ืžื—ืฉื‘ื•ืŸ ืžื“ืขื™ ื’ืจืคื™, ืžืชืžื˜ื™ืงื” PRO

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ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
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ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
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ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ืื ืืชื ืžื—ืคืฉื™ื ืืคืœื™ืงืฆื™ื™ืช ืžื—ืฉื‘ื•ืŸ ื’ืจืคื™ ื”ืขื•ื‘ื“ ื‘ืฆื•ืจื” ื—ืœืงื” ื•ืจืฆื™ืคื”, ื—ื™ืคื•ืฉื›ื ื”ื•ืฉืœื! ื”ืžื—ืฉื‘ื•ืŸ ื”ื’ืจืคื™ ืฉืœ Mathlab ื”ื™ื ื• ืžื—ืฉื‘ื•ืŸ ื’ืจืคื™ ืžื“ืขื™ ืžืฉื•ืœื‘ ืขื ืืœื’ื‘ืจื”, ื•ื”ื•ื ืžื”ื•ื•ื” ื›ืœื™ ืžืชืžื˜ื™ ื—ื™ื•ื ื™ ืขื‘ื•ืจ ืชืœืžื™ื“ื™ื ื‘ื‘ื™ืช ืกืคืจ ื™ืกื•ื“ื™, ืกื˜ื•ื“ื ื˜ื™ื ื‘ืžื›ืœืœื•ืช ื•ืื•ื ื™ื‘ืจืกื™ื˜ืื•ืช, ื•ื‘ืขืฆื ืขื‘ื•ืจ ื›ืœ ืžื™ ืฉื–ืงื•ืง ืœื™ื•ืชืจ ืžืžื—ืฉื‘ื•ืŸ ื‘ืกื™ืกื™. ื”ืืคืœื™ืงืฆื™ื” ื ื•ืขื“ื” ืœื”ื—ืœื™ืฃ ืžื—ืฉื‘ื•ื ื™ื ื’ืจืคื™ื™ื ืžื’ื•ืฉืžื™ื ื•ื™ืงืจื™ื, ื•ื”ื™ื ืžืชืื™ืžื” ื›ืžืขื˜ ืœื›ืœ ืžื›ืฉื™ืจ ื ื™ื™ื“ ื•ื˜ืื‘ืœื˜ ืขื ืื ื“ืจื•ืื™ื“.

ื™ืชืจ ืขืœ ื›ืŸ, ื”ืžื—ืฉื‘ื•ืŸ ื”ื’ืจืคื™ ืฉืœ Mathlab ืžืฆื™ื’ ื—ื™ืฉื•ื‘ื™ื ืชื•ืš ื›ื“ื™ ื‘ื™ืฆื•ืขื ื‘ืื™ื›ื•ืช ื”ืžืกืš ื”ื’ื‘ื•ื”ื” ืฉืœ ืžื›ืฉื™ืจื›ื, ืžื” ืฉืžืงืœ ืขืœ ื”ืžืฉืชืžืฉ ืœื”ื‘ื™ืŸ ืืช ื”ื—ื™ืฉื•ื‘ื™ื ื•ืœืจืื•ืช ืื•ืชื ื‘ืฆื•ืจื” ื‘ืจื•ืจื”. ืœืืคืœื™ืงืฆื™ื” ื–ืืช ืฉืชื™ ื™ืชืจื•ื ื•ืช ื’ื“ื•ืœื™ื. ืจืืฉื™ืช, ื”ื™ื ืžืฉืžืฉืช ื›ืžื—ืฉื‘ื•ืŸ ืžื“ืขื™ ืžืฆื•ื™ืŸ, ืืš ื™ื•ืชืจ ืžื–ื”, ื”ื™ื ืžืฆื™ื’ื” ืืช ืฉืœื‘ื™ ื”ื‘ื™ื ื™ื™ื ืฉืœ ื”ื—ื™ืฉื•ื‘ื™ื ื‘ืžื”ืœืš ื”ื”ืงืœื“ื”. ืชื›ื•ื ื” ื–ื• ืžืืคืฉืจืช ืœืžืฉืชืžืฉื™ื ืœืฆืคื•ืช ื‘ืžื”ืœืš ื”ื—ื™ืฉื•ื‘ื™ื ื•ืœืœืžื•ื“ ื›ื™ืฆื“ ื”ื ืžืชื‘ืฆืขื™ื ื•ืื™ืš ืœืžืฆื•ื ืืช ื”ืชืฉื•ื‘ื” ื”ืกื•ืคื™ืช. ืฉื ื™ืช, ื”ื™ื›ื•ืœืช ื”ื’ืจืคื™ืช ืฉืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื™ื ืžื“ื”ื™ืžื”! ืœื ื–ืืช ื‘ืœื‘ื“ ืฉื”ืžื—ืฉื‘ื•ืŸ ืžืฆื™ื’ ืืช ื”ื’ืจืคื™ื ื‘ืฆื•ืจื” ื—ื“ื” ื•ื™ืคื”, ืืœื ื”ื•ื ื‘ื ื•ืกืฃ ื™ื•ืฆืจ ื•ืžืฆื™ื’ ื‘ืื•ืคืŸ ืื•ื˜ื•ืžื˜ื™ ืืช ืขืจื›ื™ ื”-X ื•ื”-Y ืฉืœ ื”ืฆื™ืจื™ื.

