text:
UTPA STEM/CBI Courses/Materials/Material Properties

Course Title: Material Properties

Lecture Topic: Nanomaterials

Instructor: Dr. Kamal Sarkar

Institution:UTPA

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Understand behaviors of materials at the "nano" level. "Nano" is a dimension that is a billionth of a meter. Billion is real big numbr, like there are six and a half billion people in the world. If you reduce the size of the earth by a billion times, it will become the size of a soccer ball. If you do reduce it agian by billion times, it will become the size of a "Bucky Ball", one of the famous carbon nanomaterial.
 * Material behavior is significantly different in the nano level and significantly different from their "bulk" cousins. Example, a typical rope made by,say carbon nanofibers, can stop a 747 jet!
 * Nanomaterials have interesting properties that are not found in common bulk materials. Example, melting point of gold nanoparticles depend on size!

 * Sub Objectives- The objectives will require that students be able to: Why nanomaterials behave differently?!
 * Bulk properties of materials are controlled impurities, defects, etc. In nanomaterials most of these defects and impurities do not exist because of sheer size.  Typical defects are in the size of microns.  Since defects are significantly larger than nanomaterials, they are typically extremely pure.  As a result, their strengths increase significantly and behave diffrently.
 * Another interesting aspect of nanomaterials is the increase in surface by several orders of magnitude. As a result, any propery that depends on surface area increases by orders of magnitude. Solubility is a good example. Catalytic behavior is another one. These properties increases by several orders of magnitude.

 * Difficulties- Students may have difficulty:
 * Understanding the size of a nanometer. How small is a nanometer?
 * They understand millimeter and probably micron size. One millimeter is 1,000 microns. Understanding hunderds of micron ie tenths of a millimeter is conceivable. Beyond that is difficult to fathom.

 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
 * Our hair is about 50 microns. To get 50 nm (nanometer) you have to divide the hair to thousand pieces to make each piece 50 nm. (Talk about splitting hairs!)
 * To understand the consequence of size increase, let's do a thought experiment. If you take a palm size sugar crystal and drop it in a bucket of water, it will take days to dissolve. Take the same crystal and grind it into small grains, it will take, may be an hour, to dissolve.  If we could make nano-sugar, the whole thing will dissolve in seconds.

Model of Knowledge

 * Concept Map
 * Developing understanding of how small is small. Edinburg is  samll town in Texas and students are familiar with it.  UT Panam is a building in the city of Edinburg. Students have a pretty good idea about it because they go through different parts of the univeristy on a daily basis. Engineering is a relatively small building in it. Class room is a fraction of the building. Cell phone of a student is a tiny equipment in the class room. Cell phone has lots of chips in it. Each chip has hundreds of electrical components (say, resistors) in it. Now consider a resistor relative to the city of Edinburg. Current through a resistor or power needed for a chip is orders of magnitude relative to the power needed for the city of Edinburg.  Similarly, nanomaterials are orders of magnitude smaller compared to its cousin bulk material.

 * Content Priorities
 * Enduring Understanding
 * Small is different!
 * Problems of city of Edinburg is fundamentally different from the defects in chip or resistor! Good thing about problems of big things is that you can see it. Say a building lost its power supply and there is no electricity in the building. You cannot see the defects in a chip or resistor. You cannot see them.  You have to use different tools to "measure" the defects to fix it.  Therefore, problem solving tools and techniques will be fundamentally different.

Size is different. Our hair is 50 microns. Smallest thing you can see is 10 microns. Anything smaller than that cannot be seen without magnification. Spider web is one of the most common stuff we have seen that is closest to nanofibers. If you can see under a powerful microscope (say electron microscope), you could see some nanofibers. At such a small size the material behavior also changes dramatically. Color of silver nanoparticles changes with size. Inherently, nanofibers are significantly stronger than their "bulk" cousins because nanofibers are too small to have defects and hence significantly stronger.
 * Important to Do and Know
 * Small is different!
 * Worth Being Familiar with
 * Nanomaterials are a new class of materials that have dramatically different behaviors than commonly available bulk materials. As a result, they have important new applications. Since nanomterials have significantly higher surface area and hence significantly increased solubility (in water), they can have potential application as a carrier for drugs that are typically insoluble in water. Important research is going on to use nanomaterials as a carrier of drugs. One imortant benefit of such an application is dramatic reduction in side effects of the carrier of the drug, typically, a lipid (castor oil, as an example). Since nausea, lack of appetite, weight loss, loss of hair are typical side effects of typical cancer drugs, nanofibers can potentially remove those side effects.

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Identify methods of making nanomaterials.
 * Find out few nanomaterials that are commonly available.
 * Homework (individual)
 * Identify two nanomaterials of your interest and compare their physical properties.

 * Summative Assessment
 * Write a reoprt on application of biologically active materials that are commonly used for regeneration of bone tissue.

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * Understand the
 * What are nanomaterials?
 * Why they are different from bulk materials? Identify few selected applications of nanomaterials.
 * Google by identifying key words like nano, electrospinning, micron, electron microscope, etc.
 * Research on application of nanomaterials for biomedical applications

THE CHALLENGE

How small small can be?

GENERATE IDEAS

What is small? Relative or absolute? How we measure small? Just seeing? Or with Microscope? How powerful microscopes can be? How small can we see with electron microscope? Bugs? Bacterias? Large molecules? Atoms?! Electrons?!!!

MULTIPLE PERSPECTIVES

Small bugs. Spider webs? Optical microscope. Microscope. Google images.

RESEARCH & REVISE Google image, electron microscope, nanofibers, gold nanoparticles, bacteria, cells, ECM (Extracellualr matrix), nanopores in cell, Ion channels,...

TEST YOUR METTLE

Identify a biologically active nanomaterial and see how how many research articles have bee published on that nanomaterial in last five years.

GO PUBLIC

Instructor will discuss these questions with the the students both as individuals & groups.

Pre-Lesson Quiz

 * 1) What is nano?
 * 2) What is a nanomaterial?
 * 3) Is there a difference between gold powder and gold nanoparticle?
 * 4) Does size matter?
 * 5) Which is more easily dissolved? Sugar crystal? Granulated sugars from the same crystal? Why?
 * 6) What is size of your hair?
 * 7) What is the smallest size you can see with the naked eye?

