text:
User:Egm6321.f11.team4.shin.js/HW6

= Problem R*6.3 - Invalid solution = From [[media:Pea1.f11.mtg35.djvu|Mtg 35-4]]

Given
The first homogeneous solution: Trial solution: Characteristic equation:

Find
Explain why $$\displaystyle r_2(x)$$ is not a valid root, i.e., $$\displaystyle u_2(x) = e^{xr_{2}(x)}$$ is not a valid solution.

Solution
- Solved on our own Validity of $$\displaystyle u_2(x) = e^{xr_2(x)}$$ can be shown by substituting $$\displaystyle y= u_2(x) $$ into the Eq. (4.1). Before the substitution, compute the first and the second derivatives of $$\displaystyle y $$. Substitute $$\displaystyle y, y^{'}, y^{''}$$ in the Eq. (3.6) into the Eq. (3.1), - As shown in the Eq. (3.7), $$\displaystyle u_2(x) $$ is not a valid homogeneous solution.

Author
Contributed by Shin

= Problem R*6.4 - 2nd homogeneous solution by variation of parameters = From [[media:Pea1.f11.mtg35.djvu|Mtg 35-4]]

Given
Application: King 2003 p.28

Find
For the L2-ODE-VC Eq. (4.1), select a valid homogeneous solution, and call it $$\displaystyle u_1 $$. Find the 2nd homegeneous solution $$\displaystyle u_2(x) $$ by variation of parameters, and compare to $$\displaystyle e^{xr_2(x)} $$.

Solution
- Solved on our own Let trial solution be: Then, characteristic equation is: After factoring, the Eq. (4.3) becomes: Therefore, the first homogeneous solution is: Since it was proven that $$\displaystyle r_2(x) $$ is not a valid root in the problem R*6.3, $$\displaystyle r_2(x) $$ is ignored. The second homogeneous solution can be obtained using the equation (4) in the class note [[media:Pea1.f11.mtg34.djvu|34-5]]. The Eq. (3.6) depicts the equation (4) in the class note [[media:Pea1.f11.mtg34.djvu|34-5]]. The term $$\displaystyle a_1(x)$$ is determined by changing the form of the Eq. (4.1) as follows. First, the term $$\displaystyle \frac{1}{h(x)} $$ is first computed in order to solve the Eq. (4.7). Substitute $$\displaystyle a_1(x) $$ in the Eq. (4.9) into the Eq. (4.8), then compute $$\displaystyle \frac{1}{h(x)} $$, Then, substitute $$\displaystyle \frac{1}{h(x)} $$ from the Eq. (4.10) into the Eq. (4.7), - Since the second homogeneous solution has the form of $$ \displaystyle u_2(x) = -x $$, $$ \displaystyle u_2(x) = e^{x r_2(x)} $$ is not valid solution.

Author
Contributed by Shin

title: User:Egm6321.f11.team4.shin.js/HW6


text:
User:7yl4r

I am a Physics BS pursuing a masters in EE. I have a diverse number of interests but am currently trying to learn more about robotics and human-computer interaction. I find that teaching and learning very much go hand-in-hand; I love this project and am trying my best to find ways to contribute. I am not new to wikimedia projects, but I have not done much editing; please bear with me and don't hesitate to call me out if I'm doing something wrong.

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

title: User:7yl4r


text:
User:Palluri9407/enes100/Electric Cars v.2

Link to project ekart v.2 team page.

Give instructor top 3 project choice list

 * 1. Electric Cars
 * 2. Helicopter
 * 3. Hover Craft

Write problem statement
How can we develop the electrical system that goes on our ekart?

Assign Task1

 * Mount the motor on to the e kart
 * Mount the charged batteries and connect them to the motor

Compare actual work done to Task1
Mounted the motor and the batteries on to the go kart frame

Week1 Narrative
After I mounted the motor and the batteries I shifted my attention towards the ESC. I researched many different websites in order to find out a way to program the ESC to our specifications.

Some of the websites visited:
 * ehow.com
 * wattflyer.com
 * myrcguide.com

After doing the research I was able to work on the ESC and program it to our specifications.

I was also able to take out the contactors from the forklift that was donated to us. We plan on using these contactors on the go kart.

These are some of the directions that I used to take out the contactors safely and efficiently.

 * Wear safety goggles
 * Make sure their is no voltage running through the contactors
 * Take off all the wiring that is connected to the contactors
 * Once they are off, take out the frame that is holding it together
 * Finally unbolt the screws on the back to remove it from its place.
 * Make sure it is in working condition and that nothing is wrong with it.
 * Remove safety goggles

Week1 Peer Review
Peer review

Assign Task2
Finish working on the electrical system and mount it on the go kart frame

Compare actual work done to Task2
Worked on the ESC system with Criveros0248.

Week 3 Narrative
After working for a little bit on the ESC system, I shifted most of my attention towards the braking system of the go kart. The problem that I had was that the brakes were there, but the connection to the brakes did not exist. I had to improvise of some kind of a way to control the braking system. The solution that I came up with was to install a second pedal and connect it with the linking rods that were available for use.

First to install the braking pedal and system, I had to remove every thing on the go kart frame.

These were the tools that I used to build the system.
 * Linking Rod
 * Pivot
 * Pedal

To build the system I simply connected the linking rod and the pivot to the rod that was connected to the brake on the rear axle. Then I connected the other end of the rod to the pedal up front beside the gas pedal. It is built in such a way that when you push the pedal, the rods that are attached to it will pull the brake to slow the car down.

Week 3 Peer Review
Peer review

Assign Task4
Put all the components back on the go kart and finish up all the work that was left over to start doing test runs.


text:
User:RyanPak/enes100/Escher

Link to [RP] team page.

Week0 Activities
Research Escher concepts and ideas.

Write problem statement
Create a model inspired by Escher.

Assign Task1
Determine materials for Escher project, create basic design and research designs for Escher.

Compare actual work done to Task1
Completed necessary materials list, figured out the trick behind the Escher optical illusion.

Assign Task2
Begin blueprints for Escher project.

Compare actual work done to Task2
Blueprints being worked on, figuring out Google Sketch

Assign Task3
Begin gathering materials for Escher construction, continue blueprints for illusion.

Compare actual work done to Task3
Have a lot of wood ready to be cut and shaped to match the Escher design, figuring out angles on blueprint. Construction to begin soon.

Compare actual work done to Task4
Rationalize differences

title: User:RyanPak/enes100/Escher


title: File:Motor4.jpg


title: File:Pea1.f11.spring.svg


text:
User talk:Biodivsoc sebastian

 Hello Biodivsoc sebastian, 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! --Abd 00:21, 14 November 2011 (UTC)

title: User talk:Biodivsoc sebastian


text:
User talk:Laveol

 Hello Laveol, 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! --Abd 00:28, 14 November 2011 (UTC)

title: User talk:Laveol


text:
User:Egm6321.f11.team2.Xia/RP6.6

=R*6.6 - Finding L2-ODE-VC =

Given
Trial solution

$$\displaystyle y(x) = \frac {e^{rx}}{\sin x}$$ (6.6.1)

and characteristic equation.

$$\displaystyle (r-2)(r-\frac {1}{1+x})=0$$ (6.6.2)

Find
Find an L2-ODE-VC whose characteristic equation is 6.6.2

Solution
From 6.6.1, we have

$$\displaystyle y'= \frac{r\,{e}^{r\,x}}{\mathrm{sin}\left( x\right) }-\frac{{e}^{r\,x}\,\mathrm{cos}\left( x\right) }{{\mathrm{sin}\left( x\right) }^{2}}$$ (6.6.3)

$$\displaystyle y''= \frac{{r}^{2}\,{e}^{r\,x}}{\mathrm{sin}\left( x\right) }+\frac{{e}^{r\,x}}{\mathrm{sin}\left( x\right) }-\frac{2\,r\,{e}^{r\,x}\,\mathrm{cos}\left( x\right) }{{\mathrm{sin}\left( x\right) }^{2}}+\frac{2\,{e}^{r\,x}\,{\mathrm{cos}\left( x\right) }^{2}}{{\mathrm{sin}\left( x\right) }^{3}}$$ (6.6.4) then

$$\displaystyle y'=\left(r-\frac{\,\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}\right)\frac{{e}^{r\, x}}{\mathrm{sin}\left(x\right)}$$ (6.6.5)

$$\displaystyle y''=\left({r}^{2}+1-\frac{2\, r\,\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}+\frac{2\,{\mathrm{cos}\left(x\right)}^{2}}{{\mathrm{sin}\left(x\right)}^{2}}\right)\frac{{e}^{r\, x}}{\mathrm{sin}\left(x\right)}$$ (6.6.6) So we can assume that

$$\displaystyle a_{2}(x)\left({r}^{2}+1-\frac{2\, r\,\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}+\frac{2\,{\mathrm{cos}\left(x\right)}^{2}}{{\mathrm{sin}\left(x\right)}^{2}}\right)\frac{{e}^{r\, x}}{\mathrm{sin}\left(x\right)}+a_{1}(x)\left(r-\frac{\,\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}\right)\frac{{e}^{r\, x}}{\mathrm{sin}\left(x\right)}+a_{0}(x)\frac{{e}^{r\, x}}{\mathrm{sin}\left(x\right)}=0$$ (6.6.7)

$$\displaystyle a_{2}(x){r}^{2}+\left(a_{1}(x)-a_{2}(x)\frac{2\,\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}\right)r-a_{1}(x)\frac{cos\left(x\right)}{\mathrm{sin}\left(x\right)}+a_{2}(x)+a_{2}(x)\frac{2\,{\mathrm{cos}\left(x\right)}^{2}}{{\mathrm{sin}\left(x\right)}^{2}}+a_{0}(x)=0$$ (6.6.8) comparing 6.6.8 with the 6.6.2 we have

$$\displaystyle a_{2}=x+1$$ (6.6.9) $$\displaystyle a_{1}=2(x+1)\frac{\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}-(2x-3)$$ (6.6.10) $$\displaystyle a_{0}=1-x-(2x-3)\frac{\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}$$ (6.6.11) Thus

$$\displaystyle \left(x+1\right)y''+\left(2(x+1)\frac{\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}-(2x-3)\right)y'+\left(1-x-(2x-3)\frac{\mathrm{cos}\left(x\right)}{\mathrm{sin}\left(x\right)}\right)y=0$$ (6.6.12)

title: User:Egm6321.f11.team2.Xia/RP6.6


text:
Helicopter/Howard Community College/Fall2011/501 Drones

Problem Statement
-Have Arduino to work the DC motor

-Translate instructions to operate Logview and battery charging into a tutorial

-Find the most suitable connector for a homemade version of the helicopter

Team Members

 * Dcalderon
 * Andyn6361
 * Dkromer1996

Summary

 * Dcalderon was tasked to have a motor and a ESC work with an arduino to push in making a homemade helicopter. He went through a problem as he wasn't able to determine the inputs of the three wires he had for the motor. He proceeded to discuss his problem to the class and it was concluded that it didn't matter. After having his problem solved, he went on to attach the motor onto the board.
 * Andyn6361 was tasked to make a tutorial in charging the lithium-polymer battery and document the charging with the Logview software.
 * Dkromer1996 was tasked to find the name of the connector that would connect the lithium-polymer battery to the helicopter. He discovered the batteries use EC3 connectors and began the process of purchasing the connector. He then proceeded to practice soldering to gain some experience in soldering.

