, experiment, question, test
 * Synthesis: arrange assemble, collect, combine, compose, construct, creat, design, plan, propose
 * evaluation：appraise, argue, assess, defend, evaluate, judge, measure, select, support, value

Quiz
{Which one of the following activates does not help to build critical thinking skills? +Comprehension -Evaluation -Analysis -Synthesis
 * type="[]"}
 * Comprehension is a lower level cognitive activity in Bloom's Taxonomy.

{Which one of the following questions from an undergrad level architecture class requires higher level thinking activities? -Which architect designed the east wing of the National Gallery of Art (Washington, D.C.)? +Combine two architecture styles and design a square fountain for your hometown. -Use your own term to define "Bauhaus". -Illustrate the structure of a typical Gothic architecture in pencil sketches.
 * type="[]"}
 * selection1--knowledge, selection2--analysis and synthesis, selection3--comprehension, selection4--application.

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text:
Instructional design/Generate PBL Problems/3.1 Group collaboration rules

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How to enhance collaboration
Collaboration is also a very import problem feature in PBL teaching, as you can remembered from the video that we watched in the “Lesson Introduction” part, a student expressed his feeling, “you have to involve into this process the whole time, you don’t want to let other people in the group down by not doing you parts…” so a problem that instructor generated should also includes collaboration.

However, collaboration is not as simple as instructors assign a problem to a group of students, it requires carefully designed rules for group members to follow. In fact, how to group students and create rules for them to follow are not included in the “generate PBL problem” process, but they are very important in the process of solving problems, so several tips of how to group students as well as ensuring the quality of collaboration will be provided in the following part.

Tips of enhancing collaboration in PBL.
 * Same goal: usually, the problem should be assigned to a group of students who have a similar interest; thus they can work towards the same goal. In each group, group members’ abilities might vary from each other.
 * Ground rules: at the beginning of group working, each group should generate ground rules based on their situation, such as, a weekly group meeting.

 * Shared leadership: groups members should take turns to be the leader so that each student is aware of their group progress; it is also a way to ensure everyone’s opinion is being heard by the whole group.

 * Weekly report: each group should report their weekly progress by the current group leader.

 * Peer assessment: it is important for group member to have peer assessment in the middle of the group working.

 * Individual contributions: each group member should report individual contributions to the group working at the end of the class.

Quiz
{Based on the tips given above, which professor should CHANGE his/her strategy when grouping students? } -Professor Brennan asks his students to turn in a reflection paper which indicates individual contribution at the end of this semester. +Professor Stinson assigns each team with a group leader at the beginning of this PBL teaching. -Professor Audrey asks her students to finish a Peer Assessment form in the middle of this class. -Professor Young asks his students to post their weekly progress online.
 * It might be better for Professor Stinson to use "Shared leadership" strategy so that every group members are actively involved into this problem solving process.

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text:
Exemplar answers to Question 1

1. Mr. Anderson teaches geography in a middle school of Indiana. One day, he is teaching his 16 students about the factors that affect average temperature. Instead of doing a lot of talking himself, Mr. Anderson decides to make students think and discover.
 * a. If Mr. Anderson uses the Inquiry Teaching way of articulation, what would he ask students to do?

 * Mr. Anderson may first ask students to list some factors that they deem to affect average temperature, and then ask questions as entrapment to help students find their misunderstanding, if any. He may also try to get students to systematically test out their hypotheses, for example, by comparing temperature in different places in the real world.

 * (This is actually a real-life example. Two excerpts below show what Anderson has done.)

Forming Hypotheses S:  Some other factor besides north-south distance must also affect temperature. RA: Yes! Right! What could this factor be? S:  I don't have any idea. RA: Why don't you look at your map of North America. Do you see any differences between Montana and Newfoundland? S:  Montana is in the center of the country. Newfoundland is on the ocean. RA: Do you soppose that distance from the ocean affects temperature? S:  I'm not sure. It would just be a guess. RA: True! The name for such a guess is a hypothesis. Supposing the hypothesis were correct, what exactly would you predict? S:  The further a place is from the ocean, the lower the temperature will be in the winter.

Evaluating Hypotheses RA: How could you test your hypothesis? S:  By comparing temperatures of places different distances form the ocean. RA: Very good. Let's do that. Suppose we take St. Louis, Missouri. Which would be best to compare, Atlanta, Georgia, or Washington, D. C.? S:  I would pick Washington. RA: Why? S:  Because it's at the same latitude as St. Louis. RA: Why is that important? S:  Well, if Atlanta were warner, I wouldn't know whether it was because it was nearer the ocean or further south.

There are no standarded answers to each question. Find something interesting from diverse answers from other learners!

title: Exemplar answers to Question 1


text:
User:D34THT4X

D34th T4x
reaping the benefits on rent to the dirt plots death tax noun a tax on the estate of the deceased person [syn: inheritance tax]

interests: vocals guitar 35mm sharpie netbook android ipod kindle local travel

Student of Life

 * Computer Applications for Business
 * Hardware/OS-Software for Computer Repair
 * Programming for Business Applications
 * Web Design

title: User:D34THT4X


text:
TESOL/What is it (kitchen)

Identify
{ They are long and thin. They are made of wood. You use them to eat. { chopsticks|Chopsticks }
 * type="{}" }

{ It is rectangular. It has a handle on top. You use it to cut cheese or vegetables into small pieces. { Grater|A grater|grater|a grater }
 * type="{}" }

{ It is round. It is made of ceramic, wood, or plastic. You can hold soup with it. { Bowl|A bowl|bowl|a bowl }
 * type="{}" }

{ It is cylindrical. It has two handles, one on each end. You use it to make a pizza crust or pie crust. { Rolling pin|A rolling pin|rolling pin|a rolling pin }
 * type="{}" }

Describe
Let's change. Choose one but don't say which one it is. Tell me about it. I'll ask you questions.
 * What is it made of?
 * What does it look like?
 * What is it used for?

title: TESOL/What is it (kitchen)


text:
User talk:Mbaig5753/enes100/My Work P3

Sam
 * Good job practicing those cutting skills! Maybe you can give me a hand on my airplanes!

Nathan
 * Nice job!

Erika
 * Looks like you have a clear model, i can't wait to test it!!

week 1 p3 grading 1sfoerster (talk) 19:39, 24 April 2012 (UTC)
 * 10/10/50 .. good job ... keep working ...

Sam
 * Nice job with your presentation!!

Erika I like your new modifications, it looks like you put a lot of work into this model.

week 2 p3 grading
 * 10/10/30 ... good work

Nathan
 * Sweet plane man.

week 3 p3 grading
 * 10/10/30 ... good work ... no time aloft measurement ... for either airplane or bag ... were they different? .. is any progress being made?

Sam
 * Excellent teamwork!

Erika All your ideas came together nicely and your plane looks great!

Nathan Great work!

week 4 p3 grading 1sfoerster (talk) 18:26, 15 May 2012 (UTC)
 * 10/10/10 ... still no data

title: User talk:Mbaig5753/enes100/My Work P3


text:
User talk:Emspangler/enes100/My Work P3

Sam
 * Keep up the good work! Can't wait to see your airplane!

Mirza I like your ideas Erika, really want to see what your'e airplane looks like. Nathan
 * Nice job! Nice idea to use the foam.

week 1 p3 grading 1sfoerster (talk) 19:41, 24 April 2012 (UTC)
 * 10/10/50 ... there is a special foam glue ... I am going to look for it ... you need to find a link and order some ... need the smallest quantities possible ... it is nasty stuff.

Sam
 * Great effort building the airplane!

Mirza
 * Good job presenting Erika... i want to see how your airplane turns out you had some really good ideas when you presented in class. I want to see how it all comes together.

week 1 p3 grading 1sfoerster (talk) 16:36, 1 May 2012 (UTC)
 * 10/10/30 ... would be more if I could watch video .. is marked private .. that means no one can see it .. move to next week if you fix privacy for points

Mirza
 * Good job Erika I like how you shorted the base. Seems like that helped.

week 3 p3 grading 1sfoerster (talk) 12:43, 8 May 2012 (UTC)
 * 10/0/30 ... video shows how long it was in the air ... when there is not success, then need to record each failure ... you did not record each failure ... now everyone else that comes along will repeat what you did ... record with pictures, with drawings, with details so the others can replicate the failure ... need to use these failures to motivate the tension that determines what to do next .. you have not made positive comments on team mates pages or listed something to do next

Sam
 * Excellent teamwork!

Mirza
 * Really enjoyed working with you good stuff.

Nathan
 * Nice job!

week 4 p3 grading 1sfoerster (talk) 18:30, 15 May 2012 (UTC)
 * 10/10/50 .. great job and beginning to collect some data

title: User talk:Emspangler/enes100/My Work P3


text: Instructional design/Reducing cognitive load in multimedia instruction/Cognitive Theory of Multimedia Learning/Paivio's Model of Dual-coding Theory


text:
User talk:Sczxsy

Welcome
 Hello Sczxsy, 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. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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.
 * Explore Wikiversity with the links to your left.