Test Your Mettle Quiz

 * 1) What is electrospinning?
 * 2) What are the advantages of nanomaterials?
 * 3) What specific characteristic of nanomaterials you can use for biomedical applications?
 * 4) What characteristics of nanomaterials we can take advantage in the next five years?
 * 5) "There is plenty of room at the bottom." Who said this? (He is considered the father of nanotechnology.)
 * 6) Explain: "There is plenty of room at the bottom."
 * 7) Can you think of a strategy to deliver drug to a cancer cell?


text:
UTPA STEM/CBI Courses/Algebra/Right Triangle Problems

Course Title: Intermediate Algebra

Lecture Topic: Right Triangle Problems

Instructor: Rommel Garza

Institution: South Texas College

Backwards Design
Course Objectives

 * Primary Objectives- By the next class period students will be able to:
 * Identify a Right Triangle problem
 * Setup an equation to solve the Right Triangle problem
 * Solve a Right Triangle problem

 * Sub Objectives- The objectives will require that students be able to:
 * Set up real world problems involving radical equations.
 * Solve Radical Equations.

 * Difficulties- Students may have difficulty:
 * Recall the formula needed for Right Triangle Problems, Pythagorean Theorem a2+b2=c2
 * Set up the radical equation
 * Finding exact answers to radicals
 * Finding approximate answers to radicals
 * Rounding numbers to the nearest tenths, hundredths, etc...

 * Real-World Contexts- A variety of real world problems translate into right triangle problems. There are many ways students can use this material in the real-world, such as:
 * Determining the height of buildings, height of trees, height of an antenna etc.
 * Determining the distance between two points
 * Builders laying the foundation for the corners of a building

Model of Knowledge

 * Concept Map
 * To accurately make a 90 degree angle using Pythagorean Theorem

 * Content Priorities
 * Enduring Understanding
 * Solving real life application problems that require radical equations
 * Important to Do and Know
 * Simplifying radicals
 * Approximating radicals
 * Worth Being Familiar with
 * Pythagorean Theorem
 * Names of the sides of a right triangle

Assessment of Learning

 * Formative Assessment
 * In Class (groups)
 * Students work in groups on selected right triangle problems and present it to the entire class
 * Homework (individual)
 * Students work on assigned problems and bring the difficulties to the next class
 * Summative Assessment
 * In class quiz over the lesson

Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
 * Identify radical equations
 * Set up application problems involving radical equations
 * Solve Radical Equations and applications.
 * Identify a right triangle problem
 * Use the Pythagorean theorem to solve the right triangle problem
 * Solve the radical equation for a right triangle problem

THE CHALLENGE

STC will be hosting a women's fast pitch softball game. You and your team members have been asked to use their multi-purpose sports field and set up the bases for the softball diamond. You are limited to the use of rope and a 100 ft measurement tape.

GENERATE IDEAS

How would we be able to find solutions for this type of problem?

MULTIPLE PERSPECTIVES

 * Research surveying
 * Pythagorean Theorem
 * Radicals

RESEARCH & REVISE

Gather information about a women's fast pitch softball diamond

TEST YOUR METTLE

GO PUBLIC
 * Do a smaller scale experiment and see if we can relate the solution to a bigger scale.
 * Write a procedure for laying out your own women's fast pitch softball diamond.

Share & present their procedure for laying out a women's fast pitch softball diamond to the entire class.

Pre-Lesson Quiz

 * 1) What is the relationship between the sides of a right triangle?
 * 2) If you know the length of two sides of a right triangle. What is the exact and approximate length of the third side?

Test Your Mettle Quiz

 * 1) What is the approximate and exact length of the diagonal of a regulation soccer field?

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


text:
User:Crusader8389

I'm a mathematics major doing research in chemistry (undergraduate).

title: User:Crusader8389


text:
UTPA STEM/CBI Courses/Calculus/Calculus I

The following cycles are currently in classroom testing:

 * Legacy Cycles
 * lead designer: Will Watkins
 * Graphing
 * lead designer: Will Watkins
 * Derivative Algorithm
 * lead designer: Will Watkins
 * Differentiation and Derivatives
 * lead designer: Tsay
 * WFFs, Algebraic Expressions, and Derivatives
 * lead designer: Will Watkins
 * Limits
 * lead designer: Huaien Li
 * Why Derivatives Work
 * lead designer: Will Watkins
 * Kidnapper's Headquarters
 * lead designer: Will Watkins
 * Car Trip
 * lead designer: Will Watkins

Partially funded by U.S. Department of Education Grant #ED-grants-051308-002. University of Texas-Pan American, Edinburg, TX

Dr. Will Watkins is using these cycles in a current Calculus I course.

Report
Summer 2009

Mathematics

LC CBI Calculus Course Design Team

partially funded by U.S. Department of Education Grant #ED-grants-051308-002

Team Members:
 * Dumitru Caruntu (Mechanical Engineering/UTPA)
 * Huaien Li (Mathematics/STC)
 * Jenq-Jong Tsay (Mathematics/UTPA)
 * Will Watkins (Mathematics/UTPA)

Abstract A CBI module is defined (by the Calculus LC CBI Course Design Team) to be complete once it is fully developed as a webpage. This report discusses the mechanisms, processes and rational used by the Team to produce complete CBI modules. Finally a list shows the current status of each module being developed. Appendices contain supporting documentation.

Introduction The Calculus LC CBI Course Design Team (CBI Calculus Team) is one of five design teams partially funded by U.S. Department of Education Grant #ED-grants-051308-002. The grant provided a number of full day workshops teaching the teams Challenge Based Instruction (CBI) concepts and beginning the design process. After completing the workshops, the CBI Calculus Team meet every Tuesday and Thursday beginning in May and then throughout June and July. Emails, an online forum, BlackBoard, WebWork, Google Docs, and a webpage server are used to enhance communication between CBI Calculus Team members.

Early on it was clear that the CBI Calculus Team has a spectrum of ideas regarding what could and should be accomplished by a CBI module. The team members bring various perspectives to the table. The team includes an engineer, a specialist in mathematics education, and one mathematician from STC and another from UTPA. All members of the team have experience teaching calculus.

The Team began by identifying the objectives and concepts to be met in the Calculus I course. Syllabi from UTPA, STC and other institutions were reviewed. The textbooks used at STC and UTPA are both made available to members of the Team. The objectives for the course are divided into four major concept areas and each member has accepted the challenge of creating modules for one of the concepts areas. Although an individual member is responsible for each concept area, Team members feel free to contribute ideas and module development in any of the areas. Drafts of modules are distributed through emails, posted online, and printed copies are reviewed at the Tuesday/Thursday meetings. Modules that have been formulated as webpages are available on a server for the Team members review. At the sametime the modules are being reviewed, the Team is formulating strategies for evaluating them (see appendices for evaluation documents).

