OpenLLM-France/wikimedia huggingface dataset:
# How people learn: brain, mind, experience and school
## Why is this study group needed?

Wikiversity needs to be able to plan and create effective learning experiences for participants.
"Technology can help to create an active environment in which students not only solve problems, but also find their own problems. This approach to learning is very different from the typical school classrooms, in which students spend most of their time learning facts from a lecture or text and doing the problems at the end of the chapter." Technology to Support Learning --JWSchmidt 03:49, 18 December 2006 (UTC)

## What does this study group hope to archive?

This study group aims to identify how this can be done drawing on the information provided at the website How people learn: brain, mind, experience and school.

## Who is this project for?

This project is for anyone who is interested in how to improve learning.

### Active participants

* Mystictim 20:39, 16 December 2006 (UTC)
* --JWSchmidt 03:43, 18 December 2006 (UTC)
* vannin 23 February 2007 (UTC)
* Dionysios $^{(talk)}$, a Participant in the Wikiversity School of Advanced General Studies, Date: 2007-07-06 (July 6, 2007) Time: 1206 UTC

## When will this project take place?

The initial phase of this project will be conducted during January 2007.

## How will this project be conducted?

If you would like to take part in this project you can begin by reading the executive summary of the website How people learn: brain, mind, experience and school. The main strand of this project will be a critical reading of this website.

## Resources
### Related learning projects

* Learning to learn a wiki way
* About learning a report by Demos study group aims to investigate the implications of this report for Wikiversity in general and this learning project specifically.

### Websites

How people learn: brain, mind, experience and school

### Documents

About learning

## Project Outcomes
### Selected quotes from the report

"Social opportunities also affect motivation. Feeling that one is contributing something to others appears to be especially motivating (Schwartz et al., in press). For example, young learners are highly motivated to write stories and draw pictures that they can share with others. First graders in an inner-city school were so highly motivated to write books to be shared with others that the teachers had to make a rule: "No leaving recess early to go back to class to work on your book" (Cognition and Technology Group at Vanderbilt, 1998)" Learning and Transfer
# How things work college course/Air drag drop experiment

THIS PAGE NEEDS TO BE MOVED TO A SUPPATE OF Physics and Astronomy Labs

## How much does air drag slow a falling object?

This is a high level investigation that can be appreciated at all levels. We will investigate this experimentally using no equipment except a ruler. Theoretical investigations will be at the advance Matlab/Calculus level.

### Initial results

We dropped a variety of objects from the top second floor guardrail outside the Physics lab.
* The estimated height was either 17 or 20 feet, made using only the one foot squares on floor, body height, and a belief that floors are typically 10 feet.
* Just for fun, each class will estimate that height using only paper and the one-foot squares on the floor.
* Clay, steel, and styrofoam balls were dropped. Also dropped was a ping-pong ball.
* The first question is this: Is a clay ball an acceptable proxy for a steel ball? (We don't want to drop steel balls because they damage the floor. In our investigation a cushion was placed on the floor for the steel ball.
** The answer was "definitely" bot one inch and half inch diameter clay ball fell as fast as the 3/4 inch steel ball.
* The required "head start" was about 1 meter for the ping pong ball.
** Mass = 2.4 gm = .0024 kg
** Diameter = 40 mm = 0.04 m

## Copied from Wikipedia

Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation:
    $F_{D}\,=\,{\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A$
where
    F$_D$ is the drag force,
    ρ is the density of the fluid,
    v is the speed of the object relative to the fluid,
    A is the cross section area, and
    C$_D$ is the drag coefficient – a dimensionless number.
The drag coefficient depends on the shape of the object and on the Reynolds number:
    $R_{e}={\frac {vD}{\nu }}$
where D is some characteristic diameter or linear dimension and ν is the kinematic viscosity of the fluid (equal to the viscosity μ divided by the density). At low Reynolds number, the drag coefficient is asymptotically proportional to the inverse of the Reynolds number, which means that the drag is proportional to the speed. At high Reynolds number, the drag coefficient is more or less constant. The graph to the right shows how the drag coefficient varies with Reynolds number for the case of a sphere.

## Matlab simulation code

This code simulates the situation with and without air drag.