Story
With the Ar.Drone costing about 300 dollars, the team's main goal is to develop parts for a homemade version of the Ar.Drone. For this project, we decided to have an arduino control a motor that would propel a board and find the best battery for flight.

Material List
Dual power unit

Lithium-polymer batteries

Software List
Logview - Documents charging batteries

Time
Our teammates are spending approximately 4 hours in class and 5 hours outside of class. Also, we are spending 1-2 hours on wikiversity to write about personal page. Most of time, we spend our time working on project and document information.

Tutorials
The link to the tutorial of charging batteries and documenting using Logview software can be clicked here.

Next Steps
The next step is to finish up with the connection of the motor and the arduino to get the arduino to run the motor. everything that is needed is on the board.


text: Category:Dementia

title: Category:Dementia


text:
Dementia

This is a start page for learning about dementia (from the Latin for "without mind").

See also: Caregiving and dementia.

What is dementia?
Dementia is a gradual, serious loss of global cognitive ability in a previously unimpaired person, beyond what might be expected from normal aging.

Dementia is a very significant world-wide health care issue.

See also:
 * Dementia (Wikipedia)
 * What is Dementia? (Alzheimer's Australia fact sheet:)

How does dementia feel?

 * Read this Alzheimer's message board discussion about how it feels to have dementia and how this varies between people
 * Watch this 5 min. video about dementia and motivation

The numbers

 * 36 million people in the world have dementia (Banerjee, 2012)
 * It will double by 2030 and there will be 115 million with dementia by 2050
 * The social cost is enormous - US$600 billion per year (bigger than the biggest company of the world and biggest than cancer, diabetes, etc., i.e., around 1% of the world's economy, equivalent to the 18th biggest economy of the world)
 * 60% of the costs of aging care are due to dementia

See also: Alzheimer's disease facts and figures (Alzheimer's Association, USA, 2013)

Myths about dementia

 * It is not a normal part of ageing
 * That nothing can be done to help prevent or treat dementia
 * Stigma of dementia prevents discussion with the person with dementia
 * Having dementia means that a person is completely dependent

Types of dementia
Here is a description of some of the more well-known types of dementia (Access Economics, 2009) -
 * Alzheimer’s Disease, most common and usually affects the temporal lobes of the brain with consequent deterioration in memory,
 * Vascular Dementia, caused by mini strokes and more sudden onset than Alzheimers, can occur anywhere in the brain,
 * Dementia with Lewy Bodies (abnormal proteins form in certain areas of the brain) tends to affect the visual cortex among other areas of the brain,
 * Frontal Lobe and Fronto-Temporal Dementia (eg Pick’s Disease where abnormal amounts of tau protein form in nerve cells)
 * Alcohol-related Dementia (Korsakoff’s Syndrome)
 * Parkinsons Disease (affects nerve cells’ production of dopamine, which affects muscle movement and balance)
 * Huntingtons Disease is usually hereditary (behaviour changes such as irritability, moodiness, restlessness, paranoia and psychosis may be evident before movement problems emerge such as jerking movements, unsteady walking, involuntary facial movement)
 * AIDS-related Cognitive Decline

For more information, see Types of Dementia (Alzheimer's Australia)

What is needed?

 * National Dementia Strategies to prioritise health-care goals and strategies
 * Vision
 * System change
 * Ambition in scale
 * Investment
 * Commitment over time
 * Leadership
 * Health Promotion campaigns to educate carers, families, health professionals
 * Good-quality earlier diagnosis and intervention
 * Only a third of most of people with dementia received any special health care assessment or diagnosis. When they do it is:
 * late in the illness too late to enable choice
 * at a time of crisis
 * too late to prevent harm or crises.

Quality of life
Quality of life (QOL) is unrelated to severity of dementia. However, there is considerable variability in QOL. Quality of understanding, diagnosis, and care then are important aspects of the health and well-being of those with dementia.

title: Dementia


text:
User:Drew Dollas/enes100/Glorious2/Batteryrecharge

1. Go into the Thunder AC6 settings on the dual power unit, and use the "Batt. Type" button to locate the USB and temperature settings. Turn on USB and turn off Temperature.

2. Load the CP210x USB to UART Bridge VCP Drivers (makes the USB look like a Com Port) https://www.silabs.com/products/mcu/Pages/USBtoUARTBridgeVCPDrivers.aspx

3. Load the logview software http://www.logview.info/cms/e_logview_info.phtml

Power up the charger, plug the USB in the computer and hopefully it will detect the new device and load the USB drivers..

Run the Log View Program select English

Select the DEVICE Bantam E-station BC6 charger.. select in DEVICE Open Port Recording

To start charging batteries using the charger -

1. Use program select to choose your type of battery

2. Change the amp and volt values on the charger to the voltage of the battery, and the recommended charge amps specified on the battery

3. Hold the start button

It should require you to hit start once more, and then it will start charging. It will show you the current voltage of the battery, the charging rate, and the time it has been charging. As it charges, if it is connected to the logview program, you should be able to see a graph forming. If you cannot, try changing the tabs below the graph from "Graph," to "Analog View" or "Digital View."


text:
Talk:Robotics

How to Merge/link with Similar Content
I'm new to editing here. I suppose this is considered a 'topic' of multidisciplinary engineering, which is 'department' of the 'school' of engineering. Did I get that right? =) Anyway, point is, I'm trying to work out how to work this page in with existing content. It seems to me that one should not come up with such a stub when searching for a topic. Something like the structure of Chemistry makes most sense to me, but since this is more a 'topic' than a 'school' I suppose links to specific content pages would be located here. Would love to hear thoughts. Otherwise I suppose I'll just go ahead and adopt this page and work at it. =) 7yl4r 02:23, 14 November 2011 (UTC)

Difenation?
What? "Requested content Please give something about embedded in a single difenation" It's been on this page a while; I don't understand what it is talking about. Perhaps it was supposed to read 'definition'? I'll probably delete it I guess... I feel pretty weird about removing something I don't understand though. 7yl4r 02:33, 14 November 2011 (UTC)

Content sub headings
I would like to put more structure before starting on some content! I think that robotics should be split between mobile and static - alternatively split between levels of difficulty / ability? Or both? Which first? Then splitting mobile into: land, sea, under water, amphibious, air borne, space - any objections? --Sirnails (discuss • contribs) 21:45, 14 March 2014 (UTC)

Updating the course?
Is there an interest in updating this course? I have an interest in creating a new course on "modeling of mechanical robotics." Thank you. Admazzeo (discuss • contribs) 21:44, 3 January 2020 (UTC)

 * There's not much here. If you have a vision for making this a meaningful resource, go for it! -- Dave Braunschweig (discuss • contribs) 01:04, 4 January 2020 (UTC)

title: Talk:Robotics


text:
File:IMG 0577.JPG

Licensing
for school project

title: File:IMG 0577.JPG


text: File:IMG 0560.JPG

title: File:IMG 0560.JPG


text:
Talk:Engineering Projects/Robot arm/Howard Community College/Fall2011/502 TFCW

Sweet arm, bro. =) 7yl4r 03:46, 14 November 2011 (UTC)

100/100 good job .. 1sfoerster 21:21, 16 November 2011 (UTC)


text:
User:Egm6321.f11.team4.allen/HW7

= Problem R*7.4 Laplacian in Elliptic Coordinates = From [[media:Pea1.f11.mtg41.djvu|Mtg 41-1]]

Given
The Laplacian operator for general coordinates is given by $$\nabla^{2} u = \Delta u = \frac{1}{h_1h_2h_3} \sum^3_{i=1}\frac{\partial}{\partial\xi_i} \left[ \frac{h_1h_2h_3}{(h_i)^2} \frac{ \partial u}{ \partial\xi_i} \right]$$. The elliptic coordinates are given by $$\displaystyle \xi_1 = \mu $$ $$\displaystyle \xi_2 = \nu $$. The scale factors for the elliptic coordinates $$\displaystyle (\mu, \nu)$$ are given by $$\displaystyle h_{\mu} = h_{\nu} = a \sqrt{\sinh^2{\mu} + \sin^2{\nu}}$$.

Find
Verify the Laplacian in elliptic coordinates is given by $$\displaystyle \nabla^{2} u = \Delta u= \frac{1}{a^{2} \left( \sinh^{2} \mu + \sin^{2}\nu \right)} \left( \frac{\partial^{2} u}{\partial \mu^{2}} + \frac{\partial^{2} u}{\partial \nu^{2}} \right) $$.

Solution
Since this is 2-D problem, the Laplacian operator for general coordinates is reduces to $$\Delta u = \frac{1}{h_1h_2} \sum^2_{i=1}\frac{\partial}{\partial\xi_i} \left[ \frac{h_1h_2}{(h_i)^2} \frac{ \partial u}{ \partial\xi_i} \right]$$. The above equation expands to $$\Delta u = \frac{1}{h_1 h_2} \left[ \frac{\partial}{\partial\xi_1} \left( \frac{h_1 h_2}{(h_1)^2} \frac{\partial u}{\partial\xi_1} \right) + \frac{\partial}{\partial\xi_2} \left( \frac{h_1h_2}{(h_2)^2} \frac{\partial u}{\partial\xi_2} \right) \right] $$. Since $$\displaystyle h_{\mu} = h_{\nu} $$, the following terms cancel out: $$\displaystyle \cancel{\frac{h_1 h_2}{(h_1)^2}} $$ and $$\displaystyle \cancel{\frac{h_1 h_2}{(h_2)^2}} $$. With $$\displaystyle \xi_1 = \mu $$, $$\displaystyle \xi_2 = \nu $$ and $$\displaystyle h_{\mu} = h_{\nu} = a \sqrt{\sinh^2{2\mu} - \sin^2{2\nu}}$$, the Laplacian reduces to $$\displaystyle \Delta u= \frac{1}{a^{2} \left( \sinh^{2} \mu + \sin^{2}\nu \right)} \left( \frac{\partial^{2} u}{\partial \mu^{2}} + \frac{\partial^{2} u}{\partial \nu^{2}} \right) $$.