 * 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.
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You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! Cirt (talk) 16:20, 21 April 2012 (UTC)

-- Cirt (talk) 16:20, 21 April 2012 (UTC)

Copyright problems on photos
Hello. There is a problem with one or more files you have uploaded. Every file you upload must have a clear statement of the copyright position. If you took the photos yourself, add PD-self if you are placing it unreservedly in the public domain. If you wish to retain minimal rights, add Cc-by-sa-3.0. If you did not take the photo, please add an explanation of why it can be hosted here. I am afraid that if you do not do this, the file wil be deleted. Let me know if you have any problems.--Collingwood (talk) 12:11, 2 July 2012 (UTC)

title: User talk:Sczxsy


text:
User:Yanacochito~enwikiversity

This is the Yanacochito User page.

The user Yanacochito is an engineer who is interested in inexpensive ways to complete his professional development requirement.

The real Yanacochito is a cartoon safety mascot for the Yanacocha mine near Cajamarca, Peru.

title: User:Yanacochito~enwikiversity


text:
TESOL/English proficiency levels

Beginner
This stage involves building fluency with essential, everyday English. There is a basic stock of about 2000 words that the student must practice using until they can use fluently. The student must gain a number of stock phrases, and must be able to make questions.

In practical terms, this student aims to be able to survive in an English-speaking environment.

Resources: Category:Beginner English

Intermediate
This stage involves learning to navigate more complicated situations like apologies, negotiations over price and so on, or giving an opinion or disagreeing politely. At this stage fluency in basic English is not a problem but students need support with more complicated grammar like past participles or new uses of familiar structures.

In practical terms, this student aims to be comfortable in a variety of everyday situations in an English-speaking environment.

Resources: Category:Intermediate English

Advanced
This stage involves developing control of language so that a student can moderate the level of politeness or strength of their language appropriate to the situation. The student should be able to judge the meanings of unknown words from context or by analogy with previously learned language. At this stage students can start practicing using English in formal situations like meetings at work or formal ceremonies like weddings. Their vocabulary should include not just everyday English but vocabulary usually used in writing. This student should understand common idioms and be able to manipulate them.

In practical terms, this student aims to be able to participate and take an active role in a business meeting by volunteering ideas, explaining their logic, and politely agreeing and disagreeing with colleagues.

Resources: Category:Advanced English

title: TESOL/English proficiency levels


text:
User:Gidee07

Gidee07 is a young lad studying Pharmacy.

title: User:Gidee07


text:
User talk:Mayue

 Hello Mayue, 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. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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.
 * Explore Wikiversity with the links to your left.

 * 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.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Collingwood (talk) 18:49, 21 April 2012 (UTC) --Collingwood (talk) 18:49, 21 April 2012 (UTC)

Copyright problems on photos
Hello. There is a problem with one or more files you have uploaded. Every file you upload must have a clear statement of the copyright position. If you took the photos yourself, add PD-self if you are placing it unreservedly in the public domain. If you wish to retain minimal rights, add Cc-by-sa-3.0. If you did not take the photo, please add an explanation of why it can be hosted here. I am afraid that if you do not do this, the file wil be deleted. Let me know if you have any problems.--Collingwood (talk) 12:03, 2 July 2012 (UTC)

title: User talk:Mayue


text:
User talk:Yanacochito~enwikiversity

 Hello Yanacochito, 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. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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.
 * Explore Wikiversity with the links to your left.

 * 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.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Collingwood (talk) 18:52, 21 April 2012 (UTC) --Collingwood (talk) 18:52, 21 April 2012 (UTC)

Your account will be renamed
Hello,

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

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

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

Sorry for the inconvenience.

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

Renamed
 This account has been renamed as part of single-user login finalisation. If you own this account you can |log in using your previous username and password for more information. If you do not like this account's new name, you can choose your own using this form after logging in: . -- Keegan (WMF) (talk) 06:25, 19 April 2015 (UTC)

title: User talk:Yanacochito~enwikiversity


text:
User talk:D34THT4X

 Hello D34THT4X, 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. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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.
 * Explore Wikiversity with the links to your left.

 * 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.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Collingwood (talk) 18:53, 21 April 2012 (UTC) --Collingwood (talk) 18:53, 21 April 2012 (UTC)

title: User talk:D34THT4X


text:
User talk:Gidee07

 Hello Gidee07, 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. All users are expected to abide by our Privacy policy, Civility policy, and the Terms of Use while at Wikiversity.

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.
 * Explore Wikiversity with the links to your left.

 * 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.
 * Follow Wikiversity on twitter (http://twitter.com/Wikiversity) and identi.ca (http://identi.ca/group/wikiversity).

You don't need to be an educator to edit. You only need to be bold to contribute and to experiment with the sandbox or your userpage. See you around Wikiversity! --Collingwood (talk) 18:54, 21 April 2012 (UTC) --Collingwood (talk) 18:54, 21 April 2012 (UTC)

title: User talk:Gidee07


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Talk:Instructional design/Reducing cognitive load in multimedia instruction/Find and Fix

Paste your notes from What's Wrong with this Picture here.

Find and Fix video on the Cognitive Theory of Multimedia
-Eliminate the background music and remove the icons for sound and organizing images. The effect is too crowded with the music, the narration, the icons and the animation. 23.31.51.209 (discuss) 00:57, 2 March 2023 (UTC)


text:
How to make a test protocol for ATX power supplies

 * 1. Get a small power resistor( 1 ohm preferred)

 * 8. Make a table and put the records on it

ATX Power Supply Test Protocol


text: Category:Articles containing German language text


text:
User:Egm4313.s12.team11.sheider/R.7.4: K 2011 p.482 pb. 12

Problem Statement
Find the Fourier series of the given function which is assumed to have a period of $$ 2 \pi \!$$. Show the details of your work.

Sketch or graph the partial sums up to that including $$ cos(5x) \!$$ and $$ sin(5x) \!$$

Given:

$$f(x) = |x| \!$$

Solution
The Fourier series of a function with a period of $$ p = 2\pi \!$$ is defined:

$$ f(x) = a_{0} + \sum_{n=1}^{\infty } (a_{n}cos(nx) + b_{n}sin(nx))\!$$

Where:

$$ a_{0} = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) dx \!$$

$$ a_{n} = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) cos(nx) dx \!$$

$$ b_{n} = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) sin(nx) dx \!$$

This particular function given in the problem can be also defined in a piecewise manner over this interval, namely:

$$ f(x) = \left\{\begin{matrix} -x \text{ if } -\pi \leq x \leq 0\\x \text{ if } 0 \leq x \leq \pi \end{matrix}\right. \!$$

Calculating the first term $$ a_{0} \!$$:

$$ a_{0} = \frac{1}{2\pi} \left ( \int_{-\pi}^{0} -x dx + \int_{0}^{\pi} x dx \right) \!$$

$$ a_{0} = \frac{1}{2\pi} \left ( \left [\frac{-x^2}{2} \right ]_{-\pi}^{0} + \left [\frac{x^2}{2} \right ]_{0}^{\pi} \right)\!$$

$$ a_{0} = \frac{1}{2\pi} \left ( - \left(\frac{-\pi^2}{2}\right ) + \left (\frac{\pi^2}{2}\right)\right) \!$$

$$ a_{0} = \frac{1}{2\pi} (\pi^2) \!$$

$$ a_{0} = \frac{\pi}{2} \!$$

Calculating the coefficient $$ a_{n} \!$$:

$$ a_{n} = \frac{1}{\pi} \left( \int_{-\pi}^{0} -x cos(nx) dx + \int_{0}^{\pi} x cos(nx) dx \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( - \int_{-\pi}^{0} x cos(nx) dx + \int_{0}^{\pi} x cos(nx) dx \right ) \!$$

Using integration by parts with the following substitutions:

$$ u = x \!$$ and therefore $$ du = dx \!$$

$$ dv = cos(nx)dx \!$$ and therefore $$ v = \frac{1}{n}sin(nx) \!$$

This yields for the integral:

$$ a_{n} = \frac{1}{\pi} \left( -\left[\frac{1}{n} x sin(nx) - \int \frac{1}{n}sin(nx)dx \right]_{-\pi}^{0} + \left[\frac{1}{n} x sin(nx) - \int \frac{1}{n}sin(nx)dx \right]_{0}^{\pi} \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( -\left[\frac{1}{n} x sin(nx) + \frac{1}{n^2}cos(nx) \right]_{-\pi}^{0} + \left[\frac{1}{n} x sin(nx) + \frac{1}{n^2}cos(nx) \right]_{0}^{\pi} \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( -\left[\frac{1}{n^2} - \left (\frac{1}{n} (-\pi) sin(-n\pi) + \frac{1}{n^2}cos(-n \pi) \right) \right] + \left[\frac{1}{n} \pi sin(n\pi) + \frac{1}{n^2}cos(n\pi) - \frac{1}{n^2} \right] \right ) \!$$