Team Collaboration The following mechanisms are used to facilitate collaboration amongst Team members.

Tuesday/Thursday meetings. These regularly scheduled face-to-face meetings provide the basis of our collaboration. Each of us feel a responsibility to report progress at the meeting, we give encouragement and critiques about the progress, and future directions evolve through the discussion. We agreed early on to bring printed reports to the meetings. Most recent versions of these reports are attached as appendices to this report. Online Forum. In our earliest meetings we considered using an online forum as a place to post our progress and carry out our discussions. A sub-forum entitled “CBI (Challenge Based Instruction)” was created in the existing http://math.utpa.edu/forum. At first, the forum was open to anyone on the World Wide Web. Seven discussion topics were posted and then was abandoned by the Team. Although the forum did not catch the interest of the CBI Calculus Team, it did attract significant world wide interest. Logs from the forum show that one of the topics was viewed 66,299 times, and the topic viewed least often had 27,875 hits. Within the topic posts were 5 PDF files, one of which was downloaded 12,251 times. The PDF file downloaded the least number of times was downloaded 5,920 times. The math forum has since been password protected. (See the Appendices for the PDF files posted to the Forum.) The CBI Calculus Team worked best with printed reports brought to the Tuesday/Thursday meetings. BlackBoard. BlackBoard became the depository for our draft documents. All four team members are familiar with BlackBoard and have used it at one time or another. We asked the Center for Distance Learning to create and empty BlackBoard shell and grant each of us designer priviledges. We then created a folder for each of us where we have deposited drafts. Email. Team members regularly email each other. Reports are made available through emails prior to the Tuesday/Thursday meetings. Email is also used to discussing conflicts in meeting times. Discussions are seldom done through emal. Google Docs. The Team maintains two documents on Google Docs. One is a spreadsheet indicating the progress being made on individual modules. The other is a list of resources including contact information for people on campus (who can help us make videos, who is our BlackBoard IT person, etc.) and webpages of interest (Blackboard, WebWork, Google Docs, VaNTH*ERC, etc.). WebPage Server. The Mathematics Department has provided a folder where Team members can sftp the webpage version of their modules. A list of available modules can be seen at http://www.math.utpa.edu/cbi/watkins/index.html (anything else we should put here?)

Progress on Modules When our Team began we shared a spectrum of ideas regarding what a CBI module is and what objectives and expectations are appropriate. On one extreme:

Definition One “A CBI module begins with a problem that is beyond the reach of the students. As they progress through the module new concept and skills are taught in such a way that the student sees how they can be used to solve the problem.” (An example is Micky’s acceleration concept draft.)

On the other extreme

Definition Two “A CBI module begins with challenges that are accessible to the student. By completing the module the student obtains experience that is referenced and used as a basis for developing and defining key concepts in future modules and lectures.” (An example is Will’s graphing concept draft.)

Drafts of new modules appear to fit at different points on the spectrum. While we write the modules, we are developing and rewriting our rubrics for defining and evaluating. Our understanding of module continues to mature as the modules are developed, and hence the our definition and process of evaluation is also maturing.

Our process for developing a module begins when a Team member prepares a concept draft including suggestions for each of the six CBI components (Challenges, Develop Ideas, Multiple Perspectives, Research and Revise, Test your Mettle, and Go Public). That written concept draft is discussed by the Team and the individual member begins to “flesh out” the ideas, often rewriting the concept draft a number of times (current concept drafts are in the Appendices). At some point, development of the module is turned over to webpage design. At that point are rewrites are done in the webpage—meaning the final webpage may differ from the concept draft.

List of Appendices
Appendix A: Reports Posted on Forum

 * The Study of Speed: Inquiry into the Nature of Motion (12,251 downloads)
 * UTPA Mathematics Department Colloquium Report (5,920 downloads)
 * STEM Learning Community for Prepared Freshmen (5,924 downloads)
 * Evaluating Mathematics Courses in the Core (6,938 downloads)
 * Computers in the Tutoring Labs (6,935 downloads)

Appendix B: Google Documents
 * CBI Resources
 * CBI Calculus Project Development

Appendix C: Most Recent Concept Drafts
 * Challenge Based Instruction for Limits and Continuity, Huaien Li, July 1, 2009
 * Challenge Based Instruction Calculus I (Objectives), Dumitru Caruntu, June 8-23, 2009
 * Rules for Finding Derivatives of Elementary Functions, Will Watkins, June 22, 2009
 * CBI Discussion of Limits, Will Watkins, June 17, 2009
 * Math 1401 Graphing Module, Will Watkins, (undated)
 * CBI, The Slingshot, Will Watkins, April 2, 2009
 * CBI, The Car Trip, Will Watkins, June 16, 2009
 * Calculus Knowledge Base, Will Watkins, (undated)
 * VaNTH-ERC Workshop, Objectives, Will Watkins, March 6, 2009
 * CBI, Calculus I Objectives, Dumitru Caruntu, June 8-23
 * CBI, Car Racing Module, Dumitru Caruntu, June 23-30, 2009
 * CBI, Area fit Module, Dumitru Caruntu, July 1-7
 * CBI, Inertial Navigation Module, Dumitru Caruntu, July 7-15, 2009
 * CBI, Beam Bend Module, Dumitru Caruntu, July 15-23

Appendix D: Rubrics for Evaluating Modules
 * CBI Star-Legacy Module Checklist, June 22, 2009
 * CBI Module Evaluations, Will Watkins (undated)

Appendix E: Webpages

http://www.math.utpa.edu/cbi/watkins/index.html


text:
User:NelsonRhiannon5577

About me
Hello! My name is Rhiannon Nelson. My username is actully my real name switched up backwards. I wouldv'e used "Mother Goose" but I think that name would be tooken. I'm a 16 year old girl interested in parenting since my mom doesn't let me babysit. Ilove pizza.

My Name Is Rhiannon! Don't Forget! It's like a set. Education nation! Utation!

title: User:NelsonRhiannon5577


text:
User talk:NelsonRhiannon5577

 Hello and Welcome to Wikiversity NelsonRhiannon5577! You can contact us with questions at the colloquium or me personally when you need help. Please remember to sign and date your finished comments when participating in discussions. The signature icon above the edit window makes it simple. All users are expected to abide by our Privacy, Civility, and the Terms of Use policies 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.