= Problem R7.5 Laplacian in Parabolic Coordinates = From [[media:Pea1.f11.mtg41.djvu|Mtg 41-2]]

Given
The Laplacian operator for general coordinates is given by $$\nabla^{2} u = \Delta u = \frac{1}{h_1h_2h_3} \sum^3_{i=1}\frac{\partial}{\partial\xi_i} \left[ \frac{h_1h_2h_3}{(h_i)^2} \frac{ \partial u}{ \partial\xi_i} \right]$$. The parabolic coordinates are given by $$\displaystyle \xi_1 = \mu $$ $$\displaystyle \xi_2 = \nu $$. The scale factors for the parabolic coordinates $$\displaystyle (\mu, \nu)$$ are given by $$\displaystyle h_{\mu} = h_{\nu} = \sqrt{\mu^2 + \nu^2}$$.

Find
Verify the Laplacian in elliptic coordinates is given by $$\displaystyle \nabla^{2} u = \Delta u= \frac{1}{\mu^2 + \nu^2} \left( \frac{\partial^{2} u}{\partial \mu^{2}} + \frac{\partial^{2} u}{\partial \nu^{2}} \right) $$.

Solution
Since this is 2-D problem, the Laplacian operator for general coordinates is reduces to $$\Delta u = \frac{1}{h_1h_2} \sum^2_{i=1}\frac{\partial}{\partial\xi_i} \left[ \frac{h_1h_2}{(h_i)^2} \frac{ \partial u}{ \partial\xi_i} \right]$$. The above equation expands to $$\Delta u = \frac{1}{h_1 h_2} \left[ \frac{\partial}{\partial\xi_1} \left( \frac{h_1 h_2}{(h_1)^2} \frac{\partial u}{\partial\xi_1} \right) + \frac{\partial}{\partial\xi_2} \left( \frac{h_1h_2}{(h_2)^2} \frac{\partial u}{\partial\xi_2} \right) \right] $$. Since $$\displaystyle h_{\mu} = h_{\nu} $$, the following terms cancel out: $$\displaystyle \cancel{\frac{h_1 h_2}{(h_1)^2}} $$ and $$\displaystyle \cancel{\frac{h_1 h_2}{(h_2)^2}} $$. With $$\displaystyle \xi_1 = \mu $$, $$\displaystyle \xi_2 = \nu $$ and $$\displaystyle h_{\mu} = h_{\nu} = \sqrt{\mu^2 + \nu^2} $$, the Laplacian reduces to $$\displaystyle \Delta u= \frac{1}{\mu^2 + \nu^2} \left( \frac{\partial^{2} u}{\partial \mu^{2}} + \frac{\partial^{2} u}{\partial \nu^{2}} \right) $$.

title: User:Egm6321.f11.team4.allen/HW7


text:
Wikiversity:Types of user accounts

In a sense, on Wikiversity all users are equal: all people contributing to the project are expected to stick to the same rules, and when it comes time to discuss how to manage issues, all contributors have an equal voice. That said, there is a difference in what different contributors can do.

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In terms of editing, IP editors can edit any unprotected page. However, they are unable to create new pages or upload files, and their edits tend to be given special attention by those looking at recent changes.

Registered users
New users are able to make changes to unprotected resources (which is the default status for the vast majority of pages), but are not able to edit protected resources or to upload files. By having an account, they are no longer identified by their IP address, which provides a greater degree of privacy. The single account name also makes it easier for contributors to build a positive reputation and relationships with other contributors.

The unified login (SUL) process permits users with an account to have a common username across all the Wikimedia Foundation projects. Thus the same username and password could be used to log into Wikiversity, Wikipedia, Wikibooks and Wikimedia Commons, to name but four of the projects.

See also: Why create an account

Autoconfirmed editors
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Established users
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title: Wikiversity:Types of user accounts


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User:Billinghurst/common.css

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title: User:Billinghurst/common.css


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User:Egm6321.f11.team1/report6.bensplaypen.R*6.5

= Problem R*6.4 For a L2-ODE-VC using variation of parameters find the 2nd homogeneous solution and compare =

Reference Lecture 35-4 found here:[[media:pea1.f11.mtg35.djvu|Mtg 35]]

Given
The following liner, second order, ordinary differential equation, with varying coefficients (L2-ODE-VC)

$$\displaystyle (x - 1) y'' - x y' + y = x$$ $$\displaystyle (6.4.1) $$

Find
A valid homogeneous solution and call it $$\displaystyle u_1 $$

Find the particular solution using variation of parameters method and compare it to $$\displaystyle e^{xr_2(x)} $$

Solution
Lets start by validating that the homogeneous solution selected below

$$\displaystyle u_1 = e^x $$ $$\displaystyle (6.4.2) $$

Use the trial solution:

$$ \displaystyle u_1(x) = e^{rx}$$ $$\displaystyle (6.4.3) $$

Differentiate the above to get $$ \displaystyle u'_1(x) = r e^{rx}$$ $$\displaystyle (6.4.4)$$

$$ \displaystyle u''_1(x) = r^2 e^{rx} $$ $$\displaystyle (6.4.5)$$

Plugging these derivatives and the trial solution into 6.4.1 yields $$ \displaystyle \left[(x-1) r^2 - rx + 1\right] e^{rx} = 0$$ $$\displaystyle (6.4.6)$$

Rearranging by grouping the terms with x from above yields

$$ \displaystyle \left[(r^2 - r) x + (1 - r^2)\right] e^{rx} = 0$$ $$\displaystyle (6.4.7)$$

In order for the above equation to be equal to zero, the following equations must be satisfied

$$ \displaystyle r^2 - r = r (r - 1) = 0 $$

$$ \displaystyle 1 - r^2 = -(r + 1)(r - 1) = 0 $$ $$\displaystyle (6.4.8)$$

The solution of the above equations is $$\displaystyle r=1$$. So 6.4.3 can be written as

$$ \displaystyle u_1(x) = e^x $$ $$\displaystyle (6.4.9)$$

Which is a valid homogeneous solution

So now lets find the 2nd homogeneous solution using variation of parameters

We can rewrite 6.4.1 as

$$ \displaystyle y'' + \underbrace{\frac{-x}{x-1}}_{a_1(x)} y' + \underbrace{\frac{1}{x-1}}_{a_0(x)} y  = \underbrace{\frac{x}{x-1}}_{f(x)} $$ $$\displaystyle (6.4.10) $$

Using equation (4) from page 34-5 of the class notes [[media:pea1.f11.mtg34.djvu|Mtg 34 (b)]] the following expression for the 2nd homogeneous solution is obtained:

$$\displaystyle {u}_{2}(x)= \underbrace{{u}_{1}(x)}_{{e}^{x}} \int \frac{1}{ u_1^2(x)}exp[-\int \underbrace{a_1(x)}_{\frac{-(x)}{x-1}} \ dx] \ dx $$ $$\displaystyle (6.4.11) $$

Using Wolfram Alpha to evaluate both integrals and simplify it can be shown that

$$\displaystyle {u}_{2}(x)= x $$ $$\displaystyle (6.4.12)$$

Which is the 2nd homogeneous solution

This can can then be compared to $$\displaystyle e^{xr_2(x)} $$ as requested

if $$\displaystyle r_2(x) = ln(x)/x $$ the expressions for $$\displaystyle{u}_{2}$$ are equivalent

= R*6.5: Find Two Homogeneous Solutions using a Trial Solution =

Reference lecture notes page 36-3 found here [[media:pea1.f11.mtg36.djvu|Mtg 36]]

Given
Find u1 and u2 of Equation 6.5.1 below using the trial solution given in equation 6.5.2:

$$\displaystyle (x +1) y'' - (2x+3)y' + 2y = 0 $$ (6.5.1)

$$\displaystyle y(x)=e^{rx}$$ (6.5.2)

Solution
Lets start by differentiating the trial solution as follows:

$$ \displaystyle y'(x) = r e^{rx}$$ (6.5.3)

$$ \displaystyle y''(x) = r^2 e^{rx}$$ (6.5.4)

The next step is to plug the derivatives and the original trail function into equation 6.5.1 as follows:

$$ \displaystyle e^{rx}\left[(x+1)r^2-(2x+3)r+2\right]=0 $$
(6.5.5)

Divide $$ \displaystyle e^{rx} $$ by both side and group all the $$ \displaystyle x $$ terms to obtain:

$$ \displaystyle x(r^2-2r)+(r-2)(r-1)=0$$
(6.5.6)

The following conditions must be satisfy for equation 6.5.6 to be true:

$$ \displaystyle r(r-2)=(r-2)(r-1)=0 $$
 (6.5.7)

In order for 6.5.6 to be true it can be seen that $$ \displaystyle r=2 $$
(6.5.8)

The first homogeneous solution is obtained by plugging equation 6.5.8 into the trial solution given in equation 6.5.2:

$$ \displaystyle u_1(x)=e^{2x} $$
(6.5.9)

Using equation (4) from page 34-5 of the class notes [[media:pea1.f11.mtg34.djvu|Mtg 34 (b)]] the following expression for the 2nd homogeneous solution is obtained:

$$ \displaystyle u_2(x)=u_1(x)\int{u_1^{-2}(x)e^{-\int{a_1(x)}\,dx}}\,dx$$
(6.5.10)

Equation 6.5.1 can be rearranged into the desired form shown:

$$ \displaystyle y''-\underbrace{\frac{2x+3}{x+1}}_{a_1}y'+\underbrace{\frac{2}{x+1}}_{a_0}y=0$$
 (6.5.11)

The value for $$ \displaystyle a_1 $$ from equation 6.5.11 is then substituted into equation 6.5.10, additionally the first homogeneous solution from equation 6.5.9 is substituted to solve for the second homogeneous solution as shown:

$$ \displaystyle u_2(x)=e^{2x}\int{e^{-4x}e^{\int{\frac{2x+3}{x+1}}\,dx}}\,dx$$
 (6.5.12)

Evaluating the inner most integral yields:

$$ \displaystyle u_2(x)=e^{2x}\int{(x+1)e^{-2x}}\,dx$$
(6.5.13)

Finally evaluating the last integral and simplifying yields:

$$ \displaystyle u_2(x)=\frac{-1}{4}(2x+3)$$
(6.5.14)

This is the 2nd homogeneous solution.


text:
Talk:Engineering Projects/Engines/Howard Community College/fall2011/550 QSM

project engine discussion.


text:
User:Egm6321.f11.team2.rho/HW6

=R*6.1- Solve Nonhomogeneous L2-ODE-CC=

Given
As an application of nonhomogeneous L2-ODE-CC:

2nd exactness condition for N2-ODES is:

For problme 2, integrating factor is

Find
1. Find the PDEs that governs the integrating factor $$\displaystyle h(x,y)$$ using 2nd exactness condition for N2-ODEs

2. Solve (6.1.1) using trial solution for integrating factor of $$\displaystyle h(t)={{e}^{\alpha t}}$$

2.1) Find $$ (\bar a_1,\bar a_0)$$ in terms of $$ (a_0,\ a_1,\ a_2) $$.