## References and links

* ↑ https://en.wikipedia.org/w/index.php?title=Drag_(physics)&oldid=628942721
* ↑ Note that for the Earth's atmosphere, the air density can be found using the barometric formula. It is 1.293 kg/m$^3$ at 0 °C and 1 atmosphere.
# How things work college course/Breaking broomstick demonstration

This is not really a lab but a demonstration. I am looking for ways to make it more educational. These are ideas I have jotted down.

## Waves that travel at the same speed for all wavelengths

* Light in vacuum
* Sound
* Transverse and longitudinal waves on a string
* Shallow water waves (approximately)

## Waves that travel at a speed that depends on wavelength

* Bending waves.
** AJP
** Youtube demonstration at Wright State showing how things can go wrong
** Slow motion youtube demonstration
* Whistler waves
* Schrodinger waves
* Light waves in materials
** Explains chromatic abberation
** Used to calculate how much plasma is between the stars
# How the sky moves
## Rotating Earth

The earth spins on a tilted axis much like a top. therefore;
* Stars like the sun rise from the east and go west
* Moving East or west doesn't change the stars you see. however moving North and South greatly changes the stars.
* An accurate diagram of the earth moving against the stars isn't very helpful in figuring out Where the stars are because, if your looking AT the earth you don't share the same perspective as people ON the earth do.
* Rather you need a different perspective.

## The celestial sphere; a different perspective

The celestial sphere is an imaginary rotating sphere of "gigantic radius", concentric and coaxial with the Earth. All objects in the sky can be thought of as lying upon the sphere. Projected from their corresponding geographic equivalents are the celestial equator and the celestial poles.
This sphere can be reduced to two dimensional maps; much in the same way that we can map a three dimensional map of the earth into a two dimensional map.
* If the map shows all the stars, the northern reaches will be highly distorted
* If we break the map into segments we can minimize distortion.
Most importantly, from our perspective the Earth doesn't seem to spin. Rather The celestial sphere seems to spin. it appears to spin (in the North) about the bright star polaris (which is very close to the north celestial pole). Thus we need to orient our two dimensional map to account for the movement of the earth. Keep in mind that our lattitude, north and south will determine how much of the celestial sphere we see.
if we live between the equator and the north pole, (most of the worlds population) in the far north we actually see the north stars after they have spun below the north star. Because of this and depending on how far north we live, we might see some of the constellation as the spin around the north star. These constellations are circumpolar (or visible all year round). (see activity).
people living further south will see more stars since they can see stars near the south celestial hemisphere.

## How the sky rotates during time and date

The celestial sphere rotates every 23 hours 56 minutes. The sun rotates every 24hours, thus moving against the backdrop of the stars. Thus both time and date come into play when determining what the stars will look like.
As the night get later the sky will rotate about the north star. Each night the sky will look four minutes later each night, with the evening sky swallowing early rising constellations and the morning sky, retreating and allowing you to see new constellations.
Thus when we're learning constellations. we first start by learning the North constellations, that in the most populate area of the world is visible year round. Next we learn each season; spring, summer, fall and winter. These will be the constellations visible shortly after dusk (when most people observe). If you still up later, you can begin to see the next season's stars. The advantage of staying up late to see the next season's stars is that you can see the same sight for a while 3-6months.
# Informal learning activities/PbH

*  [[w:{{{1}}} {{{2}}} {{{3}}}|{{{2}}}]]{{../{{{4}}}}} ({{{3}}})
This sets up an item in Places & Buildings lists, where {{{1}}} {{{2}}} {{{3}}} is the Wikipedia link, {{{2}}} is the name infix and the main name to be displayed, {{{4}}} is the country or area abbreviation, and {{{3}}} is the hint to the nature of the item.
# Informal learning activities/PBwMo