 * Enable VisualEditor under Beta settings to make article editing easier.
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You do not 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! --Dave Braunschweig (discuss • contribs) 00:26, 10 January 2022 (UTC)

Welcome to my talk page! My talk page is used to discuss problems or to give me a concern/good message. I expect that you respect my talk page and that you do not post any rude content, crude content, or bad language as even If i'm 16! I do not use bad language. But one more thing about my talk page! This is a talk page which you can use to discuss User:NelsonRhiannon5577. Please remember to sign and timestamp your posts by typing four tildes (NelsonRhiannon5577 20:21, 16 April 2010 (UTC)). Alternatively, use the icon. What I mean is that when you are done with your message, sign your username initials.

What is wikiversity
What is Wikiversity and how do you use it? I do not know how to use it as I am a new user and I need some help. Whoever helps will get a surprise. Thank you! --NelsonRhiannon5577 20:24, 16 April 2010 (UTC)

 * See What is Wikiversity? -- Dave Braunschweig (discuss • contribs) 00:26, 10 January 2022 (UTC)

title: User talk:NelsonRhiannon5577


text:
User talk:La la means I love you

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

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

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

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 20:24, 16 April 2010 (UTC)

title: User talk:La la means I love you


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User talk:Tacs~enwikiversity

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

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

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

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 23:32, 16 April 2010 (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 Tacs. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Tacs~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 23:44, 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) 06:23, 19 April 2015 (UTC)

title: User talk:Tacs~enwikiversity


text:
User talk:Audiosmurf

 Hello Audiosmurf, 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.
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 * Find out about research activities on 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! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 23:56, 16 April 2010 (UTC)

Thanks
Thanks for cleaning up and doing some patrolling. I deleted the "Doody" page. Ottava Rima (talk) 23:57, 16 April 2010 (UTC)

title: User talk:Audiosmurf


text:
Talk:Virtual reality

A page discussing the role that virtual reality may play for wikiversity
I am new to this wikiversity, and I await feedback. My intention is mostly to get these ideas out there since I believe that the future of virtual learning is, more than just within reach, hitting us on the nose. Tesseract2

title: Talk:Virtual reality


text:
Virtual reality

The human brain has evolved to learn most effectively by actively engaging its environment and using all its senses for feedback. Thus it is virtual reality (or virtual simulation) that provides our greatest hope of tapping into human learning potential. The future of learning may indeed be virtual worlds, built to teach and practice anything a human would wish to know. Creating enough virtual worlds to represent the massive Wikipedia databases could only be possible with the "anyone can contribute" philosophy that made Wikipedia so successful. Each section here attempts to address the various challenges faced by the world community if we ever hope to establish Wikiversity's WikiWorlds project as THE way to learn.

The Hardware
The hardware needs to be cheap and compact enough to be easily brought into people's homes. Ideally, all the components could fit into a package the size of the printer box. Luckily the necessary hardware already exists.
 * Video Goggles/Glasses, rather than a large and obtrusive display
 * Input Devices that are intuitive and engaging . Note that the motion detection technology in these devices could be used to also track head movements, an important part of allowing the user to turn their head and have the display change. Note the PS3 move may need to be modified to allow input from TWO cameras since virtual reality users will often rotate in their chair away from one camera (see next point).
 * Other older existing technologies, including headphones, a microphone (for voice commands and typing), and even a simple swivel chair (to allow the user to rotate in all directions and see all around the virtual world). Of course, even these simple technologies come in varieties especially conducive to VR (for example, this chair)

The Virtual Worlds
A database of virtual learning worlds. Obviously a wiki community could provide all of the content, and so the real challenge is to program a "world builder" that is intuitive and fun enough for the community to use. One source of inspiration may be the level creator in Little Big Planet, a title for the Sony PS3.

Learning Principles
Virtual Worlds should focus on using well-established learning principles:
 * Free recall is a better way to review than recognition (e.g. short answer versus multiple choice)

Learning Tasks

 * (3D Modelling) Explore the digital tools for creating virtual reality in learning resource about 3D Modelling.
 * (3D Objects) A virtual world consists of 3D objects that are placed in the virtual world. A forest that consists of only one type of trees (all trees look the same) provides unrealistic user experience (UX) of the virtual world. Explore concepts of randomizations of objects and surfaces e.g. in Blender.
 * (Random Colors) Youtube Video Blender applied on random leaf color or create the [visualisation of a large forest]
 * (Random Size and Location) Blender Tutorial: Cut Random Size And Positioned Circular Holes In A Sphere

title: Virtual reality


text:
User talk:Jonah~enwikiversity

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

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

 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
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title: User talk:Jonah~enwikiversity


text:
User:Shaunvogels2010

Shaun Vogels
Bachelor of Education (Secondary-Science) ACU 1992 Teaching Experience 19 years

title: User:Shaunvogels2010


text:
BCP/Lathyrus vernus

Lathyrus vernus

title: BCP/Lathyrus vernus


text:
BCP/Lathyrus vernus/Logs

Recent Logs

 * Anna reg 12:36, 17 April 2010 (UTC)

title: BCP/Lathyrus vernus/Logs


text:
User talk:Aw1387

 Hello Aw1387, and welcome to Wikiversity! If you need help, feel free to visit my talk page, or contact us and ask questions. After you leave a comment on a talk page, remember to sign and date; it helps everyone follow the threads of the discussion. The signature icon in the edit window makes it simple. To get started, you may

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User talk:Shaunvogels2010

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User talk:Tesseract2

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User:Swapnil.sahoo~enwikiversity

"The individual has always had to struggle to keep from being overwhelmed by the tribe. If you try it, you will be lonely often, and sometimes frightened. But no price is too high to pay for the privilege of owning yourself" -- Hamare ek German philosopher bhai (Friedrich Nietzsche).There is a fine line that separates experiencing the biggest high of your life and the feeling of absolute worthlessness when your dreams are just a moment before they enter the domain of reality where they will fate up as "make" or more commonly "break" .Well,I am not really the ace at academics and have had my dark ages(hopefully it's over). I am the guy who has lots of wishes and desires.Sometimes I feel I am working hard to achieve this while rest of time I am still way below my potential.Hope this life's puzzles dovetail soon!!!This is but a small snapshot of the roller coaster ride that I am about to take. Well,"As long as one keeps searching, the answers come."

title: User:Swapnil.sahoo~enwikiversity


text:
User:Egm6341.s10.Team4.roni/HW7/7.4

= Problem 4: Discrete Population Dynamics - Logistic Map - Chaotic System - Period Doubling =

Given
Class notes and Pages 454-456 King et al 2003 - An Introduction to Chaotic Systems.