2.2) Find the quadratic equation for $$\displaystyle \alpha $$.

2.3) Reduced-order equation: lead to

$$\displaystyle e^{\alpha t}[\bar a_1y'+\bar a_0y]=\int e^{\alpha t}f(t)dt$$

$$\displaystyle \bar a_1y'+\bar a_0y=e^{-\alpha t}\int e^{\alpha t}f(t)dt$$

2.4) Use the IFM to solve the equation in part 2.3.

2.5) Show that

$$\displaystyle  \alpha \beta = \frac {a_0}{a_2}$$.

$$\displaystyle  \alpha+\beta=\frac{a_1}{a_2}$$

2.6) Deduce the particular solution $$\displaystyle y_P(t)$$ for general excitation $$\displaystyle f(t)$$

2.7) Verify result with table of particular solutions for

$$\displaystyle f(t) = t exp(bt) $$

2.8) Solve the nonhomogeneous L2-ODE-CC with the following excitation

Hyperbolic function: $$\displaystyle f(t) = tanh t $$

For the coefficients (a0,a1,a2),consider two characteristic equations:

2.8.1) $$\displaystyle (r+1)(r-2) = 0$$

2.8.2) $$\displaystyle (r-4)^2 = 0 $$

2.9) For each case in questions 2.8.1 and 2.8.2, determine the fundamental period of undamped free vibration, and plot the solution for the excitation for about 5 periods, assuming zero initial conditions.

Part 1
Multipling $$\displaystyle H(t,y)$$ in the both sides, (6.1.1) can be rewritten as follows:

In the 2nd exactness condition,

From (6.1.5) and (6.1.6), We can get the following relation:

Assuming that H(t,y) and F(t,y) are only the functions of t in (6.1.2) and (6.1.3), and P=y', we can get the following relations in the 2nd exactness condition:

From (6.1.9) and (6.1.10), we can get the following result:

Part 2.1
where $$ \bar{a}_2 = 0 $$

$$ \frac{d}{dt}\Big[e^{\alpha t}(\bar{a}_1y'+\bar{a}_0y) \Big] = e^{\alpha t}\Big(\bar{a}_1 y + (\alpha \bar{a}_1+\bar{a}_0)y' + \alpha \bar{a}_0 y \Big) = e^{\alpha t}\big[a_2y+a_1y'+a_0y\big] \! $$

Thus, we can the the following relation.

$$ \bar{a}_1 = a_2 \! $$

$$ \bar{a}_0 = a_1 - \alpha a_2 = a_0/\alpha \! $$

Part 2.2
Multiplying $$\displaystyle \alpha $$ in the both second and third sides of (6.1.9) and rewriting it, we can get the following quadratic equation.

Part 2.3
From Part 2.1,

The above function can be rewriten as follows:

where $$ \beta=\frac{\bar a_0}{\bar a_1}$$

Part 2.4
The integrating factor to use IFM is $$ \bar{h}(t) = exp \Big[ \int \underbrace{\frac{\bar{a}_0}{\bar{a}_1}}_{\beta} dt \Big] = e^{\beta t} \! $$

The IFM would be used for the solution as follows: $$\displaystyle y(t)=\frac{1}{\bar h(t)}\int^t \bar h(s)B(s)ds $$ The result of Part 2.3 will be devided by $$\displaystyle \bar a_1 $$ to obtain B(s). $$\displaystyle y'+\beta y = \frac{e^{-\alpha t}}{\bar a_1} \int e^{\alpha t}F(t)dt = B(s) $$ Then we can combine $$\displaystyle h(t), \ B(s) $$ into $$\displaystyle y(t) $$ to find

Part 2.5
$$ \beta = \frac{\bar{a}_0}{\bar{a}_1} = \frac{a_0/\alpha}{a_2} $$

Multiplying $$\displaystyle \alpha $$ in the both first and last sides of the above equation, we can get the following:

$$ \alpha\beta = \frac{a_0}{a_2} $$

$$ \beta = \frac{\bar{a}_0}{\bar{a}_1} = \frac{a_1 - \alpha a_2}{a_2} = \frac{a_1}{a_2} - \alpha $$

Thus, $$ \alpha + \beta = \frac{a_1}{a_2} $$

Part 2.6
When $$\displaystyle \alpha $$ and $$\displaystyle \beta $$ are the roots of the characteristic equation, the homogeneous solution is

The particular solution $$\displaystyle y_P(t) $$ is

Part 2.7
Since $$\displaystyle F(t) = t e^{bt} $$,

Part 2.8.1
Thus, the L2-ODE is given by

coefficients $$\displaystyle {{a}_{0}}$$, $$\displaystyle {{a}_{1}}$$, $$\displaystyle {{a}_{2}}$$ are

From the root of the above characteristic equations, we can see the following:

$$\displaystyle \alpha=-1, \beta=2$$

The excitation is hyperbolic function as follows: $$\displaystyle f(t)=tanh(t)$$

With the website of "wolframalpha", the general solution y(t) is $$\displaystyle y(t)=\frac{1}{6}\left[1+2e^{-2t}log(e^{2t}+1)-4e^ttan^{-1}(e^{-t})\right]$$

Part 2.8.2
Thus, the L2-ODE is given by

The coefficients $$\displaystyle {{a}_{0}}$$, $$\displaystyle {{a}_{1}}$$, $$\displaystyle {{a}_{2}}$$ are

From the root of the above characteristic equations, we can see the following:

$$\displaystyle \alpha=\beta=4$$

The excitation is hyperbolic function as follows: $$\displaystyle f(t)=tanh(t)$$

With the website of "wolframalpha", the general solution y(t) is $$\displaystyle y(t)=-\frac{Li_2(-e^{2t}\cdot e^{-4t})}{2}-\frac{e^{-2t}}{2}+\frac{1}{16}$$

=R*6.7- Homogeneous Solution of Legendre Function Using Variation of parameters=

Given
The general form of the Legendre Equation is

$$\displaystyle P_2(x)$$ should be

for the following result of $$\displaystyle Q_2(x)$$

Find
Show

using the Method of Variation of Parameters.

Solution
When n=2, the given Legendre Equation is as

(6.7.4) cam be rewritten as follows:

Let $$\displaystyle y(x) = U(x)\cdot {u}_{1}(x)$$ and $$\displaystyle P_2(x) = {u}_{1}(x)$$.

where $$\displaystyle \begin{align} &y = U {u}_{1} \\ &y' = U {u}_{1}'+U' {u}_{1} \\ &y= U {u}_{1}+2U' {u}_{1}'+U'' {u}_{1} \\ \end{align} $$

To reduce the order of (6.7.6), $$\displaystyle Z:=U'$$ willb be used.

To use integrating factor method, we first need to find the integrating factor, h(x), as follows:

The soloution of Z is

From the definition of Z(x)= U',

Solving y(x) with U(x),

2nd homogeneous solution is

Thus,

title: User:Egm6321.f11.team2.rho/HW6


text:
User:Asatya/enes100/Boating

Link to Boating

Give instructor top 3 project choice list
My top 3 projects I selected are model boat, bridges, and static electricity. I ended up in the model boat team.

Write problem statement
The goal of this project is to build a model boat that can move by remote control. So I decided to look for a radio control car and take it apart and learn how the car move by remote control. Then I will use that part from inside of the rc car that receives radio waves from remote control and then put it for the boat I am going to make. I want that rc car part for the boat to function. It's the function part. Also I will think of a design of the boat. I don't want the boat to have too much mass or else the boat won't move freely. I want to keep the boat lighter mass as possible. So I am thinking about plastic soda bottles.

Assign Task1
So the assignment for task one is to learn how the radio control car functions by the remote control.

Compare actual work done to Task1
Rationalize differences

Week1 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week1 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task2
Record what you are planning on doing for the team during the weekend between week1 and week2 of the project here.

Compare actual work done to Task2
Rationalize differences

Week2 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week2 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task3
Record what you are planning on doing for the team during the weekend between week2 and week3 of the project here.

Compare actual work done to Task3
Rationalize differences

Week3 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week3 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task4
Record what you are planning on doing for the team during the weekend between week3 and week4 of the project here.

Compare actual work done to Task4
Rationalize differences

Week4 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week4 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Complete Project Page
Follow the "project done" format.

Start Next Project Week0 activities
During this week you will perform the week0 activities of the next project.

title: User:Asatya/enes100/Boating


text:
User:Dcaldero8983/enes100/drones

This is a link to my team page Drones

Give instructor top 3 project choice list
For my third project, I chose my top three preferences in the exact order. 1. Helicopter 2. Illuminate Clothing 3. Cavitation

Write problem statement
I chose to stay with the same project once again. This time i am continuing on working with the Arduino Uno and a DC Motor. I will try to retrace the professor's stimulation of an Arduino Duemilanove with a ESC computer and a motor.

Assign Task1
Continue working with the motor shield and try to solve my problem with why the DC Motor is not working with the code i am trying given provided by ladyada.net

Compare actual work done to Task1
After the demonstration, I wanted to incline more on working with a motor and an ESC with the Arduino just like the professor should in class as a demonstration. So this week I stopped working with the motor shield and started to work on a motor that i had to put together and connect an ESC to it. Well working with the motor brought up some frustration since i have never before worked with a motor yet alone put one together.