Places & Buildingsː M⇒ O__  O ther initialsː   Ac  Df
 Gi  Jl
(«»Mo⇓⇓)
 Pr
 Su  Vz
*  Majuba SAfrc
(Hill)   •  Mammoth USA
(Cave)   •  Manaslu Npl
(mountain)   •  Mancetter Englnd
(village)   •  Marrakesh Mrc
(city)   •  Maroilles Frnc
(commune)   •  Marshalsea Englnd
(prison )   •  Martello BrEmp
(tower)   •  Masuria Plnd
(region)  
*  Memel Blrs /Lthn
(River)   •  Memphis Egpt
(city )   •  Mercia Englnd
(kingdom )   •  Merv Trkmnstn
(oasis)   •  Messina Itly
(Strait)  
*  Michilimackinac USA
(region)   •  Milvian Itly
(Bridge)   •  Minas Cnd
(Basin)   •  Minsk Blrs
(city)   •  Miryang SthKr
(city)   •  Missolonghi Grc
(municipality)  
*  Mochlos Grc
(island)   •  Molland Englnd
(village )   •  Monza Itly
(comune)   •  Morea Grc
(kingdom )   •  Morelia Mxc
(city)   •  Morwenstow Crnwl
(parish)   •  Moulinette Cnd
(town )   •  Mountmellick Irlnd
(town)   •  Moytura Irlnd
(battleground)  
*  Mpumalanga SAfrc
(province)  
*  Mullingar Irlnd
(town)   •  Murrumbidgee Astrl
(River)
Places & Buildingsː N__
*  Naas Irlnd
(town)   •  Nadvirna Ukrn
(city)   •  Nafpaktos Grc
(town)   •  Nain Cnd
(Province)   •  Nairn Sctlnd
(town)   •  Najd SdArb
(region)   •  Namdaemun SthKr
(Gateway)   •  Namirembe Ugnd
(Hill)   •  Napanee Cnd
(town )   •  Naqada Egpt
(town)   •  Napton Englnd
(village)   •  Narenta Blkns
(river)   •  Narva Estn
(city)   •  Natron Egpt
(Valley)   •  Natural USA
(Bridge)   •  Nauvoo USA
(city )   •  Navan Irlnd
(town)  
* Nene Englnd
(River)   •  Neva Rsa
(River)   •  Newry NIrlnd
(city)  
*  Nicomedia Bthyn
(city )   •  Nikolskoe Rsa
(Cemetery)   •  Nine Englnd
(Stones)   • Nipissing Cnd
(Lake)  
*  Noel Park Englnd
(community)   •  Nordstrand Grmny
(peninsula)   •  Northwest Cnd
(Passage)  
*  Nuraghe Srdn
(tower)   •  Nussdorf Astr
(canal)  
*  Nyuserre Egpt
(Pyramid)
Places & Buildingsː O__
*  Ouagadougou BknFs
(city)   •  Oare Englnd
(village)   •  Oaxaca Mxc
(City)  
*  Oddingley Englnd
(village)  
*  Ohrid Mcdn
(city)  
*  Oise Blgm/Frnc  
(river)  
*  Ojai USA
(city)  
*  Olalla Cnd
(community)   •  Olivet Jrslm
(Mount)   •  Olney Englnd
(town)   •  Olomouc Mrv
(city)   •  Oltu Trky
(district)  
*  Ongar Englnd
(station)  
*  Orchomenus Grc
(city )   •  Orenburg Rsa
(city)   •  Orontes ME
(River)  
*  Osawatomie USA
(city )   •  Osnabrück Grmny
(city)   •  Osrhoene Msptm
(kingdom )   •  Ossetia Ccss
(region)   •  Ossory Irlnd
(kingdom )   •  Ostrołęka Plnd
(town)   •  Oswestry Englnd
(town)  
*  Otranto Itly
(comune)  
*  Oude Ind
(region)   •  Oudenaarde Blgm
(municipality)   •  Oughterard Irlnd
(town )   •  Ourcq Frnc
(river)   •  Ourense Glc
(Province)   •  Ouse Englnd
(River)  
*  Oxus ME
(River)
# Informal learning activities/PbG

* {{{1}}}  [[w:{{{1}}} {{{2}}}|{{{3}}}]]{{../{{{4}}}}} ({{{5}}})
This sets up an item in Places & Buildings lists, where {{{1}}} {{{2}}} is the Wikipedia link, {{{1}}} is the name prefix and {{{3}}} is the main name to be displayed, {{{4}}} is the country or area abbreviation, and {{{5}}} is the hint to the nature of the item.
# Informal learning activities/PBwPr

