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Geogebra
Matlab
Punoi:Selma Selishta
Cfare eshte Geogebra?
 Eshte nje sowftware dinamik I
matematikes pa pagese per te gjitha
nivelet e arsimit qe bashkon
gjeometrine, algjebren , tabelat,
grafiket,statistikat ne nje pakete te
lehte per t’u perdorur.
 Eshte ne dispozicion ne shume
platforma me aplikacionet e veta te
desktopit per Windows,macOS dhe
Linux, me aplikacionet e tabletave per
Androit,IPAD dheWindows dhe me
aplikacionin e saj te internetit bazuar
ne teknologjine HTML5.
2
Themeluesi i saj.
 Eshte zhvilluar nga nje student I
doktoratures Markus Hohenwater dhe
si e tille eshte pa pagese.
 Eshte i perkthyer ne mbi 45 gjuhe te
ndryshme.
 Ka 500000 vizitor ne muaj.
3
Si mund ta perdorim?
 Klikojme https://www.geogebra.org/
 Shfaqen dy mundesi:Start graphing
dhe classroom resourcs.
 Klikoni mbi start graphing.
“
Llogaritja grafike
5
Mund te ndryshojme sipas
zgjidhjes ne:
1. Llogaritje grafike
2. Gjeometrike
3. 3D grafike
4. Geogebra klasike:
• Ekuacionet
• Matricat
• Grafiket
• Probabilitet
Mund te ndertojme shumekendesh,rreth.
Mund te heqim pingulen mbi nje drejtez,te tregojme drejtezat
paralele,tangjentet .
Te gjeme siperfaqen,madhesin e kendit,gjatesin e seg.
6
 Ndertojme piramid ,sfere, kub.
 Planin qe kalon ne 3 pika.
 Ndertojme vektore.
7
 Ka nje sere
programesh nese
deshironi ti shkarkoni
ne celularin tuaj.
Sa aplikacione kemi?
 Geogebra graphing
calculator.
 Geogebra 3D.
 Geogebra geometry.
 Geogebra cas
calculator.
 Geogebra scientific.
8
Opsioni classroom resources
9
probabilitet
trigonometri
geometry
Matlabi
10
Nisi te krijohet ne 1970 nga Cleve
Moler.
E krijoi per t’u ardh ne ndihme
studentave.
Gjete nje perdorim te madh ne
matematiken e aplikuar.
11
 Eshte nje gjuhe programimi per aplikime
shkencore numerike.
 Bazat e ketij softweri jane matricat.
 Posedon nje numer mjaft te madh
modulesh te projektuara deri me sot.
 Eshte i fuqishem dhe i lehte per t’u
perdorur.
12
 Eshte nje program me pagese
nese ne duhet ta kemi ne
kompjuterin tone.
 Por mundem ta shkarkojme edhe
ne celularet tone Androit, İOS por
qe smund te kemi versionin e
fundit te programit.
13
Matlabi sot
 Matlabi perdoret nga mbi 1 milion
perdoruesa.
 Perdoret ne 5000 universitete.
 Ka mbi 100 produkte.
14
Place your screenshot here
15
 E shkarkojme ne playstore
appstore.
 Klikojme mbi ikone.
 Shkruaj email dhe kodin.
 Dhe me pas futesh ne
program.
16
Kemi komandat e programit
Place your screenshot here
17
 Ndertojme funksione.
 Gjejme vlerat e integraleve
derivateve.
 Ndertojme parcela 2D-3D.
Krijimi i nje parcele
vlerash te nje funksioni
“
▸ Kur harroj qofte edhe
nje shenje pikesimi ne
momentin qe I japim
komandes se
ekzekutimit del gabimi
jone.
18
“  Ndertimi i nje funksioni
te grades se dyte.
Per me ndertuar funksionin
x^2+y=0 shkruajme
>> y = 2;
>> ezplot('x^2+y')
19
Ndertimi I funksioneve trigonometrike
 >> t=linspace(0,10,500);
 >> y = exp(-t).*sin(10*t);
 >> plot(t,y)
20
▸ >> x = linspace(0,pi,50); y = exp(-x).*sin(8*x);
▸ >> plot(x,y,'--
sb','linewidth',2,'markersize',8,'markerfacecolor','g')
21
3-D
22
Ngjashmerit e tyre
23
Pjesen e llogaritjeve ,grafikut dhe gjeometris.
Munde te shkarkohen ne app store.
Kane shumëllojshmëri ngjyrash për të dalluar midis funksioneve të
shumëfishta.
Jane te dobishem ne klase .
Kto programe mundësojnë krijimin e llogarisë dhe identifikimin duke përdorur
një llogari Google ose një llogari email standard.
Ndryshimet
 Matlabi ne kompjuter eshte me pages.
 Perdoret nga inxhiniera.
 Eshte gjuhe programimi i shkalles me te larte.
 Ka komanda me shume.
 E meta e tij eshte se filet e shkruar ne versionin
paraprak nuk funksionojne sic duhet ne versionin e ri.
 Gjene edhe vlerat e integraleve derivateve serive etj.