Given factor r -represents the growth from generation to the next [[media:Egm6341.s10.mtg39.djvu|39-3]]

Find
Run the given Code to reproduce plots 15.6 and 15.7 in King et al 2003.

Solution
 original Code

 Matlab Code:

Plot 1 shows the results from running the original code

 Modification to the original Code

 Matlab Code:

Plot 2 shows the results from running the modified code

Discussion:

From Plot 2 One can see that when r=4, a small change in the input of the initial x value would give apparently a random nature of solution and divergence after about 50 iterations. The 0 marker in blue are for x=0.1 starting point and the x markers in green are for x=0.1+1e-16. Initially (up to about 50 iterations) the x and o symbols fall one on to of the other (giving same solution) and diverging after about 50 iterations.

Author
Solved and typed by - Egm6341.s10.Team4.roni 18:49, 18 April 2010 (UTC) Proof read by -

title: User:Egm6341.s10.Team4.roni/HW7/7.4


text: File:RP HW 7 4.png

title: File:RP HW 7 4.png


text: File:RP HW 7 4b.png

title: File:RP HW 7 4b.png


text:
User:Egm6341.s10.Team4.roni/HW7/7.10

= Problem 10: Parameterization of an Ellipse =

Given
Result from HW problem 7.9 [[media:Egm6341.s10.mtg42.djvu|42-1]], which is:

$$\displaystyle Eq. (1)  \qquad    \frac{x^2}{a^2}+ \frac{y^2}{b^2}=1 $$

Show
That the arc length dl comes to:

HW 7.10 on slide [[media:Egm6341.s10.mtg42.djvu|42-2]]

$$\displaystyle

Eq. (2) \qquad  dl= \sqrt{dx^2+dy^2} $$

Solution
Geometrically:

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

 * [[Image:RP_HW_7_10c.png]]
 * }.
 * }.
 * }.

Eq. (3) \qquad  dl^2= {dx^2+dy^2} $$

Eq. (4) \qquad  dl=  \sqrt{dx^2+dy^2} $$

and also:

Eq. (5) \qquad  dl =   \left( \sqrt{1+  \left( \frac{dy}{dx}\right)^2} \right) dx

$$

 * {| style="width:20%" border="0"

$$\displaystyle dl= \sqrt{dx^2+dy^2} $$
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |

 * style= |
 * }
 * }

Author
Solved and typed by - Egm6341.s10.Team4.roni 18:50, 18 April 2010 (UTC) Reviewed by -

title: User:Egm6341.s10.Team4.roni/HW7/7.10


text:
User talk:Xiiiamen

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title: User talk:Xiiiamen


text:
User:Sj/random log

April 17 2010
20 random links turned up:

3 deletion 5 cleanup or rename desperately needed 5 bloom clock 1 simplified encyclopedia article

1 good article 1 section of a fascinating monograph Biogeochemical_Selectiveness_of_Cedars_Over_Metamorphic_Rocks_of_the_Escambray_Complex,_Sancti_Spíritus,_Cuba 1 excellent psych tutorial Psychology_102/Tutorials/Sensation_and_perception

1 inexplicable physics page 1 Extraordinary School Project 1 abandoned page about a software project -- QuantLib

title: User:Sj/random log


title: File:Likertq2.png


title: File:Multchoiceq2.png


title: File:Openq2.png


text:
User talk:Dayimichelle

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

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Feel free to leave a message on my talk page if you have any questions or need help. --mikeu talk 07:17, 18 April 2010 (UTC)

title: User talk:Dayimichelle


text: File:Level 1 qtypes.png

title: File:Level 1 qtypes.png


text:
User:Gryphoenix

16, and ready to learn :)

title: User:Gryphoenix


text:
User talk:Zj

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title: User talk:Zj


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User talk:Gryphoenix

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title: User talk:Gryphoenix


title: User:Egm6341.s10.Team2/HW7


text:
University of Florida/Egm6341/s10.Team2/HW7

Statement
Pg.38-4 Show the case of stable growth for Verhulst equation

Author
Egm6341.s10.team2.lee 20:56, 23 April 2010 (UTC)

Statement
P.39-1

Solution
We have Verhulst model or the Logistic equation as P.38-3

$$\dot{x}=\frac{dx}{dt}=rx(1-\frac{x}{x_{max}})$$

Separating variables and integrating we have

$$\int_{x_0}^{x}\frac{x_{max}}{x(x_{max}-x)}dx=\int_{t_0=0}^{t}rdt$$

which can be written as

$$\int_{x_0}^{x}\frac{1}{x}dx+\int_{x_0}^{x}\frac{1}{(x_{max}-x)}dx=\int_{t_0=0}^{t}rdt$$

We get

$$log_e(\frac{x}{x_0})-log_e(\frac{x_{max}-x}{x_{max}-x_0})= r(t-0)$$

$$\frac{x(x_{max}-x_0)}{x_0(x_{max}-x)}=e^{rt}$$

Rearranging we have

$$x=\frac{x_{max}x_0e^{rt}}{x_{max}+x_0(e^{rt}-1)}$$

Author
--Egm6341.s10.team2.niki 12:31, 23 April 2010 (UTC)

===problem 3: Hermite-Simpson Algorithm to solve for the non-linear first order differential equation i.e. Verhulst population growth model on Pg.38-3 ===

Statement
Pg.39-1

Use the Hermit-Simpson Algorithm to integrate the Verhulst population growth model on Pg.38-3:

$$ \frac{\mathrm{d} x}{\mathrm{d} t}= r x\left ( 1-\frac{x}{x_{max}} \right ) $$

Consider the following: $$x_{max}=10 \;\; r=1.2 \;\; t\in \left [ 0,10 \right ] $$ and Case 1: $$\; x_{0}=2$$ Case 2: $$\; x_{0}=7$$

And also plot the two cases using matlab.

Solution
Matlab code

THE PLOT SHOWING THE POPULATION CHANGE W.R.T TIME, HERE VERHULST MODEL IS USED TO COMPUTE THE POPULATION WHERE XO=INITIAL POPULATION=2

THE PLOT SHOWING THE POPULATION CHANGE W.R.T TIME, HERE VERHULST MODEL IS USED TO COMPUTE THE POPULATION WHERE XO=INITIAL POPULATION=7

Author
Solved by--Srikanth Madala (SM)

Statement
Pg.40-1

Produce the diagrams showing the bifurcation diagram for the logistic map and its sensitivity to initial conditions, as shown on figures 15.6 and 15.7, of the book "Differential Equations: Linear,Nonlinear,Ordinary,Partial" by King,Billingham and Otto (Pg.455-456).