Places & Buildingsː P⇒ R__  O ther initialsː   Ac  Df
 Gi  Jl
 Mo
(«»Pr⇓⇓)
 Su  Vz
*  Palakkad Ind
(Fort)   •  Palermo Itly
(city)   •  Palk Ind/SrL  
(Strait)   •  Pamphylia Trky
(region )   •  Panopolis Egpt
(city)   •  Paphos Cyprs
(city)   •  Par Crnwl
(village)   •  Pasadena USA
(city)   •  Patiala Ind
(city)   • Novi  Pazar Srb
(city)  
*  Pelusium Egpt
(city )   •  Perast Mntngr
(town)   •  Pergamon Grc/Trky  
(city )   •  Perim Ymn
(island)   •  Petworth Englnd
(town )   •  Pewsey Englnd
(village)  
*  Phrygia Antl
(kingdom )  
*  Picenum Itly
(region )   •  Picton Cnd
(community)   •  Pinkie Sctlnd
(House)   •  Pirot Srb
(city)  
*  Pöcking Grmny
(town)   •  Podesta PcfOcn
(island )   • Lake  Poopó Blv
(salt flat)   •  Porlock Englnd
(village)   •  Portumna Irlnd
(town)   • Cerro  Potosí Blv
(mountain)   •  Poughkeepsie USA
(city)   •  Powderham Englnd
(Castle)  
*  Prut EErp
(river)
Places & Buildingsː Q__
*  Qaitbay Egpt
(Citadel)   •  Qays Jrdn
(town)   •  Qalqilya Plstn
(city)  
*  Qeshm Irn
(island)  
*  Qianling Chn
(Mausoleum)   •  Qinghai Chn
(Lake)  
*  Qom Irn
(city)  
*  Quamby Astrl
(Bluff)   •  Quantock Englnd
(Hills)   •  Quarndon Englnd
(village)   •  The Quarry Englnd
(park)  
*  Queanbeyan Astrl
(city)   •  Quedlinburg Grmny
(town)   •  Queenston Cnd
(town)   •  Queenstown SAfrc
(town)   •  Quelimane Mzmbq
(seaport)   • Le  Quesnoy Frnc
(commune)   •  Quethiock Crnwl
(parish)   •  Quetta Pkstn
(city)  
*  Quiévrain Blgm
(municipality)   •  Quiggins Englnd
(market )   •  Quimper Brtny
(commune)   •  Quinte Cnd
(Bay)   •  Quirinal Itly
(Hill)   •  Quito Ecdr
(city)  
*  Qumran Isrl
(cemetary )
Places & Buildingsː R__
*  Ragusa Esclvn
(republic )   •  Razlog Blgr
(resort)  
*  Red Flag Chn
(Canal)   •  Redruth Crnwl
(town)   •  Rennell SlmnIi
(Island)   •  Restormel Crnwl
(Castle)   •  Rethel Frnc
(commune)   •  Reuss Swzlnd
(river)  
*  Rhodope Grc
(Mountains)   •  Rhyl Wls
(community)  
*  Rijswijk Nthrlnds
(town)   •  Rinteln Grmny
(town)   •  Rizal Phlpns
(province)  
*  Rochdale Englnd
(Cenotaph)   •  Rockefeller USA
(Center)   •  Rocroi Frnc
(commune)   •  Rondebosch SAfrc
(Fountain)   •  Rogaland Nrwy
(county)   •  Rohtas Ind
(Fort)   •  Rollright Englnd
(parish)  
*  Rügen Grmny
(island)   •  Rumelia Blkns
(peninsula)   •  Runcorn Englnd
(port)   •  Rushley Englnd
(Island)  
*  Rye Englnd
(resort)  
*  Rzhev Rsa
(town)
# Informal learning activities/PBwVz