Note that for all n = 1,2,3... : $$ sin(n\pi) = 0 \!$$ as $$ sin(\pi) = sin(2\pi) = sin(3\pi) ... = 0 \!$$ therefore these terms are evaluated as zero, which yields:

$$ a_{n} = \frac{1}{\pi} \left( -\left[\frac{1}{n^2} - \left (0 + \frac{1}{n^2}cos(-n \pi) \right) \right] + \left[0 + \frac{1}{n^2}cos(n\pi) - \frac{1}{n^2} \right] \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( -\frac{1}{n^2} + \frac{1}{n^2}cos(-n \pi) +  \frac{1}{n^2}cos(n\pi) - \frac{1}{n^2} \right ) \!$$

Note that $$ cos(-x) = cos(x) \!$$ therefore:

$$ a_{n} = \frac{1}{\pi} \left( -\frac{1}{n^2} + \frac{1}{n^2}cos(n \pi) +  \frac{1}{n^2}cos(n\pi) - \frac{1}{n^2} \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( -\frac{2}{n^2} + \frac{2}{n^2}cos(n \pi) \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left (\left ( -\frac{2}{n^2} \right )(1 - cos(n \pi) \right )\!$$

$$ a_{n} = -\frac{2}{n^2\pi} \left (1 - cos(n \pi) \right )\!$$

To evaluate the term $$ (1-cos(n\pi)) \!$$:

Note that $$ cos(n\pi) = -1 \!$$ for odd n values as $$ cos(\pi) = cos(3\pi) = cos(5\pi) ... = -1 \!$$

And that $$ cos(n\pi) = 1 \!$$ for even n values as $$ cos(2\pi) = cos(4\pi) = cos(6\pi) ... = 1 \!$$.

Therefore, it can be concluded that for odd n values:

$$ (1-cos(n\pi)) = 1-(-1) = 2 \!$$

And for even n values:

$$ (1-cos(n\pi) = 1-(1) = 0 \!$$

Therefore, for the coefficient $$ a_{n} \!$$, all even terms will equal zero while all odd terms will have a multiplier of 2, this yields (for all odd n values):

$$ a_{n} = -\frac{4}{n^2\pi} \text{ for  } n = 1,3,5... \!$$

Calculating the coefficient $$ b_{n} \!$$:

$$ b_{n} = \frac{1}{\pi} \left( \int_{-\pi}^{0} -x sin(nx) dx + \int_{0}^{\pi} x sin(nx) dx \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( - \int_{-\pi}^{0} x sin(nx) dx + \int_{0}^{\pi} x sin(nx) dx \right ) \!$$

Using integration by parts with the following substitutions:

$$ u = x \!$$ and therefore $$ du = dx \!$$

$$ dv = sin(nx)dx \!$$ and therefore $$ v = \frac{-1}{n}cos(nx) \!$$

This yields for the integral:

$$ b_{n} = \frac{1}{\pi} \left( -\left[\frac{-1}{n} x cos(nx) - \int \frac{-1}{n}cos(nx)dx \right]_{-\pi}^{0} + \left[\frac{-1}{n} x cos(nx) - \int \frac{-1}{n}cos(nx)dx \right]_{0}^{\pi} \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( -\left[\frac{-1}{n} x cos(nx) + \frac{1}{n^2}sin(nx) \right]_{-\pi}^{0} + \left[\frac{-1}{n} x cos(nx) + \frac{1}{n^2}sin(nx) \right]_{0}^{\pi} \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( -\left[0 - \left (\frac{-1}{n} (-\pi) cos(-n\pi) + \frac{1}{n^2}sin(-n \pi) \right) \right] + \left[\frac{-1}{n} \pi cos(n\pi) + \frac{1}{n^2}sin(n\pi) - 0 \right] \right ) \!$$

Note that for all n = 1,2,3... : $$ sin(n\pi) = 0 \!$$ as $$ sin(\pi) = sin(2\pi) = sin(3\pi) ... = 0 \!$$ therefore these terms are evaluated as zero, which yields:

$$ b_{n} = \frac{1}{\pi} \left( -\left[0 - \left (\frac{-1}{n} (-\pi) cos(-n\pi) + 0 \right) \right] + \left[\frac{-1}{n} \pi cos(n\pi) + 0 \right] \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( \left[\frac{1}{n} (\pi) cos(-n\pi) \right] + \left[\frac{-1}{n} \pi cos(n\pi) \right] \right ) \!$$

Note that $$ cos(-x) = cos(x) \!$$ therefore:

$$ b_{n} = \frac{1}{\pi} \left( \frac{1}{n} \pi cos(n\pi) + \frac{-1}{n} \pi cos(n\pi)  \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( 0 \right ) \!$$

$$ b_{n} = 0 \!$$ Therefore there will be no $$ sin(nx) \!$$ terms in the Fourier representation. In conclusion, the Fourier series representation for the given function is as follows:

$$ f(x) = \frac{\pi}{2} - \frac{4}{\pi} cos(x) - \frac{4}{3^2 \pi} cos(3x) - \frac{4}{5^2 \pi} cos(5x) + ... \!$$

$$ f(x) = \frac{\pi}{2} - \frac{4}{\pi}\left (cos(x) + \frac{1}{9} cos(3x) + \frac{1}{25} cos(5x) + ... \right ) \!$$

A graph of the function, and the Fourier series for $$ n = 1,3,5 \!$$ is shown below:

--Egm4313.s12.team11.sheider (talk) 06:00, 22 April 2012 (UTC)


text:
User:Egm4313.s12.team11.sheider/R.7.4: K 2011 p.482 pb. 13

Problem Statement
Find the Fourier series of the given function which is assumed to have a period of $$ 2 \pi \!$$. Show the details of your work.

Sketch or graph the partial sums up to that including $$ cos(5x) \!$$ and $$ sin(5x) \!$$

Given:

$$ f(x) = \left\{\begin{matrix} -x \text{ if } -\pi < x < 0\\\pi - x \text{ if } 0 < x < \pi \end{matrix}\right. \!$$

Solution
The Fourier series of a function with a period of $$ p = 2\pi \!$$ is defined:

$$ f(x) = a_{0} + \sum_{n=1}^{\infty } (a_{n}cos(nx) + b_{n}sin(nx))\!$$

Where:

$$ a_{0} = \frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) dx \!$$

$$ a_{n} = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) cos(nx) dx \!$$

$$ b_{n} = \frac{1}{\pi} \int_{-\pi}^{\pi} f(x) sin(nx) dx \!$$

Calculating the first term $$ a_{0} \!$$:

$$ a_{0} = \frac{1}{2\pi} \left ( \int_{-\pi}^{0} x dx + \int_{0}^{\pi} (\pi - x) dx \right) \!$$

$$ a_{0} = \frac{1}{2\pi} \left ( \left [\frac{x^2}{2} \right ]_{-\pi}^{0} + \left [\pi x - \frac{x^2}{2} \right ]_{0}^{\pi} \right)\!$$

$$ a_{0} = \frac{1}{2\pi} \left ( - \left(\frac{\pi^2}{2}\right ) + \left (\pi^2 - \frac{\pi^2}{2}\right)\right) \!$$

$$ a_{0} = \frac{1}{2\pi} \left ( -\frac{\pi^2}{2} + \pi^2 - \frac{\pi^2}{2}\right) \!$$

$$ a_{0} = \frac{1}{2\pi} \left (\pi^2 - \pi^2 \right) \!$$

$$ a_{0} = 0 \!$$

Calculating the coefficient $$ a_{n} \!$$:

$$ a_{n} = \frac{1}{\pi} \left( \int_{-\pi}^{0} x cos(nx) dx + \int_{0}^{\pi} (\pi - x) cos(nx) dx \right ) \!$$

Using integration by parts with the following substitutions for the integral $$ \int_{-\pi}^{0} x cos(nx) dx \!$$:

$$ u = x \!$$ and therefore $$ du = dx \!$$

$$ dv = cos(nx)dx \!$$ and therefore $$ v = \frac{1}{n}sin(nx) \!$$

Using integration by parts with the following substitutions for the integral $$ \int_{0}^{\pi} (\pi - x) cos(nx) dx \!$$:

$$ u = \pi - x \!$$ and therefore $$ du = -dx \!$$

$$ dv = cos(nx)dx \!$$ and therefore $$ v = \frac{1}{n}sin(nx) \!$$

This yields for the overall expression:

$$ a_{n} = \frac{1}{\pi} \left( \left[\frac{1}{n} x sin(nx) - \int \frac{1}{n}sin(nx)dx \right]_{-\pi}^{0} + \left[\frac{1}{n} (\pi - x) sin(nx) - \int -\frac{1}{n}sin(nx)dx \right]_{0}^{\pi} \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( \left[\frac{1}{n} x sin(nx) + \frac{1}{n^2}cos(nx) \right]_{-\pi}^{0} + \left[\frac{1}{n} (\pi - x) sin(nx) - \frac{1}{n^2}cos(nx) \right]_{0}^{\pi} \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( \left[\frac{1}{n^2} - \left (\frac{1}{n} (-\pi) sin(-n\pi) + \frac{1}{n^2}cos(-n \pi) \right) \right] + \left[-\frac{1}{n^2}cos(n\pi) + \frac{1}{n^2} \right] \right ) \!$$