Week1 Narrative
So in my first week, i was given a brand new Hacker Brushless Motor A10 13L and a brand new ES Thunderbird 9. So as i started working with the motor, i noticed that the manual did not teach you by steps how to put the motor together. So i researched online under this motor and i found a few websites, the most helpful was [] were i found the actyal motor online and what it includes incase i might be missing something. Also, i found a really helpful website with an actual image of my ESC that im using with a motor and how it is setup [] In addition, I also found on the web another guy who is using a very similar motor with the same ESC and I plan on using this image sort of as a guide for what my connections should look like [].

I also ran across an issue. I have three wires from the ESC; a white, red, and black wire. On my motor i also have three wires but none of them are labeled nor colored to show which wires i should connect together. I looked online but was not able to find anything and the closest i got to finding an answer is the link #2 where it shows the wiring of the ESC and a motor. In addtion to this, i want to bring up in engineering class of how i should come along with mounting this motor on a board. The reason being is that as you can see by the picture, it looks like what i will have to do is create a hole on a piece of wood that way the bottom of the motor will basically be inside the wood and only the propellers will be sticking out and visible. Maybe hearing what my classmates have to say i might be able to come up with a better solution.

Week1 Peer Review
I added good reviews on my classmates wiki pages and i am also up to date with what they are doing as far as our new project on this team.

Assign Task2
For my next task over the weekend I plan on testing the wires to see if i have connected the wires to each other correctly. I will also mount these parts to a 2"by4" piece of wood that way i wont loose anything and will make my work easier.

Compare actual work done to Task2
For my second week, i proposed my problem to the class during a presentation. That problem was that i did not not if it mattered what 3 wires i would connect from the motor which has 3 wires and the ESC which also has 3 wires. So in class, the professor told me it did not matter because the ESC programs itself to know which wire is which when it is connected and powered. So using but splices, i connected the wires together and mounted this onto my board. But at first i mounted the motor onto the board, and as you read from week one i would have to make a hole through the board in order to get my motor on. So i did that, i drilled a whole through a board in order for my motor to spin freely on it without being disrupted or contacted. I didnt use any screws to keep the motor in place, what i used was epoxy, which i mixed carefully and applied to the motor, and i let it set for a few hours before it hardened. Now the motor will not come off at all, which is what i wanted from the beginning. Next i had to mount the ESC to the board, and to do this i would have to drill 2 small holes and strap the ESC to the board, the only problem is that i do not have a drill at home so i will drill these holes in the class room. In addition, im also adding the Arduino to the board and i will strap it onto the board, not glue it. Rationalize differences

Week2 Narrative
After letting the epoxy set, i connected the motor and ESC, as you can see in the pictures. I only have a small problem but nothing major, i will have to take the but splice off the red cable because it doesnt give that much room for the motor's wire to go in. That i will take care of in class since it is nothing major and only takes a few seconds. I also took a picture of the Arduino on the board just to have the sense of exactly how my project is going to look like and how my wiring is going to be set up. I now also need to strap the Arduino onto the board so that is more holes that i now need to make on the board and again i will strap the Arduino just as i will with the ESC.

Week2 Peer Review
I looked at both of my team mates wiki pages on Sunday and i found nothing under their second week. I added on their discussion pages that i didnt see anything and saved that on their page.

Assign Task3
For my next task, i will plan on getting some current over to the ESC to see if it will power the ESC. The ESC should make a noise if the wires are connected to each other correctly. I will also strap the Arduino onto the board and proceed with my attempt to mock the professor's project.

Compare actual work done to Task3
Rationalize differences

Week3 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week3 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task4
Record what you are planning on doing for the team during the weekend between week3 and week4 of the project here.

Compare actual work done to Task4
Rationalize differences

Week4 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week4 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Complete Project Page
Follow the "project done" format.

Start Next Project Week0 activities
During this week you will perform the week0 activities of the next project.

title: User:Dcaldero8983/enes100/drones


text:
User:Asatya/enes100/Model Boat

Link to Boating

Give instructor top 3 project choice list
My top 3 projects I selected are model boat, bridges, and static electricity. I ended up in the model boat team.

Write problem statement
The goal of this project is to build a model boat that can move by remote control. So I decided to look for a radio control car and take it apart and learn how the car move by remote control. Then I will use that part from inside of the rc car that receives radio waves from remote control and then put it for the boat I am going to make. I want that rc car part for the boat to function. It's the function part. Also I will think of a design of the boat. I don't want the boat to have too much mass or else the boat won't move freely. I want to keep the boat lighter mass as possible. So I am thinking about plastic soda bottles.

Assign Task1
So the assignment for task one is to learn how the radio control car functions by the remote control.

Compare actual work done to Task1
Right now I am planning of a design of what the model boat should look like.

Week1 Narrative
I want to use soda plastic bottles for the structure of the boat because they contain lighter mass to support the boat. We don't want to make it heavier or else the boat wont move properly.

Week1 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task2
I will continue and figuring out the perfect design of the model boat I where should I put the RC reveiver part piece from RC car.

Compare actual work done to Task2
I will look for objects of building a model boat.

Week2 Narrative
A week ago I bought a 2-liter bottle of Pepsi. I emptied it by drinking the whole bottle. I will use the empty Pespsi bottle for the base of the model boat. Then I took the RC car apart and found a green circuit board where it receives signal waves from the remote control of the car. The goal is to figure out where to put that circuit board on the empty soda bottle. Looks like I need another 2-liter empty soda bottle to complete the base of the boat. I want to put the circuit board between the bottles.

Week2 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task3
I will get another empty 2 liter bottle and enrich the boat's design.

Compare actual work done to Task3
I will design the model boat by using the following materials.

a. 2 2-Liter plastic soda bottles

b. 3 rectangular balsa wood pieces with lengths 23cm and widths 7.8cm.

c. PC fan

d. 9-Volt battery

Week3 Narrative
First, I super glued the 2 big plastic bottles together and let them stand vertically for them to dry. The reason I let them stand vertically is to make it look perfect. I waited for two hours for the glue to dry. Then I cut 3 balsa wood rectangular pieces. Each has a lengh of 23cm and width 7.8cm. Then I super glued them on one side of the soda bottles to create the base of the boat. I let them dry overnight. Next step is to get the PC fan working. In order to charge the PC fan, I need a 9-volt battery. I saw this youtube video,where this person charged the PC fan with 9-volt battery to get the boat to move.So the following day, I went to the dollar store and purchased some 9-volt batteries. I attached the PC fan wires to the 9-volt battery and it worked! Right now, the goal is to place the PC fan connected to the 9-volt battery on the model boat. On a Friday night, I super glued the PC fan boat on the back of the model boat and I waited for a couple of hours for the glue to dry. On Saturday morning, I filled a large container with water. There was a problem. The boat sank backwards vertically. So I got a help from my brother to hold the center of the boat. While he holded the boat, I attached the PC wires to the battery. The good news is that the boat moves but the bad news is that the boat moved backward!. So that's another problem. So there are two problems so far. One, the boat sank backwards vertically because it did no achieve equilibrium. That means there's more mass on the back of the model boat then the front or the middle. In order for the boat to reach perfect equilibrium, I should do center mass. So I took off the PC fan and super glued again in the middle of the boat to achieve the center mass. Another problem is that the boat moved backwards because the air is blowing toward the front side of the boat. In order for the boat to move forward, I need to turn the PC fan backwards for the air to go in the opposite direction. If the air of the PC fan goes backwards, that means the boat moves forward where I wanted. The link to the boat http://www.youtube.com/watch?v=WKBHfgjVzjs

Week3 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task4
I will figure out the steering mechanism of the model boat. I will use RC parts.

Compare actual work done to Task4
Rationalize differences

Week4 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week4 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Complete Project Page
Follow the "project done" format.

Start Next Project Week0 activities
During this week you will perform the week0 activities of the next project.

title: User:Asatya/enes100/Model Boat


text:
Talk:Engineering Projects/Engines/Howard Community College/Fall2011/550 QSM

100/100 ... 1sfoerster 21:43, 15 November 2011 (UTC)


text:
User:Mbaig7172/enes100/engine

link to the team page:qjb-eng

Give instructor top 3 project choice list
Sterling Engines

Bridges

Escher

Write problem statement
Create a working sterline engine at low-cost.

Assign Task1
Research how a sterling engine works.

Gather the proper materials. Find the lowerst price.

Email teacher about the materials I would like to get ordered.

Compare actual work done to Task1
I went online and researched sterling engines

-A sterling engine is a heat operated engine that converts heat energy to mechanical work. The cyclic compression and expansion changes the pressure of the gas which creates a series of events that converts the energy into mechanical work.

Basic parts of sterling engine:

Piston

Heat Source

Cylinder

Unfortunately I did not email the teacher on the parts I would like to buy. However, I did accomplish one of my tasks which was to find youtube videos that provide a video guide on how to create a sterling engine at low cost.

I went to team QSM's page (http://en.wikiversity.org/wiki/Engines/Howard_Community_College/Fall2011/550_QSM) to understand where they went wrong or what went right. I know they followed a video guide from http://www.youtube.com/user/muddymuddymuddmann.

I saw the video and it was very helpful I want to follow muddymuddymuddmans video guide to create my sterling engine

Materials:

Tin can

Hot glue gun

2 CD's

Metal Coat Hanger

Sealant

Week1 Narrative

Websites that I used to understand how sterling engines work

http://www.howstuffworks.com/stirling-engine.htm

http://en.wikipedia.org/wiki/Stirling_engine

Link to my video guide:

http://www.youtube.com/user/muddymuddymuddmann

Assign Task2
Record what you are planning on doing for the team during the weekend between week1 and week2 of the project here.

Compare actual work done to Task2
Made a rough sketch of the sterling engine in google sketch up.

Total time spent in Week 2: 2 hours

Week2 Narrative
Upload photos to wikimedia. Upload video to youtube. Convert all spreadsheets, documents, and presentations to wiki format and create wiki subpage of your page for each of them. Link to them here in a narrative that tells a story. High light the problems (engineering problems) you had and how you solved them.

Week2 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Assign Task3
Make a google sketch-up design of the sterling engine. Email teacher about parts,materials

Compare actual work done to Task3
• Designed a sketch of a sterling engine I want to resemble on Google Sketch Up. I wanted to make a simple design. Had difficulty modeling the metal rod that runs horizontally from one end of the displacer to the other. The metal rod should be bent in 90° angles but sketch up can not extend objects on a smooth surface.

•Total Time Spent: 1.5 hours

Assign Task4
•Start building the sterling engine.

•Compile and buy necessary materials.