Places & Buildingsː V⇒ Z__  O ther initialsː   Ac  Df
 Gi  Jl
 Mo  Pr
 Su
(«»Vz⇓⇓)
*  Vaal SAfrc
(River)   •  Valdivia Chl
(city)   •  Valentia Irlnd
(Island)   •  Valjala Estn
(Stronghold)   •  Valladolid Spn
(city)   •  Vancouver Cnd
(city)   •  Vardar EErp
(river)   •  Varese Itly
(city)   •  Varna Blgr
(city)   •  Vauxhall Englnd
(Gardens)  
*  Veii Itly
(city )   •  Veraguas Pnm
(Province)   •  Vercelli Itly
(city)   •  Verulamium Englnd
(town )  
*  Vigo Glc
(municipality )   •  Vilama Arg/Blv  
(caldera)   •  Viljandi Estn
(town)   •  Vintry Englnd
(ward)   •  Visoko BsnHzgv
(city)   •  Vistula Plnd
(river)   •  Vizianagaram Ind
(Fort)  
*  Vlissingen Nthrlnds
(city)   •  Vlorë Albn
(municipality)  
*  Volhynia EErp
(region)  
*  Vráble Slvk
(village)
Places & Buildingsː W__
*  Wakeman USA
(village)   •  Walcheren Nthrlnds
(island )   •  Wallachia Rmn
(region)   •  Wanamaker USA
(Organ)   •  Wappinger USA
(town)   •  Wattisfield Englnd
(village)  
*  Weehawken USA
(town)   •  Weser Grmny
(river)   •  Westport Irlnd
(town)  
*  Whanganui NZ
(city)   • Wharfe Englnd
(River)   •  Whitehall Englnd
(Palace )   •  Whiteinch Sctlnd
(district)  
*  Wicklow Irlnd
(Way)   •  Wil Swzlnd
(city)   •  Winneba Ghn
(town)   •  Wirral Englnd
(Peninsula)  
*  Włodawa Plnd
(Synagogue)  
*  Wolfenbüttel Grmny
(town)   •  Wolin Plnd
(town)   •  Wonthaggi Astrl
(town)  
* Mount  Wrangell USA
(volcano)   •  Wrigley USA
(Building)  
*  Würzburg Grmny
(city)  
* Wye UK
(River)
Places & Buildingsː X__
*  Xai-Xai Mzmbq
(city)   •  Xàtiva Spn
(town)  
*  Xcalak Mxc
(village)  
*  Xenia USA
(city)   •  Xerxes Grc
(Canal )  
*  Xingu Brzl
(River)
Places & Buildingsː Y__
*  Yackandandah Astrl
(town)   •  Yangon Mynmr
(city)   • Yare Englnd
(River)   •  Yarrow Sctlnd
(parish)   •  Yaxley Englnd
(village)   •  Yazoo USA
(River)  
*  Yeavering Englnd
(hamlet )   •  Yell Sctlnd
(Sound)   •  Yellowknife Cnd
(city )   •  Yeovil Englnd
(town)   •  Yerevan Armn
(city)   •  Yering Astrl
(town)  
*  Yielden Englnd
(village)   •  Yinxu Chn
(city )  
*  Yogyakarta Indns
(city)   •  Yoho Cnd
(Park)   •  Yonne Frnc
(department)   •  York Cnd
(Factory)   •  Yosemite USA
(Park)   •  Youghal Irlnd
(town)   • d'Youville Cnd
(Place)   •  Yoxall Englnd
(village)   •  Yozgat Trky
(city)  
*  Yreka USA
(city )  
*  Yucatán Mxc
(state)   • Yungui Chn
(Plateau)
Places & Buildingsː Z__
*  Zafra Spn
(town)   •  Zagazig Egpt
(city)   •  Zagora Mrc
(town)   •  Zagreb Crt
(capital)   •  Zagros ME
(Mountains)   •  Zahamena Mdgscr
(Park)   •  Zante Grc
(island)   •  Zambales Phlpns
(province)   •  Zamboanga Phlpns
(City)   •  Zanskar Ind
(tehsil )   •  Zarzis Tns
(commune)  
*  Zeelandia Twn
(Fort)   •  Zengg Crt
(town)   •  Zerbst Grmny
(town)   •  Zeugma Trky
(city )  
*  Zhob Pkstn
(town)   •  Zhongguancun Chn
(zone)  
*  Ziguinchor Sgl
(city)   •  Žilina Slvk
(city)   •  Zittau Grmny
(city)  
*  Żmigród Plnd
(town)  
*  Znojmo Mrv
(town)  
*  Zouch Englnd
(hamlet)  
*  Zülpich Grmny
(town)  
*  Zvečan Ksv
(Fortress)  
*  Zwolle Nthrlnds
(municipality)
# Informal learning activities/PO