Note that for all n = 1,2,3... : $$ sin(n\pi) = 0 \!$$ as $$ sin(\pi) = sin(2\pi) = sin(3\pi) ... = 0 \!$$ therefore these terms are evaluated as zero, which yields:

$$ a_{n} = \frac{1}{\pi} \left( \left[\frac{1}{n^2} - 0 - \frac{1}{n^2}cos(-n \pi) \right] + \left[-\frac{1}{n^2}cos(n\pi) + \frac{1}{n^2} \right] \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left(\frac{1}{n^2} - \frac{1}{n^2}cos(-n \pi) - \frac{1}{n^2}cos(n\pi) + \frac{1}{n^2} \right ) \!$$

Note that $$ cos(-x) = cos(x) \!$$ therefore:

$$ a_{n} = \frac{1}{\pi} \left(\frac{1}{n^2} - \frac{1}{n^2}cos(n \pi) - \frac{1}{n^2}cos(n\pi) + \frac{1}{n^2} \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left(\frac{2}{n^2} - \frac{2}{n^2}cos(n \pi) \right ) \!$$

$$ a_{n} = \frac{1}{\pi} \left( \left (\frac{2}{n^2} \right)(1 - cos(n \pi)) \right ) \!$$

$$ a_{n} = \frac{2}{n^2\pi} \left (1 - cos(n \pi) \right )\!$$

To evaluate the term $$ (1-cos(n\pi)) \!$$:

Note that $$ cos(n\pi) = -1 \!$$ for odd n values as $$ cos(\pi) = cos(3\pi) = cos(5\pi) ... = -1 \!$$

And that $$ cos(n\pi) = 1 \!$$ for even n values as $$ cos(2\pi) = cos(4\pi) = cos(6\pi) ... = 1 \!$$.

Therefore, it can be concluded that for odd n values:

$$ (1-cos(n\pi)) = 1-(-1) = 2 \!$$

And for even n values:

$$ (1-cos(n\pi)) = 1-(1) = 0 \!$$

Therefore, for the coefficient $$ a_{n} \!$$, all even terms will equal zero while all odd terms will have a multiplier of 2, this yields (for all odd n values):

$$ a_{n} = \frac{4}{n^2\pi} \text{ for  } n = 1,3,5... \!$$

Calculating the coefficient $$ b_{n} \!$$:

$$ b_{n} = \frac{1}{\pi} \left( \int_{-\pi}^{0} x sin(nx) dx + \int_{0}^{\pi} (\pi - x) sin(nx) dx \right ) \!$$

Using integration by parts with the following substitutions for the integral $$ \int_{-\pi}^{0} x sin(nx) dx \!$$:

$$ u = x \!$$ and therefore $$ du = dx \!$$

$$ dv = sin(nx)dx \!$$ and therefore $$ v = \frac{-1}{n}cos(nx) \!$$

Using integration by parts with the following substitutions for the integral $$ \int_{0}^{\pi} (\pi - x) sin(nx) dx \!$$:

$$ u = \pi - x \!$$ and therefore $$ du = -dx \!$$

$$ dv = sin(nx)dx \!$$ and therefore $$ v = \frac{-1}{n}cos(nx) \!$$

This yields for the overall expression:

$$ b_{n} = \frac{1}{\pi} \left( \left[\frac{-1}{n} x cos(nx) - \int \frac{-1}{n}cos(nx)dx \right]_{-\pi}^{0} + \left[\frac{-1}{n}(\pi - x) cos(nx) - \int -\frac{-1}{n}cos(nx)dx \right]_{0}^{\pi} \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( \left[\frac{-1}{n} x cos(nx) + \frac{1}{n^2}sin(nx) \right]_{-\pi}^{0} + \left[\frac{-1}{n}(\pi- x) cos(nx) - \frac{1}{n^2}sin(nx) \right]_{0}^{\pi} \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( \left[0 - \left (\frac{-1}{n} (-\pi) cos(-n\pi) + \frac{1}{n^2}sin(-n \pi) \right) \right] + \left[- \frac{1}{n^2}sin(n\pi) - \left( \frac{-1}{n}\pi \right) \right] \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( - \frac{1}{n} \pi cos(-n\pi) - \frac{1}{n^2}sin(-n \pi) - \frac{1}{n^2}sin(n\pi) + \frac{1}{n}\pi   \right ) \!$$

Note that for all n = 1,2,3... : $$ sin(n\pi) = 0 \!$$ as $$ sin(\pi) = sin(2\pi) = sin(3\pi) ... = 0 \!$$ therefore these terms are evaluated as zero, which yields:

$$ b_{n} = \frac{1}{\pi} \left( - \frac{1}{n} \pi cos(-n\pi) -0 - 0 + \frac{1}{n}\pi   \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left(\frac{1}{n}\pi - \frac{1}{n} \pi cos(-n\pi) \right ) \!$$

Note that $$ cos(-x) = cos(x) \!$$ therefore:

$$ b_{n} = \frac{1}{\pi} \left(\frac{1}{n}\pi - \frac{1}{n} \pi cos(n\pi) \right ) \!$$

$$ b_{n} = \frac{1}{\pi} \left( \left(\frac{\pi}{n} \right)(1-cos(n\pi)) \right ) \!$$

$$ b_{n} = \frac{1}{n} \left(1-cos(n\pi) \right ) \!$$

To evaluate the term $$ (1-cos(n\pi)) \!$$:

Note that $$ cos(n\pi) = -1 \!$$ for odd n values as $$ cos(\pi) = cos(3\pi) = cos(5\pi) ... = -1 \!$$

And that $$ cos(n\pi) = 1 \!$$ for even n values as $$ cos(2\pi) = cos(4\pi) = cos(6\pi) ... = 1 \!$$.

Therefore, it can be concluded that for odd n values:

$$ (1-cos(n\pi)) = 1-(-1) = 2 \!$$

And for even n values:

$$ (1-cos(n\pi)) = 1-(1) = 0 \!$$

Therefore, for the coefficient $$ b_{n} \!$$, all even terms will equal zero while all odd terms will have a multiplier of 2, this yields (for all odd n values):

$$ b_{n} = \frac{2}{n} \text{ for  } n = 1,3,5... \!$$

In conclusion, the Fourier series representation for the given function is as follows:

$$ f(x) = 0 + \left (\frac{4}{\pi} cos(x) + \frac{4}{3^2 \pi} cos(3x) + \frac{4}{5^2 \pi} cos(5x) + ... \right ) + \left (2sin(x) + \frac{2}{3} sin(3x) + \frac{2}{5} sin(5x) + ... \right ) \!$$

$$ f(x) = \frac{4}{\pi} \left (cos(x) + \frac{1}{9} cos(3x) + \frac{1}{25} cos(5x) + ... \right ) + 2 \left (sin(x) + \frac{1}{3} sin(3x) + \frac{1}{5} sin(5x) + ... \right ) \!$$

A graph of the function, and the Fourier series for $$ n = 1,3,5 \!$$ is shown below:

--Egm4313.s12.team11.sheider (talk) 06:00, 22 April 2012 (UTC)


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User:Egm4313.s12.team11.arrieta/Report 7

Problem R7.2
Solved by Francisco Arrieta

Problem Statement
Plot the truncated series $$ u(x,t)=\sum_{j=1}^{n}a_j\cos C\omega_j t \sin \omega_j x \!$$ with $$ n=5 \!$$ and for:

$$ t=\alpha P_1=\alpha \frac{2\pi}{C\omega_1}=\alpha \frac{2L}{C} \!$$

$$ \alpha=0.5, 1, 1.5, 2 \!$$

Solution
Using:

$$ \left\{\begin{matrix} f(x)=x(x-2) \\ g(x)=0 \\ C=3 \\ L=4

\end{matrix}\right. \!$$

Then:

$$ a_j=\frac{2}{L}\int_{0}^{L}f(x)\sin \omega_j x dx \!$$

 * $$ =2\left [ \frac{(-1)^j-1}{\pi^3j^3} \right ] \!$$

$$ \therefore a_j=0 \!$$ for all even values of j

Plugging back to the truncated series:

$$ u(x,t)=\sum_{j=1}^{n}2\left [ \frac{(-1)^j-1}{\pi^3j^3} \right ]\cos [C \frac{j\pi}{L} \alpha \frac{2L}{C}] \sin[\frac{j\pi}{L}x] \!$$

 * $$ =\sum_{j=1}^{n}2\left [ \frac{(-1)^j-1}{\pi^3j^3} \right ]\cos (\alpha j2\pi) \sin(\frac{j\pi}{2}x) \!$$

For $$ n=5 \!$$ :

$$ u(x,t)=[\frac{-4}{\pi^3}\cos (2\pi \alpha) \sin(\frac{\pi x}{2})]+[\frac{-4}{27\pi^3}\cos (6\pi \alpha) \sin(\frac{3\pi x}{2})]+[\frac{-4}{125\pi^3}\cos (10\pi \alpha) \sin(\frac{5\pi x}{2})] \!$$

When $$ \alpha=0.5 \!$$ :

When $$ \alpha=1 \!$$ :

When $$ \alpha=1.5 \!$$ :

When $$ \alpha=2 \!$$ :


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TESOL/Fluency

Fluency in ESL has a slightly different meaning from fluency in general, which is facility in the use of a language. In ESL, it is restricted to speech and refers to the speaker's ability to link language units with reasonable ease and speed.