Creating Figure 15.6:Bifurcation Diagram
Logistic Map:

$$ x_{n+1} = r x_{n}(1-x_{n}) $$

The Bifurcation Diagram shows the period doubling process of the logistic map. As the constant r increases the period is doubled to 2 periods and then stability is lost which then leads to a doubling of period to 4 and so on.

The plot is as follows:

Matlab Code
Matlab code used to create the graph as outlined in Pg. 455 of King et. al

Creating Figure 15.7: Sensitivity to Initial Conditions
The Following Plot explores the big effect of a small change in the initial conditions. One can note the changes as 'n' becomes larger than 50. The graph was produced for the following Conditions:

$$ r = 4 \qquad 100 iterations \qquad IC1= 0.1 \qquad IC2=0.1+10^{-16}$$

The Following Equation was used to produce the iterations for the graph:

$$ x_{n+1} = r x_{n}(1-x_{n}) $$

Matlab Code
Matlab Code used to produce the aforementioned plot.

Author
--Egm6341.s10.Team2.GV 16:28, 23 April 2010 (UTC)

Statement
Pg.40-2

Solution
Matlab code

THE PLOT SHOWING THE POPULATION CHANGE W.R.T TIME, HERE VERHULST MODEL IS USED TO COMPUTE THE POPULATION WHERE XO=INITIAL POPULATION=2

Author
Solved by--Srikanth Madala (SM)

Statement
Pg.40-3 and Pg.41-1

Solve the following Group of ODE's as they relate to the problem mentioned in the lecture pages mentioned above. The problem is of the motion of an airplane through different maneuvers.

for a vector with the following parameters:

$$ z = [ x, y, V, \gamma ] $$ $$ \dot{z} = [ \dot{x}, \dot{y}, \dot{V}, \dot{gamma}]$$

$$ \dot{x} = Vcos (\gamma) $$

$$ \dot{y} = Vsin( \gamma) $$

$$ \dot{v} = (\frac{T-D}{m}cos( \alpha) + \frac{L}{m} sin(\alpha) - g sin(\gamma) $$

$$ \dot{\gamma} = (\frac{T-D}{mV}sin( \alpha) + \frac{L}{mV} cos(\alpha) - \frac{g}{V} cos(\gamma) $$

Initial Conditions are as follows:

$$ \gamma_{0} = 0 \quad degrees $$

$$ V_{0} = 272 \quad meters/sec $$

$$ x_{0} = 0 \quad meters $$

$$ y_{0} = 0 \quad meters $$

The Physical Modeling Parameters to be used are

$$ m = 1005 \quad Kg $$ $$ g = 9.81 \quad m/sec^{2} $$ $$ Sref = 0.3376 \quad m^{2} $$ $$ A1 = -1.9431 \qquad A2=-0.1499 \qquad A3=0.2359 $$ $$ B1=21.9 \qquad B2= 0 $$ $$ C1= 3.312 x 10^{-9} \quad Kgm^{-5} $$ $$ C2= -1.142x 10^{-4} \quad Kgm^{-4} $$ $$ C3 =1.1224 \quad Kgm^{-3} $$

$$ \rho = C1y^{2} + C2y + C3 $$ $$ L = \frac{1}{2}C_{l} \rho V^{2} Sref $$ $$ C_{l} = B1 \alpha + B2 $$ $$ D = \frac{1}{2}C_{d}\rho V^{2} Sref $$ $$ C_{d} = A1 \alpha^{2} + A2\alpha + A3 $$

The Inputs are defined as follows:

Input T:

for $$ 0\leq t<27 seconds = 6000N $$ for $$ 27\leq t<33 seconds = 1000N $$ for $$ 33\leq t \leq 40 seconds = 6000N $$

Input $$ \alpha $$:

for $$ 0\leq t<21 seconds = 0.03 $$ for $$ 21\leq t<27 seconds = 0.09 to 0.13 $$ as it varies linearly for $$ 27\leq t<33 seconds = -0.13 to -0.2 $$ as it varies linearly for $$ 33\leq t \leq 40 seconds = -0.2 to -0.13 $$ as it varies linearly

Defining the Inputs
The first part of the solution is to create a function that will calculate the thrust and angle of a attack at a particular time. The following Matlab Codes were used:

Thrust:

Angle of Attack:

Technique used to solve the problem
The overall goal is to find a solution for each of the states being considered (x,y,V,gamma).

From P 36.3, of the lectures, the following was established using the Hermite-Simpson Algorithm:

$$ Z_{i+1} = z_{i} + \frac{h/2}{3} \left[ f_{i} + 4f(g(z_{i},z_{i+1})) + f(z_{i+1}) \right] \qquad \qquad EQUATION 1$$

The Following is recognized and derived as:

$$ g(z_{i},z_{i+1}) = \frac{1}{2}(z_{i}+ z_{i+1}) + \frac{h}{8}\left[(f(z_{i}) - f(z_{i+1})\right] \qquad \qquad EQUATION 2$$

It is now necessary to define the following using the previously mentioned Eq. 1:

$$ F(Z_{i+1}) = 0 = Z_{i+1} - z_{i} - \frac{h/2}{3} \left[ f_{i} + 4f(g(z_{i},z_{i+1})) + f(z_{i+1}) \right] \qquad \qquad EQUATION 3$$

The next step is to apply the Newton Raphson Method to solve the function $$ F(Z_{i+1}) = 0 $$

A Matlab Algorithm is used to apply the Newton Raphson Method as follows:

Newton Raphson Method
Function for obtaining $$ f(z) $$

Function for obtaining $$ df(z) $$

Function for using the Newton Raphson Operations until an error threshold is reached

This Matlab code was developed using the published code of Team 3 as part of their HW 7 Report( HW 7: Team 3)

Results of Methods Used and comparison to ODE45
Plot of Horizontal Position Vs. Time

Plot of Vertical Position(Height) Vs. Time

Plot of Velocity Vs. Time

Plot of Gamma Vs. Time

From each of these plots it can be concluded that the combination of the Hermite Simpson Algorith and the Newton Raphson Method is an effective way to solve the set of ordinary differential equations without much error, as compared to ODE45 solver of Matlab. The downside to this method is that it takes a high amount of computational resources and time.