PcfOcn
This inserts a link to the country or area, in this case the Pacific Ocean, into a Places & Buildings item.
# Informal learning activities/PRc

PrtRc
This inserts a link to the country or area, in this case Puerto Rico, into a Places & Buildings item.
# Informal learning activities/PBwSu

Places & Buildingsː S⇒ U__  O ther initialsː   Ac  Df
 Gi  Jl
 Mo  Pr
(«»Su⇓⇓)
 Vz
*  Saba ME
(kingdom )   •  Samogitia Lthn
(region)   •  Sandusky USA
(city )   •  Sapperton Englnd
(Tunnel)   •  Saqqara Egpt
(cemetary)   •  Sark EChnl
(island )  
*  Scapa UK
(Flow)   •  Scilly Crnwl
(Isles)  
*  Seattle USA
(city)   •  Seram Indns
(Island)   •  Sermersooq Grnlnd
(municipality)  
*  Shambhala ??  
(kingdom )   •  The Shard Englnd
(tower)   •  Shechem Cnn
(city )   •  Shellal Egpt
(village )   •  Sherbro SrLn
(Island)   •  Shobdon Englnd
(village)   •  Shockoe USA
(Hill)  
*  Siedlce Plnd
(city)   •  Simancas Spn
(town)   •  Simeto Itly
(river)   •  Sizergh Englnd
(Castle)  
*  Skagway USA
(port)   •  Skaneateles USA
(Lake)   •  Skerryvore Sctlnd
(reef)  
*  Smyrna Grc
(city )  
*  Snoqualmie USA
(River)  
*  Sodor UK
(kingdom )   •  Southrepps Englnd
(village)  
*  Spello Itly
(town)   •  Spiez Swzlnd
(town)  
*  Srirangapatna Ind
(town)  
*  Stagno Crt
(municipality)   •  Straubing Grmny
(city)  
*  Suakin Sdn
(port)  
*  Sudetenland CzchR
(region )   •  Sutter's USA
(Mill)  
*  Sylhet Bngldsh
(city)   •  Syra Grc
(island)
Places & Buildingsː T__
*  Taapaca Chl
(volcano)   •  Taganrog Rsa
(city)   •  Tain Sctlnd
(burgh)   •  Tampere Fnlnd
(city)   •  Tarpeian Itly
(Rock)   •  Tartu Estn
(city)   •  Tay Sctlnd
(river )  
*  Tela Hds
(town)   •  Terceira NAtlOcn
(Island)   •  Terenure Irlnd
(suburb)   •  Termoli Itly
(comune)   •  Terneuzen Nthrlnds
(city)   • El  Tatio Chl
(geyser)   •  Texel Nthrlnds
(island)  
*  Thar Ind/Pkstn  
(Desert)   •  Thebes Grc
(city)   •  Thill Pkstn
(village)  
*  Ticino Swzlnd
(canton)   • Ticonderoga USA
(Fort)   •  Timika Indns
(city)   •  Tipitapa Ncrg
(municipality)  
*  Titchwell Englnd
(Marsh)  
*  Tlemcen Algr
(city)  
*  Tortola VrgnI
(island)   •  Toul Frnc
(commune)  
*  Trebizond ME
(Empire )   •  Trefeca Wls
(home )   •  Tremp Spn
(Formation)   •  Trollhättan Swdn
(city)  
*  Tübingen Grmny
(city)   •  Tulsk Irlnd
(village)   •  Tuolumne USA
(River)   •  Turan CntrlAs
(region)   •  Turl Englnd
(Street)   •  Tuskegee USA
(city )  
*  Txingudi Spn
(Bay)
Places & Buildingsː U__
*  Ube Jpn
(city)  
*  Uckermark Grmny
(region)  
*  Udine Itly
(comune)  
*  Uffculme Englnd
(village)   •  Uffizi Itly
(Gallery)  
*  Ugthorpe Englnd
(village)  
*  Uley Englnd
(village)   •  Ulla Glc
(river)   •  Ulm Grmny
(city)   •  Uluru Astrl
(iselberg)  
*  Umatilla USA
(city )   •  Umbria Itly
(region)  
*  Undavalli Ind
(Caves)   •  Unguja Znzbr
(island)  
*  Upotipotpon Astrl
(district)   •  Upottery Englnd
(village )   •  Upsettlington Sctlnd
(village )  
*  Urartu ME
(kingdom )   • Urmia Irn
(Lake)   •  Uruk Irq
(city )  
*  Ushant Brtny
(island)   •  Ushuaia Argntn
(city)   •  Ustaritz Frnc
(town)   •  Ústí nad Labem CzchR
(city)  
*  Utica Tns
(city )  
*  Uyuni Blv
(salt flat)  
*  Uzhhorod Ukrn
(city)
# Mathematics for Applied Sciences (Osnabrück 2011-2012)/Part I/Exercise sheet 16