In the seventies, it was popular to teach fluency using substitution drills. Starting in the mid 80s, a notion of message-focused fluency emerged, where fluency was considered facility in using language to express a message. In this view, form is not important as long as mistakes do not get in the way of the message. In particular, Brumfit (1984) described how to make a fluency building activities. These activities should focus on the message, have a message determined by the student speaking rather than by the teacher or textbook, and proceed with minimal teacher correction.

title: TESOL/Fluency


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TESOL/Weak forms

High-frequency words in English often have alternative forms used in unstressed speech, such as conversation, called weak forms, which are reduced forms of those words. Weak forms pose difficulty to learners of English as a second language by making listening comprehension more difficult, which can lead a learner to mishear a word which may cause the learner to infer a different context despite evidence following the misunderstood word.

High frequency weak forms
These are 51 high-frequency weak forms in English:

Homophonous weak forms
From the point of view of the listener, homophonous weak forms are identical. They sound the same. When a learner hears these forms, they have to focus to determine which word the speaker is thinking of:

title: TESOL/Weak forms


text:
User:MSB/HWR-SUN

=Summer 2012: Nachlese/Afterthoughts= In this course, the students meet weekly for class on our school's virtual island in Second Life® and also discuss in a private Moodle forum using a weekly question as their starting point. Please feel free to leave your own comments and observations on this page. For technical issues, see this page.

Forum Discussion Week One: What Are You Learning?

 * I'm always quite excited when I read the first forum thread. This week's question (the first of the course) was "What are you learning in your internship?" — A wide open question, but a question that allowed the students to bring in a wealth both of knowledge gained and issues experienced by them. Here's a selection of what students have said:
 * «I am learning to work on my own.»
 * «I'm beginning to feel responsibility towards the company I work for.»
 * «I'm learning how to communicate with business customers.»
 * «I'm learning how it feels to be at the bottom of the hierarchy.»
 * «I've learnt how to break complex tasks down, work on them and put the puzzle back together again.»
 * «I'm learning from colleagues how to deal with the data jungle in Excel spreadsheets.«
 * «I'm experiencing difficulties with SAP and wish I had seen more of it during my studies»
 * «I'm learning how to delegate to others.»
 * «I'm learning to not trust others blindly but monitor closely when I'm ultimately responsible for the outcome of the work.»
 * «I'm learning not to sell myself for less than my fair value, especially in a male-dominated work environment.»
 * «I'm realizing that communicating with colleagues is one thing, communicating with my adviser another.»
 * «I learnt that theory and practice can differ wildly, especially when working with people: there's no "perfect" person, so the theory almost NEVER applies.»
 * «I understood how different business is conducted around the world.»
 * «I keep a working diary where I try to write down everything I learn.»
 * «I learnt how to deal with stress and unpleasant colleagues.»
 * «I've learnt that pay is not the most important asset to job satisfaction.»
 * «I experienced what it feels like to get fired.»
 * «I am learning to deal with people who have different tempers.»
 * «I learnt through watching my boss who is really a good "leader", which means that he delegates the tasks fairly and at the same time he cares for the team by supporting all colleagues.»
 * «I've learnt to deal with people just pushing tasks on me—though this interrupts my personal organisation it has helped me to be more flexible.»
 * «I'm learning a lot about time management»
 * «I've learnt how to work effectively under pressure.»
 * «I learnt that it is important to think out of the box when looking for creative solutions and found that I could do it.»
 * «I'm learning to accept feedback.»

Now, what's really lovely about these results is that they mostly didn't come as bullet point lists but in the form of little stories. This is most encouraging, since being able to tell stories about your work experience (and your internal experience during the internship) is one of the key points of this supervision course. But even without the stories, the spread of lessons learnt by this group of first-time interns is astonishing! I also notice (in the complete answers) that the students make many assumptions about how work is "supposed to be". It will be interesting to question those in the course of the term.--msb 08:21, 23 April 2012 (UTC)

From Week 1: First Presentation and Role Play
We made a start in the [Berlin] lunchtime session today with a short presentation followed by role play—worked reasonably well. Assertiveness in the work place was discussed. The client (intern) highlighted the importance of feeling out the environment (and the local habits and culture) before choosing a course of action. I pointed out that it is important to have several options of behavior: if you don't feel like you have any then you're likely stuck in a particular pattern which will make it harder to respond to changes. Also, people get used to your patterns of behavior (as do you to theirs).

In the role play (everybody did just great!), the superiors showed willingness to negotiate — the question is what will happen (what will you do) if this is not the case. Hence next week's forum question challenges you to share examples of assertive behavior: non-aggressive, non-manipulative behaviors that are meant to show the other party where your boundaries are (of body, of time, of attention etc.). The best situation, of course, occurs if the intern is eager to show what s/he's made of and the boss is skilled and sensitive enough to help him test his limits.

For the presentation: it was good to have little information on the slides and cover interesting information via discussion. In the image you see my summary of the intern's scene description for the role play, highlighting the (known) situation, the complication and the actors for this RP. We also discussed (a repetition for some) ways of giving feedback: subjective ("I think/feel"), objective ("facts") and meta ("meaning, future, interpretation"). Generally, what everyone thinks of first (critique, positive or negative feedback) isn't so useful: when it comes to communication, both sides need to establish first where they stand (as subjects). A slight (true) generalization: in my experience, German professionals tend to focus too much on objective feedback ("Sachebene") when working with foreigners. They feel lost on a relationship level ("Beziehungsebene"). Good managers know when to change mode and they know which mode they're in. --Birkenkrahe (talk) 13:15, 23 April 2012 (UTC)

In the evening session, we heard from an intern who'd worked abroad in the hospitality industry. The role play dealt with him having to manage a complaining customer. It was interesting from an assertiveness (limit-setting) point of view because there seem to be no options in this situation ("client is king" summarizes the expectations: the stronger the expectations the less the apparent flexibility in the situation). In truth though, you always have the same options - usually many more than you think. The the industry and the culture or the character of the other person determine the way you communicate your boundaries, but not the need or the right to do so. I'm looking forward to deepening these issues and add examples in the weeks to come! --msb 19:45, 23 April 2012 (UTC)

From Week 2: Examples of Assertiveness
Your discussion of non/assertiveness examples is fascinating to read! However, I think I need to clarify a couple of misunderstandings: assertiveness in the sense introduced here (communicating your own boundaries) is not the same as dominance within a hierarchy, or intimidation. These are actually aggressive, non-assertive behaviors. Assertiveness is also not the same as behaving "masculine". "Masculine" societies in the sense of Hofstedte are not automatically more assertive though they may appear as more aggressive (to outsiders).

 * To behave dominantly within a hierarchy (no matter if the hierarchy is culturally sanctified or not—like in the Chinese example) is rather a weakness in terms of assertiveness. Why? Because in order to guarantee boundaries (e.g. social, cultural, professional norms) the boss needs the hierarchy, and when the hierarchy goes, there's little left. This is starkly different from commanding respect or communicating serenity, importance, influence, charisma: all of these are all indicators of "natural assertiveness". Examples: (1) there's no doubt in your mind that the old wise man knows what he's talking about. (2) when your boss speaks, she seems to create a space around herself that makes people want to let her speak...there are invisible boundaries here but they're not magical, they've been created by people's assertive behavior.

 * How to do this...is another question. It requires practice and more. It follows that "masculinity" in the sense of Hofstedte is also not assertiveness. In fact you can be male or female and be equally assertive. Males and females have cliche behaviors of non-assertive behavior: males are aggressive and females are manipulative (that's a prejudice: I've met as many manipulative males as aggressive females). "Hofstedte-masculine" societies may appear more aggressive to others, e.g. this was definitely my impression when I worked and studied among the Dutch in the Netherlands, and Germans are considered more aggressive by the British (on average), just as Germans experience British sarcasm and habit as manipulative (on average).