24
Referencat:
 https://www.geogebra.org/
 https://www.mathworks.com/products/matlab.
html
 https://en.wikipedia.org/wiki/MATLAB
25
“Arti sfidon teknologjine
ndersa teknologjia
frymezon artin”
“ Në shkencë, mrekullitë
po ndodhin gjatë gjithë
kohës”
26

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geogebra.pptx

  • 2. Cfare eshte Geogebra?  Eshte nje sowftware dinamik I matematikes pa pagese per te gjitha nivelet e arsimit qe bashkon gjeometrine, algjebren , tabelat, grafiket,statistikat ne nje pakete te lehte per t’u perdorur.  Eshte ne dispozicion ne shume platforma me aplikacionet e veta te desktopit per Windows,macOS dhe Linux, me aplikacionet e tabletave per Androit,IPAD dheWindows dhe me aplikacionin e saj te internetit bazuar ne teknologjine HTML5. 2
  • 3. Themeluesi i saj.  Eshte zhvilluar nga nje student I doktoratures Markus Hohenwater dhe si e tille eshte pa pagese.  Eshte i perkthyer ne mbi 45 gjuhe te ndryshme.  Ka 500000 vizitor ne muaj. 3
  • 4. Si mund ta perdorim?  Klikojme https://www.geogebra.org/  Shfaqen dy mundesi:Start graphing dhe classroom resourcs.  Klikoni mbi start graphing.
  • 5. “ Llogaritja grafike 5 Mund te ndryshojme sipas zgjidhjes ne: 1. Llogaritje grafike 2. Gjeometrike 3. 3D grafike 4. Geogebra klasike: • Ekuacionet • Matricat • Grafiket • Probabilitet
  • 6. Mund te ndertojme shumekendesh,rreth. Mund te heqim pingulen mbi nje drejtez,te tregojme drejtezat paralele,tangjentet . Te gjeme siperfaqen,madhesin e kendit,gjatesin e seg. 6
  • 7.  Ndertojme piramid ,sfere, kub.  Planin qe kalon ne 3 pika.  Ndertojme vektore. 7
  • 8.  Ka nje sere programesh nese deshironi ti shkarkoni ne celularin tuaj. Sa aplikacione kemi?  Geogebra graphing calculator.  Geogebra 3D.  Geogebra geometry.  Geogebra cas calculator.  Geogebra scientific. 8
  • 11. Nisi te krijohet ne 1970 nga Cleve Moler. E krijoi per t’u ardh ne ndihme studentave. Gjete nje perdorim te madh ne matematiken e aplikuar. 11
  • 12.  Eshte nje gjuhe programimi per aplikime shkencore numerike.  Bazat e ketij softweri jane matricat.  Posedon nje numer mjaft te madh modulesh te projektuara deri me sot.  Eshte i fuqishem dhe i lehte per t’u perdorur. 12
  • 13.  Eshte nje program me pagese nese ne duhet ta kemi ne kompjuterin tone.  Por mundem ta shkarkojme edhe ne celularet tone Androit, İOS por qe smund te kemi versionin e fundit te programit. 13
  • 14. Matlabi sot  Matlabi perdoret nga mbi 1 milion perdoruesa.  Perdoret ne 5000 universitete.  Ka mbi 100 produkte. 14
  • 15. Place your screenshot here 15  E shkarkojme ne playstore appstore.  Klikojme mbi ikone.  Shkruaj email dhe kodin.  Dhe me pas futesh ne program.
  • 16. 16 Kemi komandat e programit Place your screenshot here
  • 17. 17  Ndertojme funksione.  Gjejme vlerat e integraleve derivateve.  Ndertojme parcela 2D-3D. Krijimi i nje parcele vlerash te nje funksioni
  • 18. “ ▸ Kur harroj qofte edhe nje shenje pikesimi ne momentin qe I japim komandes se ekzekutimit del gabimi jone. 18
  • 19. “  Ndertimi i nje funksioni te grades se dyte. Per me ndertuar funksionin x^2+y=0 shkruajme >> y = 2; >> ezplot('x^2+y') 19
  • 20. Ndertimi I funksioneve trigonometrike  >> t=linspace(0,10,500);  >> y = exp(-t).*sin(10*t);  >> plot(t,y) 20
  • 21. ▸ >> x = linspace(0,pi,50); y = exp(-x).*sin(8*x); ▸ >> plot(x,y,'-- sb','linewidth',2,'markersize',8,'markerfacecolor','g') 21
  • 23. Ngjashmerit e tyre 23 Pjesen e llogaritjeve ,grafikut dhe gjeometris. Munde te shkarkohen ne app store. Kane shumëllojshmëri ngjyrash për të dalluar midis funksioneve të shumëfishta. Jane te dobishem ne klase . Kto programe mundësojnë krijimin e llogarisë dhe identifikimin duke përdorur një llogari Google ose një llogari email standard.
  • 24. Ndryshimet  Matlabi ne kompjuter eshte me pages.  Perdoret nga inxhiniera.  Eshte gjuhe programimi i shkalles me te larte.  Ka komanda me shume.  E meta e tij eshte se filet e shkruar ne versionin paraprak nuk funksionojne sic duhet ne versionin e ri.  Gjene edhe vlerat e integraleve derivateve serive etj. 24
  • 26. “Arti sfidon teknologjine ndersa teknologjia frymezon artin” “ Në shkencë, mrekullitë po ndodhin gjatë gjithë kohës” 26