Week 4 Narrative
Designed a rough mock up of the sterling engine I want to create. The rough draft includes the displacer, the fly wheels and the cylander. The materials used were a mango juice bottle, tooth picks, cardboard paper, electrical tape, and two CD's. I could not model the crankshaft because of its 90 degree curves. This is goIng to be a problem for when I attempt to make the real crank shaft. The two cylanders are 6cm and 4 cm in length. Total time spent: 45 minutes. I also learned how to use Picasa 3, a google app that stores pictures and documentation so it can be stored online.

Compare actual work done to Task4
https://picasaweb.google.com/110418435783924728102/ScreenCaptures#5685746997829212674

Week4 Peer Review
Go to each team mates weekly summary wiki page. Read their activities and narrative. Then go the associated discussion page. Say something positive on this page. Try some constructive criticism. Add your name and a signature ~ by entering four tildes in a row to create a time and date stamp. Create a new category if another team mate has already commented here.

Complete Project Page
Follow the "project done" format.

title: User:Mbaig7172/enes100/engine


text:
Portal:Advanced General Studies/WikiProjects

Controversies in Science: A first year university course to discuss opposing scientific (not moral) views on various scientific topics.


text:
Controversies in Science

Controversies:
 * /Water fluoridation/
 * /Was there a mitochondrial Eve?/
 * /What killed the dinosaurs/?
 * /RNA world vs metabolism first/
 * /Are humans causing global warming/?
 * nuclear power greener?
 * recycling
 * big bang
 * panspermia
 * LHC black hole risk?

template
Template:Critique of article

title: Controversies in Science


text:
Big bang

(from Controversies in Science) Hubble discovered that the farther galaxies were from us, the faster they statistically tend to be traveling away from us. This means that the galaxies tend to be spreading away from each-other, and in prior times must have been closer together. Going far enough back in time then, the matter of the universe must have been explosively spreading apart. This is referred to as a big bang, and that observation alone is enough to prove that the big bang is an accurate description of our universe down to much earlier times. Whether people realize it or not, the only question relevant to the validity of the Big bang is just how far back in time this description of the universe is accurate. Really it comes down to the question of how far back does the "classical big bang" theory, as a description of the universe which is described by the Friedmann–Lemaître–Robertson–Walker metric, work before it breaks in its description of the universe Vs what other kind of "big bang theory" works better going farther back. But, no matter what kind of theory may work better at earlier times, it MUST yield the big bang description over the time scales for which that description is already known to be valid. As such it must be "a" massive explosion of gases that created everything we know today.

Expansion is accelerating, Big bang theory is fact
The boundaries of the universe are moving because the composed homogeneous isotropic cosmic fluids. Since the boundaries are moving, it will cause a negative pressure which will equal to the energy. This will cause the universe to expand at an accelerated rate. The method to this was that the scientists measure how far the red stars are and measure the growth acceleration of the star. The results were that the dark energy is negative which is causing growth acceleration of the stars which proves that the big bang theory is correct.

Dark energy supports the classical Big Bang
Astronomers observed that the Universe appears to still be in the process of expansion, the rate of which is speeding up. This observation strongly suggests that the Universe contains dark energy, which is believed to be responsible for this increased rate of speed. Scientists currently believe that 68.3% of the universe is comprised of dark energy.

One possible theory as to why dark energy causes an increased rate of expansion suggests that there is not enough matter to slow expansion. Using this theory, expansion would continue until the Universe reaches the Big Chill. Alternatively, it would expand to such a point that it would begin to retract causing a state known as the Big Crunch.

discovery of accelerated expansion
The universe is not only still expanding, the expansion is accelerating! This supports the big bang, because if it's expanding, a long time ago it must have been smaller, which is the principle of big bang.

Astronomers support the big bang theory
The big bang theory is a comprehensive explanation of how the universe came to existence.

Always Being Tested
The big bang theory is always being tested, therefore, more knowledge is gained to support the theory.

Dueterium found in the universe matches that which was predicted to exist due to the big bang
First, Deuterium abundance does not have a current known cosmological explanation and is therefore associated with the big bang as this is the only force capable of creating an abundance. The same is true for other rare elements. Second, the discovery of blue dwarf galaxies that have an abundance of light elements such as helium and a scarcity of heavy elements such as oxygen and neon show that these are young systems, which is significant due to their positioning.

The 4He Measurements Predict Big Bang
They have found that the 4He measurements, which the theory underestimated is now vindicated by a more accurate theory.

Support of Many Sciences
There are many scientific fields that support the big bang theory. Including cosmology, astronomy, quantum physics and chemistry.

Scientists lacking creditability
Individuals who refute the big bang theory fail to mention the scientists and their credentials that support them. Further research has shown that many of these scientists are from Creationists Research Institute.

Public Representations
Highly influential public figures misunderstand the big bang theory and therefore misrepresent the theory to the public.

Understanding of the structure of energy leads to incorrect arguments against big bang theory
Einstein's Theory of Space and Time asserts that energy and light are smooth; leading to the assumption that cosmic background radiation (CBR) would be evenly distributed when observed. CBR observations have shown that radiation fluctuates over the observed area, this suggests that the big bang theory is incorrect. However, because energy is filled with hills and valleys (it is not smooth), it makes sense that we would see varying densities when observing CBR. Think of a desk, at the macro level it appears to us as smooth, but micro observations prove otherwise, this same error is akin to what's happening with the CBR related arguments disproving big bang theory.

Evidence for this error in Einstein's theory comes from the introduction of Quantum Physics to Space Time Physics supported by Stephen Hawking's Theory of Hawking Radiation which argues black holes convert energy information into different forms.

The Universe as made up of plasma
In 1896, Kristian Birkeland introduced the idea of Plasma Astrophysics and Cosmology. He believes that the universe is filled entirely of plasma and that the idea of a universal force (i.e. The Big Bang Theory) creating matter is flawed in theory due to the basis of this study. Birkeland observed that plasma moves and flows in the same manner in the laboratory as it does in space. Essentially this theory supports the universal concept that matter was not created through a universal force, but rather was always present.

includes the possibility of theoretical forces
The Big bang theory allows for dark energy to exist. Although observations are consistent with its existence, a material source for its tensor $$\lambda g^{\mu}_{\nu}$$ has yet to be discovered.

Stars Older than the Universe?
A particular choice of time coordinate must be made when quoting the age of the universe. The standard cosmological time coordinate for doing this corresponds to an age of 13.7 billion years old. Astrophysicists Jayant Narlikar and Vijay Mohan of the Inter-University Centre for Astronomy and Astrophysics discovered a cluster of about 50 stars which they claim to be 20 billion years old. If as they claim, the same time coordinate was used, then this would mean that the stars were born 6.3 billion years before the Big Bang is said to have occurred. The age of the stars was determined in the Hubble observatory and a Chilean observatory to study the color of the stars and the way they had been emitting energy. The stars were found to be Red Giants (stars in their late stages of life). They claim that it is therefore likely that our universe was formed through a series of events rather than just one "Big Bang". Narlikar and Mohan (and here are the two key words) "plan to" publish their findings in an international journal since the current community of Big Bang opposition is currently miniscule.

Slow and Steady Wins the Race
In order to properly understand Bondi’s theory of the steady state which rivals the Big Bang theory, we must first examine the 3 basic laws of physics. He asserts these laws hold true under any circumstance and can even be related to our universe. According to Bondi matter must be created at a continuous slow and steady rate as opposed to an initial explosion of matter as proposed by the Big Bang Theory. His theory can be proven using the tried and true laws of physics which are tangible and can proven again and again in any circumstance. He claims the big bang theory abandons these laws and requires assumptions to be made that do not follow these principles.

Inflationary Big Bang Vs Classical Big Bang
Explanation of how the Inflationary Theory disproves the Big Bang Theory by suggesting that there are numerous cosmic fire balls constantly expanding and inflating versus one cosmic fire ball creating the universe. The Inflationary Theory assumes that the universe is constantly evolving from mutations of cosmos from the parent cosmo. Hence the support of the six points made in the methodology section of this theory.

Inflation lacking observation of its field (Group 6)
There is no direct evidence that the inflation field needed for the inflationary big bang exists.

Möbius strip, infinite space?
The Big Bang theory requires the universe to expand. There are no lengthwise boundaries on a Möbius strip although the width is limited. The Möbius strip helps to explain how the universe is able to expand by looking at it as a balloon. If the Möbius strip is thought of as a balloon then the width boundary would be eliminated.

The Universe Has No Beginning? Doubts about the classical Big Bang Theory
There is considerable possibility that time reversal exists in the universe. This possibility increases upon the greater discoveries of black matter. Even if black matter were to be removed from the theory, the Big Bang Theory would be hypothetically removed as well since the Matthews claims the Big Bang Theory could not exist without it. Since black matter has not yet been proven to exist, he claims that it is therefor too early to assess the validity of the Big Bang theory.

title: Big bang


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User:Egm6321.f11.team1.colsonfe/HW6

= R*6.6 Reverse Engineering ODE Equations =

Given
Trial solutions:

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

$$
 * $$\frac{e^{rx}}{x^2}, r=\text{constant}$$
 * $$\displaystyle (Equation\;6.6.1)
 * $$\displaystyle (Equation\;6.6.1)
 * }
 * }

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

$$
 * $$\frac{e^{rx}}{\sin x}, r=\text{constant}$$
 * $$\displaystyle (Equation\;6.6.2)
 * $$\displaystyle (Equation\;6.6.2)
 * }
 * }

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

$$
 * $$\displaystyle r^2+3=0$$
 * $$\displaystyle (Equation\;6.6.3)
 * $$\displaystyle (Equation\;6.6.3)
 * }
 * }

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

$$
 * $$\displaystyle r_1=2$$
 * $$\displaystyle (Equation\;6.6.4)
 * $$\displaystyle (Equation\;6.6.4)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$
 * $$r_2(x)=\frac{1}{x+1}$$
 * $$\displaystyle (Equation\;6.6.5)
 * $$\displaystyle (Equation\;6.6.5)
 * }
 * {| style="width:100%" border="0" align="left"
 * {| style="width:100%" border="0" align="left"

$$.
 * $$\displaystyle (r-r_1)[r-r_2(x)]=0$$
 * $$\displaystyle (Equation\;6.6.6)
 * $$\displaystyle (Equation\;6.6.6)
 * }
 * }

== Find ==

Find a homogeneous L2-ODE-VC that accepts the trial solutions Equation 6.6.1 and Equation 6.6.2, and their respective characteristic equations, Equation 6.6.3, and Equation 6.6.4 thru Equation 6.6.6.