Once again: great discussion—the arguments and examples were first class. The misunderstandings are natural—they often come up around this. Nobody likes to look at their own non-assertiveness, by the way...also as a response to the quality of the discussion, we'll deal this week with the next level of behavior: how to deal with negative people. To prepare this, I've uploaded a summary of both types of negative people and ways of dealing with them that comes from Prof Harald Kjellin and was presented by him at the Consulting Forum at the HWR Berlin in January 2012 (the work goes back to work on negotiation by Axelrod and many others) — see Fig. 3. --msb (talk) 16:20, 30 April 2012 (UTC)

From Week 3: Handling Negative People
The discussion on "Handling Negative People" was a little hard-going at first. You seemed at first compelled to let us know how nice and wonderful everyone is, how devoid of negativity your workplace was. Which is great, don't get me wrong, and it may even be true! Or perhaps you're just still honeymooning...but if you indeed cannot perceive any negativity as documented in Kjellin's list in others, what about taking a look at your own behavior?

On being nice.
There was a noticeable pressure, consequently, on putting on a "nice face". While this is understandable, let me remind you what the purpose behind the anti-negativity tactics was: once you've applied your assertiveness skills (= expressed where your boundaries/limits are), you might be faced with an "operator" (of one of the twelve types). The suggested behaviors are designed to counteract them. At the same time, overdoing it turns you into one of the types yourself. The only way to learn how to deal with negative types is the same way in which we learn anything: by continuous practice and repetition. There's no point in waiting for "the big one" which makes special behaviors worthwhile. You may never meet a big bully, but instead a stream of small bullies who also sap your energy etc.

According to game theory (as explained by Prof. Kjellin in the video), when someone has behaved badly with you, it is better before simply going on, to exact some sort of (appropriate) revenge before returning to a trusted relationship. The ideal that comes through in many of your posts ("just keep going and try to stay friendly") is more likely to lead to depression or passive-aggressive (involuntary revengeful) behavior.

What if you only notice it later?
One of you said on the forum:
 * «When it comes to negative behavior that offends you and that makes you feel being treated unfair a quick reaction is indispensable in order to avoid a repetition. But many aspects that are mentioned in Prof Kjellin's Reference Guide, e.g. the charmer, are characteristics that you will notice later on. How would you then explain the situation without sounding ridiculous?»

I'm hardly ever able to produce an immediate reaction though I've got better at it over the decades...it's partly to do with the "nice boy" image (now "nice man") which used to be more important to me than it is now...in other words: this need to deal with something after the fact is really a standard situation! I also wonder what others think...

...one thing I can say is that the "sounding ridiculous" will always be there as a danger. In fact, the "negative person" counts on it to lower your defenses and to get away with it. So that fear is one of the first to let go. And you will, if it's worth it to you. When you feel really bothered or offended or sucked dry, you'll rise to the challenge. The best way if you choose to go the direct way (which involves explanation—generally: explain as LITTLE as necessary) is to talk about how the situation made you feel (assertiveness technique). Otherwise, if you can't or don't want to be direct or open (who can blame you) then go straight for the recommended tactic.

E.g. the charmer is highly manipulative—s/he knows what s/he's doing and always got away with it. Find their weakness (numbers; something that they're not competent in) and ask for exactly that...repeatedly. Don't waste time on explanation. In the case of these types, attack may the best defense.

Role Playing
For the role plays, to make them more interesting and richer in content, ask yourself the following questions beforehand (and if you forget, I'll ask them in session):
 * What did you want to get out of the situation you described? Or what do you want to get out of it?
 * What was the obstacle for you to get what you want? Or which obstacle do you foresee might stall you?
 * What are you curious about regarding the role-play itself? What would you most like to know if you had your druthers?

Next week's discussion is going to be easier...we use the recent election in France as the jumping off point to discuss "dress code". This will be our preparation for a wider discussion of workplace culture in the following week, from which we will move on to networking and knowledge sharing issues.

Defusing Outraged People
...when you're not the reason of their anger but become their target because you're in their way—this was one example we dealt with this week but didn't have time for a role play, alas. As a general rule, I suggested to resort to mirroring the other person's behavior - a technique called parallel talking - carefully of course. A little as in the sketch below, exemplary for many coaching situations I've experienced:

 * A: I'm so pissed off. They've really made me angry.
 * B: (picking up on the anger and mirroring it back) I can see you're pissed off. They really done it to you this time. This is an outrage.
 * A: That's what I'm saying. They're screwing with me (hits the table)! Bastards!
 * B: I know. You should quit. I don't think I've heard anything this bad EVER. Those ******** (indistinct strong cursing)!!!!
 * A: (after a pause, calming down because he sees himself from the outside) Well...
 * B: (keeps mirroring)
 * A: Well, it's not actually perhaps THAT bad.
 * B: Are you sure?

From Week 4: Building/Saving Work Relationships
In today's role-plays, we were looking at two very interesting issues:

 * 1) negotiating with a boss who's not happy and has begun to blame and judge you while giving unclear (possibly) contradictory instructions (perhaps because he's got no experience in supervising interns; or because he's a control-freak); in this case, you're face with a "threatening bully" (in Kjellin's list) and you should ask for very, very precise instructions as well as stay away from blaming and judging yourself (to avoid an upward spiral); in assertiveness terms you may find that proper emotional positioning ("I'm very frustrated") leads to mirroring by your boss ("I'm very frustrated, too") thereby putting you at the same level and thwarting power-play.
 * 2) getting other (regular) employees to spend time with you and teach you things in a company that's recently been acquired by another, much larger company. Because of the acquisition, the company and its employees may be in a kind of shock...which will, just as for an individual, slow down responses and can even induce collective psychosis of a low level—which means that, if this is a serious case of cultural distortion, you cannot rely on the usual social rules and regulations. Also, acquisition means that some or all processes of the old company are up in the air: there's no process security at all. Generally, an intern, at the bottom of the food chain, thrives on stable rules and regulations. In its absence, the intern must improvise which is easier with more experience. If you find that you make demands on your environment and the environment resists, you can also check your own behavior with respect to a fundamental truth: nobody will want to do something for you unless it benefits them. This means you need to identify their possible benefit—you can do that directly (asking) or indirectly (e.g. by being careful about their time, trying to ask them to tell you things during lunch etc.). In general, the more time passes, the more you'll find (unless you've screwed up seriously) that the relationships at work will deepen; people will trust you more and you're more likely to get what you want.

These are, of course, generalizations.

From Week 5: Two clean assertiveness issues
This week, we had a couple of very clear assertiveness role plays in the evening session—an opportunity to repeat what I said elsewhere (I think): there are three distinct scenarios—

 * 1) You feel bullied or attacked or perhaps you simply feel someone has stepped over your boundary. This is a case for assertiveness. The goal: to let them know what your limits are. Short of direct information, the key method is "fielding" by repeating your message consistently and simply (e.g. by saying "no", not defending, not giving reasons etc.); the first evening role play was of this sort.
 * 2) You're faced with a "negative person" (see above) in one of its many shades. Now you need to step up to the additional challenge and face the music by developing a strategy (which may not come to you immediately—this takes practice!) that matches the assault. Use Kjellin's list accordingly.
 * 3) Lastly, and we've seen an example of that in the evening, too, you may be faced with a reasonable person who meets you eye to eye, listens well, wants to help etc. In this case you simply negotiate, try to find a compromise together.

From Week 6: How do you network?
After reading the forum posts: It was interesting to see how many of you only thought of the official networking opportunities that the firm offers (or doesn't offer). And I'm surprised to read how social networking is getting a bad name in the context of work. One of you succinctly put it like this: «I really dislike networking for a professional purpose.» Well, good riddance. Networking is what most professionals, especially at upper levels, do almost for their living. I would say perhaps you didn't understand me well, but I had given you the key points of good networking by Hain — perhaps you didn't look at them. If you believe what this student believes, you may want to check them again, because networking boils down to good relationship building, a skill that no (successful) professional can really be without.

The other surprise is the lack of social media in your responses. My growing impression when I look at the world of work is that the increasing globalization leads to less physical quality time spent with less and less people, while (to get the work done) we have more and more virtual relationships. Unless you develop skills to enrich virtual relationships, too, you'll have a hard time in the international arena. Of course it is always to be preferred, and immeasurably richer, to meet up in person—but it just happens less and less. The complete, ugly truth is that networking aka relationship building got a hell of a lot more complicating in the last 10 years and is likely to get more so. However, much of this is intuition and experience, I cannot validate these claims with research—if you find something in favor or against, let me know!