Author
--Egm6341.s10.Team2.GV 23:41, 27 April 2010 (UTC)

Statement
Integrate the Logistic equation using the inconsistent Trapezoidal-Simpson approximation $$x_{i+1/2}=x_i + x_{i+1}$$

Pg.41-2

Solution
The Matlab code is a slight alteration of the code used to integrate above.

%Matlab code to integrate the the Verhulst population growth model clear; clc; xmax=10; r=1.2; t=0:0.1:10; h=0.1; %time step size syms x;  syms x11; f=r*x*(1-(x/xmax)); %case 1: when x0=2 for i=1:1:100 x1(1)=2; f1=subs(f,x,x1(i)); f11=subs(f,x,x11); x1half=((1/2)*(x1+x11))%Trapezoidal_simpson approxiamtion; f1half=subs(f,x,x1half); F=x1(i)-x11+(h/6)*(f1+f11+(4*f1half)); guessx11(i)=x1(i); dummy=1; while dummy==1 newx11(i)=guessx11(i)-((1/(subs(diff(F(i)),x11,guessx11(i))))*(subs(F(i),x11,guessx11(i)))); if double(abs(newx11(i)-guessx11(i)))<=10^(-6) x1(i+1)=newx11(i); dummy=0; break; else guessx11(i)=newx11(i); dummy=1; end end end plot(t,x1);

for $$x_0=2$$

for $$x_0=7$$

Author
--Egm6341.s10.team2.niki 20:33, 28 April 2010 (UTC)

Statement
Pg.42-1

Statement
Pg.42-1

Given the parameterization for an ellipse as follows for the x and y coordinates, Eliminate 't' as a parameter.

$$ x = a \cos(t) \qquad \qquad y = b \sin(t) $$

Solution
$$ x = a \cos(t) $$ $$ x^{2} = a^{2} \cos^{2}(t) $$ $$ y = b \sin(t) $$ $$ y^{2} = b^{2} \sin^{2}(t) $$

$$ \frac{x^{2}}{a^{2}} = \cos^{2}(t) $$ $$ \frac{y^{2}}{b^{2}} = \sin^{2}(t) $$

$$ \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = \cos^{2}(t) + \sin^{2}(t) = 1 $$ At this point t can be eliminated as a parameter.

Author
--Egm6341.s10.Team2.GV 17:51, 23 April 2010 (UTC)

Statement
Pg.42-2

Statement
Pg.42-2 To show the integral for elliptical circumference

Author
Egm6341.s10.team2.lee 20:58, 23 April 2010 (UTC)

Statement
Pg.42-2

Statement
Pg.42-2

To show that $$I=\int_{-1}^{+1}f(x)dx = \int_{0}^{\pi}f(cos\theta)sin\theta d\theta$$

Solution
We have the integral as

$$I=\int_{-1}^{+1}f(x)dx$$.

Using the transformation $$\displaystyle{x=cos\theta}$$ we have

$$\displaystyle{f(x)=f(cos\theta)}$$

$$\displaystyle{dx=-sin\theta d\theta}$$

and using the inverse transformation the limits $$\displaystyle{[-1,1]}$$ can be written $$\displaystyle{[\pi,0]}$$

thus we have

$$I=\int_{-1}^{+1}f(x)dx = \int_{\pi}^{0}-f(cos\theta)sin\theta d\theta=\int_{0}^{\pi}f(cos\theta)sin\theta d\theta$$

Author
--Egm6341.s10.team2.niki 18:47, 23 April 2010 (UTC)

Statement
Pg.42-3

We have the cosine series expressed as $$f(cos\theta )=\frac{a_0}{2}+\sum_{k=1}^{\infty }a_k cos(k\theta)$$, we need to express teh constants $$a_k$$ as

$$a_k=\frac{2}{\pi }\int_{0}^{\pi}f(cos\theta)cos(k\theta)d\theta$$

Solution
We have the given expression for the cosine series as

$$f(cos\theta )=\frac{a_0}{2}+\sum_{k=1}^{\infty }a_k cos(k\theta)$$

multiplying both sides by $$cos(m\theta)$$ where k is not the same as m and integrating we get,

$$\int_{0}^{2\pi}f(cos\theta )(cos(m\theta))=\int_{0}^{2\pi}\frac{a_0cos(m\theta)}{2}+\int_{0}^{2\pi}\sum_{k=1}^{\infty }a_k cos(k\theta)cos(m\theta)$$

Using the property of orthogonality we know that $$\int_{0}^{2\pi}a_k cos(k\theta)cos(m\theta)$$ exists only when k = m i.e

$$\int_{0}^{2\pi}f(cos\theta )(cos(k\theta))d\theta=\frac{a_0}{2}\int_{0}^{2\pi}cos(m\theta)d\theta+a_k\int_{0}^{2\pi} cos^2(k\theta)d\theta                                    $$

wkt,

$$\int_{0}^{2\pi}cos(m\theta)d\theta=0$$ and

$$\int_{0}^{2\pi}cos^2(k\theta)d\theta = \frac{2\pi-0}{2}=\pi$$

Thus we have by substituting and rearranging terms,

$$a_k=\frac{2}{\pi }\int_{0}^{\pi}f(cos\theta)cos(k\theta)d\theta$$

Author
--Egm6341.s10.team2.niki 14:43, 23 April 2010 (UTC)

Statement
Pg.42-3 Simplification of Clenshaw-Curtis Quadrature Rule

Signatures
solutions of problems 2,7,13,14 --Egm6341.s10.team2.niki 18:48, 23 April 2010 (UTC)

solutions of problems 4,6, 9 --Egm6341.s10.Team2.GV 20:58, 23 April 2010 (UTC)

solutions of problems 1,11,15 --Egm6341.s10.team2.lee 22:47, 23 April 2010 (UTC)


text:
University of Florida/Egm6341/s10.team2.niki/HW7

Statement
P.39-1

Solution
We have Verhulst model or the Logistic equation as P.38-3

$$\dot{x}=\frac{dx}{dt}=rx(1-\frac{x}{x_{max}})$$

Separating variables and integrating we have

$$\int_{x_0}^{x}\frac{x_{max}}{x(x_{max}-x)}dx=\int_{t_0=0}^{t}rdt$$

which can be written as

$$\int_{x_0}^{x}\frac{1}{x}dx+\int_{x_0}^{x}\frac{1}{(x_{max}-x)}dx=\int_{t_0=0}^{t}rdt$$