Solution
I will mirror the approach laid out in Meeting 36.

Multiply the trial solution of Equation 6.6.1 (and its derivatives) by unknown coefficients $$\displaystyle a(x)$$.

$$\left[\frac{e^{rx}}{x^2}\right]\times a_0(x)$$

$$\left[\frac{d}{dx}\left(\frac{e^{rx}}{x^2}\right)=\left(r-\frac{2}{x}\right)\frac{e^{rx}}{x^2}\right]\times a_1(x)$$

$$\left[\frac{d^2}{dx^2}\left(\frac{e^{rx}}{x^2}\right)=\left(r^2-\frac{4r}{x}+\frac{6}{x^2}\right)\frac{e^{rx}}{x^2}\right]\times a_2(x)$$

Now equate the sum of the above three results to the product of the trial solution (Equation 6.6.1) and the characteristic equation (Equation 6.6.3):

$$\frac{e^{rx}}{x^2}\left[a_2\left(r^2-\frac{4r}{x}+\frac{6}{x^2}\right)+a_1\left(r-\frac{2}{x}\right)+a_0\right]=\frac{e^{rx}}{x^2}(r^2+3)=0$$

$$a_2r^2+\left(\frac{4a_2}{x}+a_1\right)r+\left(\frac{6a_2}{x^2}-\frac{2a_1}{x}+a_0\right)=r^2+3$$

Comparing the polynomial coefficients of $$\displaystyle r$$ yields the following:

$$a_2=1, \quad a_1=-\frac{4}{x}, \quad a_0=3-\frac{48}{x^2}$$

If we define $$f:=\frac{e^{rx}}{x^2}$$, the following L2-ODE-VC will be satisfied:

Now the same technique will be applied to Equation 6.6.2 and its characteristic equation. Even though one root is a function of x, the technique is still valid as long as one root is constant. See page (36-2) in Meeting 36.

Multiply the trial solution of Equation 6.6.2 (and its derivatives) by unknown coefficients $$\displaystyle a(x)$$.

$$\left[\frac{e^{rx}}{\sin x}\right]\times a_0(x)$$

$$\left[\frac{d}{dx}\left(\frac{e^{rx}}{\sin x}\right)=\left(r-\cot x\right)\frac{e^{rx}}{\sin x}\right]\times a_1(x)$$

$$\left[\frac{d^2}{dx^2}\left(\frac{e^{rx}}{\sin x}\right)=\left(r^2-2r\cot x+\cot^2x+\csc^2x\right)\frac{e^{rx}}{\sin x}\right]\times a_2(x)$$

Now equate the sum of the above three results to the product of the trial solution (Equation 6.6.2) and the characteristic equation (Equation 6.6.6):

$$\frac{e^{rx}}{\sin x}\left[a_2\left(r^2-2r\cot x+\cot^2x+\csc^2x\right)+a_1\left(r-\cot x\right)+a_0\right]=\frac{e^{rx}}{\sin x}(r-r_1)[r-r_2(x)]=0$$

$$a_2r^2+\left(a_1-2a_2\cot x\right)r+\left(a_0-a_1\cot x +\cot^2x+\csc^2x\right)=r^2-2r-\frac{r}{x+1}+\frac{2}{x+1}$$

Comparing the polynomial coefficients of $$\displaystyle r$$ yields the following:

$$a_2=1, \quad a_1=2\cot x-\frac{1}{x+1}-2, \quad a_0=\cot x\left(2\cot x-\frac{1}{x+1}-2\right)-\cot^2x-\csc^2x+\frac{2}{x+1}$$

If we define $$f:=\frac{e^{rx}}{\sin x}$$, the following L2-ODE-VC will be satisfied:

= R*6.8 Find Solutions to L2-ODE-VC with Trial Solution and Variation of Parameters with Excitation=

Given
Two Non-Homogeneous L2-ODE-VC

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

$$
 * $$\displaystyle (x-1)y''-xy'+y=f(x)$$
 * $$\displaystyle (Equation\;6.8.1)
 * $$\displaystyle (Equation\;6.8.1)
 * }
 * }

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

$$
 * $$\displaystyle xy''+2y'+xy=f(x)$$
 * $$\displaystyle (Equation\;6.8.2)
 * $$\displaystyle (Equation\;6.8.2)
 * }
 * }

== Find ==

Find the 1st homogeneous solution by trial solution.

Find the complete solution by variation of parameters with the following excitation:

 * $$\displaystyle f(x)=x$$

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

 * $$\displaystyle f(x)=\exp(\alpha x)$$

Part 1
Find the 1st homogeneous solution by trial solution. Since we are looking for homogenous solution, $$\displaystyle f(x)=0$$. For Equation 6.8.1 we will assume the form $$\displaystyle y(x)=e^{rx}$$, where $$\displaystyle r$$ is an undetermined coefficient. Thus Equation 6.8.1 becomes:

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

$$\displaystyle (x-1)r^2-xr+1=0$$

$$\displaystyle [(x-1)r-1](r-1)=0$$

Thus the two roots are:

$$\displaystyle r_1=1$$

$$\displaystyle r_2=\frac{1}{x-1}$$

The second root is not valid, since it undermines the assumption of form in the trial solution due to it being a function of x. See R*6.3 for additional detail. Therefore the 1st homogeneous solution for Equation 6.8.1 is:

For Equation 6.8.2 we will assume the form $$\displaystyle y(x)=\frac{\sin rx}{x}$$, where $$\displaystyle r$$ is an undetermined coefficient. Thus Equation 6.8.2 becomes:

$$x\left(-\frac{(r^2x^2-2)\sin rx +2rx\cos rx}{x^3}\right)+2\frac{rx\cos rx -\sin rx}{x^2}+x\left(\frac{\sin rx}{x}\right)=0$$

$$-\frac{(r^2x^2-2)\sin rx +2rx\cos rx}{x^2}+2\frac{rx\cos rx -\sin rx}{x^2}+\sin rx=0$$

$$\frac{-r^2x^2\sin rx}{x^2}+\sin rx=0$$

$$\displaystyle -r^2\sin rx+\sin rx=0$$

$$\displaystyle 1-r^2=0$$

Thus the two roots are:

$$\displaystyle r_1=1$$

$$\displaystyle r_2=-1$$

Therefore, taking note that sine is an odd function, the 1st homogeneous solution for Equation 6.8.2 is either:

Section 1
Find the complete solution by variation of parameters to

$$\displaystyle (x-1)y''-xy'+y=x$$

$$\displaystyle y''-\frac{x}{x-1}y'+\frac{1}{x-1}y=\frac{x}{x-1}$$

Thus following the syntax of Meeting 34,

$$a_1(x)=-\frac{x}{x-1}$$

$$f(x)=\frac{x}{x-1}$$

We also deduced from Part 1 that

$$\displaystyle u_1(x)=e^x$$

Now via (4) on (34-5) of Meeting 34:

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

$$
 * $$u_2(x):=u_1(x)\int\frac{1}{u_1^2(x)}\exp\left[-\int a_1(x)dx\right]dx$$
 *
$$\displaystyle (Equation\;6.8.3)
 *
$$\displaystyle (Equation\;6.8.3)
 * }
 * }

$$u_2(x):=e^x\int\frac{1}{e^{2x}}\exp\left[-\int -\frac{x}{x-1}\right]dx$$

$$\displaystyle u_2(x)=-x$$

Now via (1) on (34-6) of Meeting 34:

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

$$
 * $$y_P(x)=u_1(x)\int\frac{1}{h(x)}\left[\int h(x)\frac{f(x)}{u_1(x)}dx\right]dx$$
 *
$$\displaystyle (Equation\;6.8.4)
 *
$$\displaystyle (Equation\;6.8.4)
 * }
 * }

Where

$$h(x)=u_1^2(x)\exp\left[\int a_1(x)dx\right]$$

$$\displaystyle h(x)=\frac{e^x}{x-1}$$

So

$$y_P(x)=e^x\int\frac{1}{\frac{e^x}{x-1}}\left[\int \frac{e^x}{x-1}\frac{\frac{x}{x-1}}{e^x}dx\right]dx$$

To find the complete solution we use (3) on (34-5) from Meeting 34, where constants are determined by initial conditions:

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

$$
 * $$\displaystyle y(x)=k_1u_1(x)+k_2u_2(x)+y_P(x)$$
 *
$$\displaystyle (Equation\;6.8.5)
 *
$$\displaystyle (Equation\;6.8.5)
 * }
 * }

Section 2
Find the complete solution by variation of parameters to

$$\displaystyle (x-1)y''-xy'+y=\sin x$$

$$\displaystyle y''-\frac{x}{x-1}y'+\frac{1}{x-1}y=\frac{\sin x}{x-1}$$

Thus following the syntax of Meeting 34,

$$a_1(x)=-\frac{x}{x-1}$$

$$f(x)=\frac{\sin x}{x-1}$$

$$\displaystyle u_1(x)=e^x$$

The solution is the same as that of Section 1, except now

$$y_P(x)=e^x\int\frac{1}{\frac{e^x}{x-1}}\left[\int \frac{e^x}{x-1}\frac{\frac{\sin x}{x-1}}{e^x}dx\right]dx$$

Section 3
Find the complete solution by variation of parameters to

$$\displaystyle (x-1)y''-xy'+y=\exp(\alpha x)$$

$$\displaystyle y''-\frac{x}{x-1}y'+\frac{1}{x-1}y=\frac{\exp(\alpha x)}{x-1}$$

Thus following the syntax of Meeting 34,

$$a_1(x)=-\frac{x}{x-1}$$

$$f(x)=\frac{\exp(\alpha x)}{x-1}$$

$$\displaystyle u_1(x)=e^x$$

The solution is the same as that of Section 1, except now

$$y_P(x)=e^x\int\frac{1}{\frac{e^x}{x-1}}\left[\int \frac{e^x}{x-1}\frac{\frac{\exp(\alpha x)}{x-1}}{e^x}dx\right]dx$$

Section 4
Find the complete solution by variation of parameters to

$$\displaystyle xy''-2y'+xy=x$$

$$\displaystyle y''-\frac{2}{x}y'+y=1$$

Thus following the syntax of Meeting 34,

$$a_1(x)=-\frac{2}{x}$$

$$\displaystyle f(x)=1$$

We also deduced from Part 1 that

$$\displaystyle u_1(x)=\frac{\sin x}{x}$$

Now via Equation 6.8.3

$$u_2(x):=\frac{\sin x}{x}\int\frac{1}{\frac{\sin^2 x}{x^2}}\exp\left[-\int -\frac{2}{x}\right]dx$$