From Week 9
My desire to comment on the sessions is still strong, but I've got typing problems, hence I have to be short. If you're interested please take a look at this presentation, esp slide no. 5 which shows how communication breaks down unless both partners of an encounter aren't in the "adult" poition. Important: check yourself how you reacted in stressful situations and if you perhaps have a tendency to behave as a "child" e.g. when meeting a superior who behaves like a "parent".

title: User:MSB/HWR-SUN


text:
TESOL/Vocabulary quiz (up)

Phrasal verbs with the preposition "up" are one of the most numerous kinds in English. This is a quiz of some of them. For a complete list, see the category at Wiktionary.

{add up to - stop counting - gather in a group - remember + have a particular effect
 * type=""}

{brush up + review, improve a skill - clean - relax, stop worrying - change one's hairstyle
 * type=""}

{choke up - say something unexpected + temporarily be too emotional to speak - strangle - be unable to sleep
 * type=""}

{cook up - remember - make oneself attractive + make an elaborate lie - continue, stay ahead
 * type=""}

{end up + conclude in, eventually do, arrive at - finish, complete, finalize - present, say, explain - send to, deliver to
 * type=""}

{freshen up + wash or groom oneself to be attractive - update information - organize to make something neater - make something more efficient
 * type=""}

{keep up - cover, keep hidden + continue, stay even or ahead, maintain - convince, persuade, force into - make someone tired
 * type=""}

{loosen up - tighten - untie - fall off + relax, loosen
 * type=""}

{meet up + meet someone, by arrangement - make something complicated - continue, stay even or ahead, maintain - get lucky
 * type=""}

{ride up - continue, stay even or ahead, maintain - finish riding + ride closer to someone - ride a long distance
 * type=""}

title: TESOL/Vocabulary quiz (up)


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User:Auro.001/Books/Computer Science

Computer Programming

 * Topic:Computer programming
 * Topic:Computing fundamentals

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User:Auro.001/Books/Computer Programming

Computer Programming

 * Topic:Computer programming
 * Topic:Computing fundamentals
 * Introduction to Computer Science
 * Introduction to Computers
 * History of computing
 * Introduction to Turing Machines
 * Basics of computer architecture
 * What is a CPU?
 * What is a motherboard?
 * Internet
 * Personal computers
 * What is an Algorithm
 * How to go about implementing a problem solution as a program
 * Development environment and language principles
 * Types and variables
 * Operators and expressions
 * Control structures
 * Procedures and functions
 * Arrays, strings and records
 * Basic I/O
 * Introduction to Programming
 * Introduction to Programming/About Programming
 * Introduction to Programming/Programming Languages
 * Introduction to Programming/Organization part 1
 * Introduction to Programming/Variables
 * Introduction to Programming/Variables part 2
 * Introduction to Programming/Variables part 3
 * Introduction to Programming/Control structures
 * Introduction to Programming/Subprograms
 * Introduction to Programming/Scope
 * Introduction to Programming in Java
 * Introduction to Programming in Java/Introduction to Java
 * Introduction to Programming in Java/Integer variables
 * Introduction to Programming in Java/Boolean Variables
 * Introduction to Programming in Java/Strings
 * Introduction to Programming in Java/Java Classes
 * Introduction to Programming in Java/Inheritance
 * Introduction to Programming in Java/Arrays
 * Introduction to Programming in Java/Swing
 * Introduction to Programming in Java/Mobile phones
 * Creating a Development Environment
 * Introduction to Programming Logic
 * Topic:Math for computer programming
 * Introduction to Math for computer programming
 * Introduction to Programming Logic/Key Terms
 * Introduction to Programming Logic/Variables
 * Introduction to Algorithms
 * Introduction to Programming Logic/Lesson 2: Conditionals and Logic
 * Introduction to Programming Logic/Looping
 * CamelCase
 * C|Topic:C
 * C/Before you start
 * Introduction to C
 * Basic output in C
 * Variables and Expressions
 * Data Types and Keywords
 * Type Qualifiers
 * Storage Classes
 * Typecasting
 * Flow control in C
 * Functions and methods in C
 * Pointers and arrays in C
 * String handling in C
 * Structs
 * Input and output in C
 * C Source Codes
 * C Preprocessors
 * Game programming
 * Topic:Object-oriented programming
 * C++
 * Introduction to C++
 * Variables and User Input
 * C++/Simple Math
 * Conditional Statements
 * Loops (C++)
 * Functions and Recursion
 * More Functions
 * C++ pointers
 * Classes and Inheritance
 * Templates in C++, part 1
 * Templates in C++, part 2
 * The STL
 * C++/STL Algorithms
 * Switching from C to C++
 * Topic:Clojure
 * HTML
 * Introduction to HTML
 * WYSIWYG vs. Manual Coding in HTML
 * Web Design/What is HTML
 * Basic formatting in HTML
 * Fonts and colours in HTML
 * Links in HTML
 * Graphical Content and Multimedia
 * Lists in HTML
 * Tables in HTML
 * Frames in HTML
 * Forms in HTML
 * Web Design/HTML Challenges
 * HTML/301 redirect
 * Basic JavaScript
 * Web Design/An Introduction to Programming with JavaScript
 * Web Design/Getting to know JavaScript events
 * Web Design/Getting to know the Document Object Model with JavaScript
 * Intermediate JavaScript
 * Web Design/JavaScript Challenges
 * Topic:MySQL
 * Introduction to Databases
 * Database management systems
 * Introduction to SQL
 * Introduction to PHP
 * Web Design/Dynamic Websites/Creating Database Tables
 * MediaWiki engine
 * Apache MySQL PHP on Mac OS X
 * Topic:Python
 * Introduction to and setup of Python
 * Basic Python data types
 * Python operators
 * Basic Python functions
 * Truth and flow control in Python
 * Object-Oriented Python
 * Python libraries
 * Topic:Algorithms and Data Structures
 * Topic:Algorithms
 * Time management for programmers
 * Bash programming
 * WINAPI Programming
 * Visual Basic .NET 2005
 * Visual CSharp.NET 2005


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Edit request
In the "Article message box types" section, remove the content and replace it with:

Like this:

--189.70.92.232 22:57, 22 April 2012 (UTC)

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User:Egm4313.s12.team1.wyattling/r7

Statement
Consider equation (5.0) below:
 * {| style="width:100%" border="0"

$$  \displaystyle <\phi_{2j-1},\phi_{2k-1}> = \int_{0}^{P}\sin{j\omega x}\cdot \sin{k\omega x}dx = 0 $$     (5.0)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

1) Find the exact integration of equation (5.0) with $$ P = 2\pi\!$$, $$ j = 2\!$$, $$ k = 3\!$$.

2) Confirm the result with Matlab's trapz command for the trapezoidal rule.

Solution
1) Substituting the given values, we get equation (5.1) below:
 * {| style="width:100%" border="0"

$$  \displaystyle <\phi_{3},\phi_{5}> = \int_{0}^{2\pi}\sin{2\omega x}\cdot \sin{3\omega x}dx = 0 $$     (5.1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Using the product and sum trigonometry identities, we can evaluate the definite integral:
 * {| style="width:100%" border="0"

$$  \displaystyle \int_{0}^{2\pi}\sin{2\omega x}\cdot \sin{3\omega x}dx = \frac{1}{2}\int_{0}^{2\pi}(\cos{\omega x}-\cos{5\omega x})dx = 0 $$     (5.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

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

$$  \displaystyle \rightarrow [\frac{1}{2\omega}{\sin{\omega x} - \frac{1}{5}\sin{5\omega x}}]_0^{2\pi} = 0 $$     (5.3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Also, $$ \omega = \frac{2\pi}{P} = 1\!$$, and substituting this into equation (5.3) allows the definite integral to be solved:
 * {| style="width:100%" border="1"

$$  \displaystyle [\frac{1}{2}{\sin{x} - \frac{1}{5}\sin{5x}}]_0^{2\pi} = 0 $$     (5.4)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

2) The following is the code for evaluating the definite integral in equation (5.1) in Matlab:

EDU>> X = 0:pi/100:2*pi;

EDU>> Y = sin(2*X).*sin(3*X);

EDU>> Z = trapz(X,Y)

Z =

-2.2633e-17

EDU>> plot(X,Y)

The returned value of the evaluated integral in Matlab is essentially equal to zero, and it can be seen in the graph that the areas under the curve cancel each other out.