We get

$$log_e(\frac{x}{x_0})-log_e(\frac{x_{max}-x}{x_{max}-x_0})= r(t-0)$$

$$\frac{x(x_{max}-x_0)}{x_0(x_{max}-x)}=e^{rt}$$

Rearranging we have

$$x=\frac{x_{max}x_0e^{rt}}{x_{max}+x_0(e^{rt}-1)}$$

Statement
We have the cosine series expressed as $$f(cos\theta )=\frac{a_0}{2}+\sum_{k=1}^{\infty }a_k cos(k\theta)$$, we need to express teh constants $$a_k$$ as

$$a_k=\frac{2}{\pi }\int_{0}^{\pi}f(cos\theta)cos(k\theta)d\theta$$

Solution
We have the given expression for the cosine series as

$$f(cos\theta )=\frac{a_0}{2}+\sum_{k=1}^{\infty }a_k cos(k\theta)$$

multiplying both sides by $$cos(m\theta)$$ where k is not the same as m and integrating we get,

$$\int_{0}^{2\pi}f(cos\theta )(cos(m\theta))=\int_{0}^{2\pi}\frac{a_0cos(m\theta)}{2}+\int_{0}^{2\pi}\sum_{k=1}^{\infty }a_k cos(k\theta)cos(m\theta)$$

Using the property of orthogonality we know that $$\int_{0}^{2\pi}a_k cos(k\theta)cos(m\theta)$$ exists only when k = m i.e

$$\int_{0}^{2\pi}f(cos\theta )(cos(k\theta))d\theta=\frac{a_0}{2}\int_{0}^{2\pi}cos(m\theta)d\theta+a_k\int_{0}^{2\pi} cos^2(k\theta)d\theta                                    $$

wkt,

$$\int_{0}^{2\pi}cos(m\theta)d\theta=0$$ and

$$\int_{0}^{2\pi}cos^2(k\theta)d\theta = \frac{2\pi-0}{2}=\pi$$

Thus we have by substituting and rearranging terms,

$$a_k=\frac{2}{\pi }\int_{0}^{\pi}f(cos\theta)cos(k\theta)d\theta$$

Author
--Egm6341.s10.team2.niki 14:43, 23 April 2010 (UTC)


text: File:RP HW 7 10c.png

title: File:RP HW 7 10c.png


text:
Transplantation

In the fourth quarter of the 20th century, scientific and technical advances allowed for the first time the use of organ transplantation in the treatment of terminal and incurable diseases.

These scientific advances include:
 * the development of immunosuppressive drugs
 * knowledge of the immune response to transplanted organs and tissues
 * knowledge of the function, molecular structure and gene structure of the major histocompatibility complex (MHC, in humans called HLA)
 * knowledge of the genetics of the MHC (particularly the HLA in humans)

Here we provide background, scientific and technical resources used in the practice of clinical transplantation. These resources include:
 * Transplantation/Haematopoietic Stem Cell
 * Transplantation/Solid Organ
 * Transplantation/The HLA System and HLA Typing
 * Transplantation/Internet Resources
 * HLA
 * HLA/Linkage Disequilibrium
 * HLA/Disease association
 * HLA/Scientific Literature
 * CWD classification of HLA alleles

title: Transplantation


text:
User:Egm6341.s10.Team4.roni/HW7

HW7.4

HW7.10

title: User:Egm6341.s10.Team4.roni/HW7


text: File:RP HW 7 4c.png

title: File:RP HW 7 4c.png


text:
User talk:Bishisht

 Hello Bishisht, 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.
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 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 19:07, 18 April 2010 (UTC)

title: User talk:Bishisht


text:
User talk:Freecat~enwikiversity

 Hello Freecat, 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.
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And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 20:40, 18 April 2010 (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 Freecat. To make sure that both of you can use all Wikimedia projects in future, we have reserved the name Freecat~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 23:32, 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) 06:08, 19 April 2015 (UTC)

title: User talk:Freecat~enwikiversity


text:
User talk:Gisowar

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

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

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

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 23:30, 18 April 2010 (UTC)

title: User talk:Gisowar


text:
User talk:Riffraffselbow

 Hello Riffraffselbow, 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.
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 * Browse Wikiversity, or visit a portal corresponding to your educational level: pre-school, primary, secondary, tertiary, non-formal education.
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 * Read an introduction for teachers and find out how to write an educational resource for Wikiversity.
 * Give feedback about your initial observations
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 * Chat with other Wikiversitans on #wikiversity-en.

And don't forget to explore Wikiversity with the links to your left. Be bold to contribute and to experiment with the sandbox or your userpage, and see you around Wikiversity! If you're a twitter user, please follow http://twitter.com/Wikiversity. --Ottava Rima (talk) 00:39, 19 April 2010 (UTC)

title: User talk:Riffraffselbow


text:
Portal:Agape World Fellowship/Colleges

Many Christian colleges and seminaries are expensive, putting scriptural study out of the reach of most casual students. This list details some free colleges and seminaries that don't charge you tuition or fees to study towards a degree. These are all real colleges and seminaries, but almost all of them are unaccredited. You will most likely be unable to use your degree in the temporal world, so don't expect to improve your career. However, you will receive a first class spiritual education at all of these schools.

 * Moriah School of Ministry - Certificate in Biblical Studies, Diploma in Biblical Studies
 * New Wine Bible Institute- Bachelor of Arts in Christian Education, Master of Theology (Th.M.)
 * North American Theological Society- Undergraduate Diploma in Ecclesiastics, Graduate Diploma in Ecclesiastics
 * Pillar of Truth Bible Institute - Bachelor of Ministry (B.Min)
 * The North American Reformed Seminary - Associate of Arts in Theological Studies (A.A.T.S.), Bachelor of Arts in Theological Studies (B.A.T.S.), Master of Arts in Theological Studies (M.A.T.S.), Master of Divinity (M.Div.), Doctor of Ministry (D.Min.)
 * United Christian Church & Bible Institute -Associate of Arts in Christian Studies (A.A.), Bachelor of Arts in Christian Theology (B.A.)

Non free colleges

 * Bible University - Certificate of Biblical Studies, Bachelor of Biblical Studies (B.B.S.), Master of Biblical Studies (M.B.S.), Doctor of Biblical Studies (D.B.S.)

title: Portal:Agape World Fellowship/Colleges


text: File:Reaction.png

title: File:Reaction.png


text:
User:Freecat~enwikiversity

I am just a physicist. See my sciencedom.com for more

title: User:Freecat~enwikiversity