Now use Equation 6.8.4, where

$$h(x)=u_1^2(x)\exp\left[\int a_1(x)dx\right]$$

$$\displaystyle h(x)=\frac{\sin^2x}{x^4}$$

So

$$y_P(x)=\frac{\sin x}{x}\int\frac{1}{\frac{\sin^2x}{x^4}}\left[\int \frac{\sin^2x}{x^4}\frac{1}{\frac{\sin x}{x}}dx\right]dx$$

To find the complete solution use Equation 6.8.5

Section 5
Find the complete solution by variation of parameters to

$$\displaystyle xy''-2y'+xy=\sin x$$

$$\displaystyle y''-\frac{2}{x}y'+y=\frac{\sin x}{x}$$

Thus following the syntax of Meeting 34,

$$a_1(x)=-\frac{2}{x}$$

$$\displaystyle f(x)=\frac{\sin x}{x}$$

$$\displaystyle u_1(x)=\frac{\sin x}{x}$$

The solution is the same as that of Section 4, except now

$$y_P(x)=\frac{\sin x}{x}\int\frac{1}{\frac{\sin^2x}{x^4}}\left[\int \frac{\sin^2x}{x^4}\frac{\frac{\sin x}{x}}{\frac{\sin x}{x}}dx\right]dx$$

Section 6
Find the complete solution by variation of parameters to

$$\displaystyle xy''-2y'+xy=\exp(\alpha x)$$

$$\displaystyle y''-\frac{2}{x}y'+y=\frac{\exp(\alpha x)}{x}$$

Thus following the syntax of Meeting 34,

$$a_1(x)=-\frac{2}{x}$$

$$\displaystyle f(x)=\frac{\exp(\alpha x)}{x}$$

$$\displaystyle u_1(x)=\frac{\sin x}{x}$$

The solution is the same as that of Section 4, except now

$$y_P(x)=\frac{\sin x}{x}\int\frac{1}{\frac{\sin^2x}{x^4}}\left[\int \frac{\sin^2x}{x^4}\frac{\frac{\exp(\alpha x)}{x}}{\frac{\sin x}{x}}dx\right]dx$$

= References =

title: User:Egm6321.f11.team1.colsonfe/HW6


text:
User talk:Palluri9407/enes100/Electric Cars v.2

Week 0
10/10 .. week 0 1sfoerster 23:38, 15 November 2011 (UTC)

Week One
Good job. This week you can help me with the ekart's circuit. Criveros0248, 1sfoerster 19:51, 20 November 2011 (UTC).

10/10/30 ... what are your specifications of the esc? how did you program it? the links are to brushless motors that require different esc's ... 1sfoerster 19:06, 21 November 2011 (UTC)

0/5/0 ... for commenting on team mates page

Thanks for your help on the braking system for the ekart. Try posting all the detailed pictures you took of your work. Criveros0248, 1sfoerster 20:24, 04 December 2011 (UTC).

10/10/50 ... good job 1sfoerster 19:32, 5 December 2011 (UTC)

It was a pleasure working with you. Thanks. Criveros0248, 1sfoerster 20:08, 11 December 2011 (UTC).

0/0/0 .. nothing to grade


text:
User talk:Jhasslinger/enes100/550 HCJ

Week 0
10/10 .. 1sfoerster 23:44, 15 November 2011 (UTC)

Week 1
0/0/0 .. nothing to grade 1sfoerster 20:09, 21 November 2011 (UTC)

Week 2
0/0/0 .. nothing to grade 1sfoerster 14:22, 28 November 2011 (UTC)

title: User talk:Jhasslinger/enes100/550 HCJ


text:
Computer model

A computer model is a computer program that is designed to simulate what might or what did happen in a situation. They are used in many ways including in economics and sciences such as astronomy, physics and biology.

Computer models are also used in fields such as earthquake performance simulation and making models of buildings. Computer models can accurately predict many things in the future provided they have information data from previous similar situations. However they are not always 100% accurate.

Other pages

 * Images for Computer model

title: Computer model


text:
Talk:Quantum harmonic oscillator

There must be a more straightforward way to reword the section related to
 * $$\frac{d^2 \psi(x)}{dx^2} = x^2 \psi(x)$$

--HappyCamper 23:14, 14 November 2011 (UTC)

title: Talk:Quantum harmonic oscillator


text:
Template:Sms

&

title: Template:Sms


text:
Template:Sms/doc

Creates an invisible sortkey for tables. The argument is prepended with  and hidden with. (Not to be confused with w:Template:Sms, which is about ships.)

title: Template:Sms/doc


text: Category:Language user templates/da

title: Category:Language user templates/da


text: File:Arduino breadboard.jpg

title: File:Arduino breadboard.jpg


text:
User talk:7yl4r

I don't come here often, if you need to get in contact please email me at murray.tylar+wiki at gmail.

Hello there, i am interested in contributing to the robotics section of wikiversity too, would you like to discuss how we should go about putting together some lessons? --Sirnails (discuss • contribs) 13:34, 10 March 2014 (UTC)
 * This user has not edited since 2011, and may not be seeing contributions here. You could try emailing the user. --Abd (discuss • contribs) 15:58, 10 March 2014 (UTC)
 * Yeah, I've been out a while and don't even remember what was going on here, but I'm game for working on the robotics section a bit. 7yl4r (discuss • contribs) 04:43, 11 March 2014 (UTC)
 * Welcome back! --Abd (discuss • contribs) 17:13, 11 March 2014 (UTC)

title: User talk:7yl4r


text:
User talk:0ctobrainz

 Hello 0ctobrainz, 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! --Abd 02:16, 15 November 2011 (UTC)

title: User talk:0ctobrainz


text:
User talk:Areil314

 Hello Areil314, 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! --Abd 02:22, 15 November 2011 (UTC)

Template
Is Critique of article template intended to be something that is to be repeated on many pages? --HappyCamper 12:47, 11 January 2012 (UTC)
 * Yes --Areil314 12:48, 11 January 2012 (UTC)
 * I think this might be helpful...for repetitive items on Wikiversity they typically go into the template namespace. Take a look at Template:Critique of article and see if putting on your pages has the effect you are looking for. --HappyCamper 12:56, 11 January 2012 (UTC)
 * thanks, I'll try that out today Areil314 12:58, 11 January 2012 (UTC)

Critique of article
I think you should make your changes here Template:Critique of article and not here, because this is the template page you want to edit. --Reder 22:41, 17 January 2012 (UTC)
 * thanks, I get it nowAreil314 23:09, 17 January 2012 (UTC)

Controversies in science
I see from your user page and from some old contributions that you have an interest in this. It's a topic that has long interested me, and particularly what is called the "demarcation problem," but also specific controversies. Let me know if you are still interested. There are many possibilities here. There is a substantial resource on Cold fusion, which is a case where popular opinion -- among scientists! -- may differ from what is found in peer-reviewed mainstream journals, say over the last decade, something I find particularly fascinating. Scientists in some cases get their news from the newspaper like anyone else, if they don't read in a field that they consider to have been rejected years earlier. --Abd (discuss • contribs) 20:31, 24 February 2014 (UTC)
 * I'd love to have a cold fusion talk with you. I know a little but would like to understand why you feel it's viable. When would you be available? Areil314 (discuss • contribs) 21:47, 24 February 2014 (UTC)
 * Well, if by talk you mean on the phone, that can be arranged. Send me an email.

 * As to cold fusion being "viable," that must mean "practical." We do not know, for sure, that cold fusion is practical. Nor, in fact, do we know that for hot fusion. Both are "real." We know what hot fusion is, very well. Reality and viability are not the same thing.

 * Cold fusion is real, we know from confirmed experimental work, but we don't know what it is, that is, what mechanism(s) is or are involved. There are now commercial enterprises claiming to have some kind of apparently low-energy nuclear reaction, in devices under development, but this is highly controversial. The patent situation with cold fusion is such that these companies cannot disclose their IP, because it's not protected. (That's all a part of the "Scientific fiasco of the century," as the skeptic Huizenga called it. The Patent Office, since very early on -- before investigation had been adequate -- considered cold fusion "impossible," i.e., any device claiming to be based on the discoveries of Pons and Fleischmann could not possibly work, like perpetual motion. That can be overcome with a working device, but, then, patent officials have refused to examine devices claimed to be working. After all, "nuclear" blah blah. Even though these devices clearly do not generate significant radiation.)

 * The pseudoskeptics think that everyone involved is blinded by dreams of limitless energy, which is a radical mischaracterization of what actually happend. This was basic research, attempting to confirm the expectations of the researchers that any deviation from the standard predictions of quantum mechanics, based on approximation necessary for the complex environment of the solid state ("condensed matter", which is very cold by comparison with hot fusion plasma), would be below experimental ability to measure. They were wrong. They were not nuclear physicists, and they made certain errors, but nobody's perfect! Their basic findings showing anomalous heat were confirmed hundreds of times. And something very specific and predictable, discovered in 1991 -- and also not expected -- has also been confirmed. The heat results are chaotic, but not the correlation of heat with helium. It's reliable and predictable, and the value is consistent with the value for deuterium fusion to helium. That does not mean that the reaction is d+d -> He-4, but that it likely starts with deuterium and ends with helium.

 * That, in a nutshell, is why I accept (not "believe") that cold fusion is real. The specific effect discovered was chaotic and extremely difficult to control, thus difficult to replicate. But it was done.

 * Our cold fusion resource is also a bit chaotic, it needs work! But the work will be done. --Abd (discuss • contribs) 22:02, 24 February 2014 (UTC)

Sure, I'll email you through the Wikiversity interface. --Abd (discuss • contribs) 00:12, 25 February 2014 (UTC)

 * How do I get email through the Wikiversity interface? Areil314 (discuss • contribs) 01:05, 25 February 2014 (UTC)

 * You check your email, that is, the email you used when you registered and agreed to accept email. I have now sent you an email.

 * You apparently did enable email, because I see "Email this user" on the left, and if I click on it, an edit screen pops up. If the address is obsolete, fix that and send me an email! (You can still send me a mail with an obsolete address, but then, I won't have a usable email address to respond to! --Abd (discuss • contribs) 02:19, 25 February 2014 (UTC)

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 * File:Irish Fluoridation.jpg

MaintenanceBot (discuss • contribs) 15:18, 16 April 2016 (UTC)

title: User talk:Areil314