    Warm-up-exercises

### Exercise

Find a zero for the function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x)=x^{2}+x-1,$
in the interval $[0,1]$ using the interval bisection method with a maximum error of $1/100$.

### Exercise

Let
    $f\colon [0,1]\longrightarrow [0,1[$
be a continuous function. Show that $f$ is not surjective.

### Exercise

Give an example of a bounded interval $I\subseteq \mathbb {R}$ and a continuous function
    $f\colon I\longrightarrow \mathbb {R}$
such that the image of $f$ is bounded, but the function admits no maximum.

### Exercise

Let
    $f\colon [a,b]\longrightarrow \mathbb {R}$
be a continuous function. Show that there exists a continuous extension
    ${\tilde {f}}\colon \mathbb {R} \longrightarrow \mathbb {R}$
of $f$.

### Exercise

Let
    $f\colon I\longrightarrow \mathbb {R}$
be a continuous function defined over a real interval. The function has at points $x_{1},x_{2}\in I$, $x_{1}<x_{2}$, local maxima. Prove that the function has between $x_{1}$ and $x_{2}$ has at least one local minimum.

### Exercise

Determine directly, for which $n\in \mathbb {N}$ the power function
    $\mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto x^{n},$
has an extremum at the point zero.

### Exercise *

Show that the Intermediate value theorem for continuous functions from $\mathbb {Q}$ to $\mathbb {Q}$ does not hold.

### Exercise

Determine the limit of the sequence
    $x_{n}={\sqrt {\frac {7n^{2}-4}{3n^{2}-5n+2}}},\,n\in \mathbb {N} .$
    Hand-in-exercises

### Exercise (2 marks)

Determine the minimum of the function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto x^{2}+3x-5.$

### Exercise (5 marks)

Find for the function
    $f\colon \mathbb {R} \longrightarrow \mathbb {R} ,x\longmapsto f(x)=x^{3}-3x+1,$
a zero in the interval $[0,1]$ using the interval bisection method, with a maximum error of $1/200$.

### Exercise (2 marks)

Determine the limit of the sequence
    $x_{n}={\sqrt[{3}]{\frac {27n^{3}+13n^{2}+n}{8n^{3}-7n+10}}},\,n\in \mathbb {N} .$
The next task uses the notion of an even and an odd function.

### Exercise (4 marks)

Let
    $f\colon \mathbb {R} \longrightarrow \mathbb {R}$
be a continuous function. Show that one can write
    $f=g+h\,,$
with a continuous even function $g$ and a continuous odd function $h$.
The following task uses the notion of fixed point.

### Exercise (4 marks)

Let
    $f\colon [a,b]\longrightarrow [a,b]$
be a continuous function from the interval $[a,b]$ into itself. Prove that $f$ has a fixed point.
# Engineering Projects/Illuminate Clothing
## Idea

Illuminate clothing using EL wire, very flat buttons, ballons, etc. and software to make a custom.

## SubSystems

Power system for EL wire Lilypad Arduino

## Colleges/Universities

    Howard Community College