Author
Solved and Typed By -

Reviewed By -

title: User:Egm4313.s12.team1.wyattling/r7


text:
University of Florida/Egm4313/s12.team11.imponenti/R7.3

Problem Statement
Find (a) the scalar product, (b) the magnitude of $$f\!$$ and $$g\!$$ ,(c) the angle between $$f\!$$ and $$g\!$$ for:

1) $$f(x)=cos(x), \ g(x)=x \ for -2 \le x \le 10\!$$

2) $$f(x)=\frac{1}{2}(3x^2-1), \ g(x)=\frac{1}{2}(5x^3-3x) \ for -1 \le x \le 1\!$$

Part 2
solved by Luca Imponenti

Scalar Product
$$=\int_a^bf(x)g(x) \ dx\!$$

$$=\int_{-1}^{1}[\frac{1}{2}(3x^2-1)][\frac{1}{2}(5x^3-3x)] \ dx\!$$
 * $$=\int_{-1}^{1}\frac{1}{4}(15x^5-4x^3+3x) \ dx\!$$
 * $$=\left. \frac{1}{4}(\frac{15}{6}x^6-x^4+\frac{3}{2}x^2)\right|_{-1}^{1}\!$$
 * $$=\frac{1}{4}[(\frac{15}{6}1^6-1^4+\frac{3}{2}1^2)-(\frac{15}{6}(-1)^6-(-1)^4+\frac{3}{2}(-1)^2)]\!$$

Since all exponents are even, everything in brackets cancels out

$$=0\!$$

Magnitude
$$\| f \|=^{1/2}=\int_{a}^{b} f^2(x) \ dx\!$$
 * $$=\int_{-1}^{1} [\frac{1}{2}(3x^2-1)]^2 \ dx\!$$
 * $$=\int_{-1}^{1} \frac{1}{4}(9x^4-6x^2+1) \ dx\!$$
 * $$=\left. \frac{1}{4}(\frac{9}{5}x^5-2x^3+x)\right|_{-1}^{1}\!$$
 * $$=\frac{1}{4}[(\frac{9}{5}1^5-2(1)^3+1)-(\frac{9}{5}(-1)^5-2(-1)^3+(-1))]\!$$
 * $$=\frac{1}{4}[\frac{4}{5}-(-\frac{4}{5})]\!$$

$$\| f \| =\frac{2}{5}\!$$

$$\| g \|=\int_{a}^{b} g^2(x) \ dx\!$$
 * $$=\int_{-1}^{1} [\frac{1}{2}(5x^3-3x)]^2 \ dx\!$$
 * $$=\int_{-1}^{1} \frac{1}{4}(25x^6-30x^4+9x^2) \ dx\!$$
 * $$=\left. \frac{1}{4}(\frac{25}{7}x^7-6x^5+3x^3)\right|_{-1}^{1}\!$$
 * $$=\frac{1}{4}[(\frac{25}{7}1^7-6(1)^5+3(1)^3)-(\frac{25}{7}(-1)^7-6(-1)^5+3(-1)^3)]\!$$
 * $$=\frac{1}{4}[\frac{4}{7}-(-\frac{4}{7})]\!$$

$$\| g \| =\frac{2}{7}\!$$

Angle Between Functions
$$cos(\theta)=\frac{}{\| f \| \| g \|}\!$$

Since $$=0\!$$ the two functions are orthogonal

$$\theta=90\!$$


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text:
User talk:Sang1938/enes100/Airplane: My Work

Nathan Nice work!

Mirza I like the illustrations looking forward to seeing it done.

Erika We're looking into the same thing! i want to see how your wings turn out this week.

week 1 p3 grading 1sfoerster (talk) 19:38, 24 April 2012 (UTC)
 * 10/10/10 ... found a starting place

Mirza Sweet looking airplane lets see whos airplane flies longer.

Erika Good idea using no glue, i can't wait to test your plane.

week 2 p3 grading 1sfoerster (talk) 16:31, 1 May 2012 (UTC)
 * 10/10/30 ... good work

Mirza I like what you have been working on.

week 3 p3 grading 1sfoerster (talk) 12:35, 8 May 2012 (UTC)
 * 0/0/0 ... nothing to grade

Mirza Enjoyed working with you good stuff!

Nathan
 * Great deterimination!

week 4 p3 grading 1sfoerster (talk) 18:25, 15 May 2012 (UTC)
 * 0/5/0 ... nothing to grade


text:
User:Jromanch0088/enes100/My Work Heli3

Write problem/project Goal
To build a quad copter controlled autonomously by the arduino

My First Task
I am going to continue testing the see saw as well as get the wireless hooked up for the arduino.

Summary of actual work over first weekend
I have gotten the see saw working consistently, I have looked into designs for the actual quad copter, and I have started messing with the bluetooth.

Dual Lift Test
In the dual lift test I attached two motors to a block of wood in order to see how much lift I could achieve from two propellers spinning at once. I drilled two holes for the motors, attached the motors to the block of wood with the X section, hooked up all the wires, then ran them all to an arduino. When we first ran a program we did not put propellers on because we were not sure what the program would do. This turned out to be a good idea This was because after testing, the motor with the pink electrical tape started sparking, something was grinding in the motor. This stopped all further testing of the dual lift test because instead of putting another motor on I decided to put it on the see saw which is explained in full detail in the next section.

See Saw
The see saw is a very useful tool we use to test out how to sync the motors up and try to achieve balance of the motors. What I did was assemble the whole see saw. The first step was to get the motors attached. This was done by drilling a hole 18 inches from the center of the see saw on both sides and then around that hole four more smaller holes were drilled in a square pattern. These holes were made so the motors shaft could go in the center hole, and the X bracket for the four holes so I could secure the motor in place without spitting the wood on the see saw. The motor was then attache by screwing it on by the four different bracket holes. This was done on both sides. After they both were secured, the arduino was added to the middle of the see saw by attaching two rubber bands to it so we could easily take it off for programming. After this the ESCs were hooked up to the motors. Then the ESCs hooked up to the arduino. Originally the ESCs were hooked up to the arduino by breadboards and then we twisted wires together, and finally I soldered them together to make the see saw less messy. The ESC power cables were hooked up by alligator clips at first. We then tried just twisting them together and that worked much worse than the aligator clips and finally I soldered them together with a triple wire solder and one open wire for easy connection to the power supplies. We also put the gyro accelerometer on the see saw. It was hooked up but we did not understand enough about it to be able to make a program that could control the motors by tilting the see saw.

First Assembly of The See Saw

Bluetooth
I have gotten the bluetooth device in and I have soldered the pins into it so we can use a breadboard. I have done brief research on how to get it working and what I have gotten so far is that i need an antenna listed here Antenna. The wiring schematics are here Wiring. The details of hooking up the bluetooth to the pc is found here tutorial. But i found a more useful tutorial here Other tutorial this one worked because this had the correct pairing code. The paring code is "1234". not "default" like the other tutorial said.

My Second Task
Get the bluetooth working for the arduino, and get the rest of the youtube videos uploaded (I was having problems uploading them).

Summary of actual work over second weekend
How is what you did different than what you planned?

Week2 Narrative
Tell a detailed story describing what you did for your team over the weekend.

My Third task
Record what you are planning on doing for the team during the third weekend.

Summary of actual work over third weekend
How is what you did different than what you planned?

Week3 Narrative
Tell a detailed story describing what you did for your team over the weekend.

My Fourth task
''Record what you are planning on doing for the team during the final weekend of project work. ''

Summary of actual work over fourth weekend
How is what you did different than what you planned?

Week4 Narrative
Tell a detailed story describing what you did for your team over the weekend.

Complete Team Page
Fill out the Team Form (should have already copied the form, created the team page, linked to it and started filling it out).

title: User:Jromanch0088/enes100/My Work Heli3


text: Template:WOTBlock

title: Template:WOTBlock


text:
Template:WOTBlock/doc

This template is used when users add to many links to sites that have a poor reputation according to WOT. Syntax:

title: Template:WOTBlock/doc


text:
University of Florida/Egm4313/s12.team11.gooding.k/R7

Scalar Product
$$=\int_a^bf(x)g(x) \ dx\!$$

$$=\int_{-2}^{10}x\cos(x) \ dx\!$$

Using integration by parts;

$$=[x\sin(x)+\cos(x)]_{-2}^{10} $$

$$=-7.68\!$$

Magnitude
$$\| f \|=^{1/2}=\int_{a}^{b} f^2(x) \ dx\!$$

$$=\int_{-2}^{10} [\cos(x)]^2 \ dx\!$$

$$=[.5(x+\sin(x)\cos(x)|_{-2}^{10}]^{1/2}$$

$$\| f \| =2.457\!$$

$$\| g \|=\int_{a}^{b} g^2(x) \ dx\!$$

$$=\int_{-2}^{10}x^2 \ dx $$ $$=[x^{3}/3]_{-2}^{10}$$

$$\| g \| =\frac{1008}{3}\!$$

Angle Between Functions
$$cos(\theta)=\frac{}{\| f \| \| g \|}\!$$

$$cos(\theta)=\frac{-7.68}{\frac{1008}{3}(2.457)}$$

$$\theta=89.47$$ The two functions are nearly orthogonal.


text:
User:FrequentIntenseMatureSuggestiveThemes

This account is locked.

Hey everyone! I'm really interested in Wikimedia Foundation. I wish I could hack WMF, but such a hack would be illegal. Anyway I do not like to hack Wikimedia because WikiVERSITY is all the place I need to become a custodian. Thank you.