ืขืžื•ื“ ืขื–ืจื” ืขื ื”ื•ืจืื•ืช ื•ื“ื•ื’ืžืื•ืช: https://help.mathlab.app
http://translate.google.com/translate?hl=en&sl=en&tl=iw&u=https://help.mathlab.app

ืืคืฉืจื•ื™ื•ืช ื‘ื’ืจืกื” ื”ืžืœืื”
* ื’ืจืคื™ื ืชืœืช-ืžื™ืžื“ื™ื™ื
* ืฉืžื™ืจืช ืงื‘ื•ืขื™ื, ืคื•ื ืงืฆื™ื•ืช ื•ื‘ื™ื˜ื•ื™ื™ื ื‘ืกืคืจื™ื”
* ืื™ืŸ ืฆื•ืจืš ื‘ื—ื™ื‘ื•ืจ ืœืื™ื ื˜ืจื ื˜
* ืœืœื ืคืจืกื•ืžื•ืช

ืžื—ืฉื‘ื•ืŸ ืžื“ืขื™
* ื‘ื™ื˜ื•ื™ื™ื ืืจื™ืชืžื˜ื™ื™ื +, -, *, /, รท
* ืฉื•ืจืฉื™ื ืจื™ื‘ื•ืขื™ื™ื ื•ืžืžืขืœื•ืช ื’ื‘ื•ื”ื•ืช ื™ื•ืชืจ
* ืคื•ื ืงืฆื™ื•ืช ืžืขืจื™ื›ื™ื•ืช ื•ืœื•ื’ืจื™ืชืžื™ื (ln, log)
* ืคื•ื ืงืฆื™ื•ืช ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช sin ฯ€/2, cos 30ยฐ, ...
* ืคื•ื ืงืฆื™ื•ืช ื”ื™ืคืจื‘ื•ืœื™ื•ืช sinh, cosh, tanh, ... (ืœื—ื™ืฆื” ืžืžื•ืฉื›ืช ืขืœ ืžืงืฉ "e" ืœื”ื—ืœืคืช ืžืฆื‘)
* ืคื•ื ืงืฆื™ื•ืช ื”ืคื•ื›ื•ืช (ืœื—ื™ืฆื” ืžืžื•ืฉื›ืช ืขืœ ืžืงืฉ ื”ืคื•ื ืงืฆื™ื•ืช ื”ื™ืฉื™ืจื•ืช)
* ืžืกืคืจื™ื ืžืจื•ื›ื‘ื™ื, ื›ืœ ื”ืคื•ื ืงืฆื™ื•ืช ืชื•ืžื›ื•ืช ื‘ืืจื’ื•ืžื ื˜ื™ื ืžืจื•ื›ื‘ื™ื
* ื ื’ื–ืจื•ืช (sin x)' = cos x (ืœื—ื™ืฆื” ืžืžื•ืฉื›ืช ืขืœ ืžืงืฉ "x^n")
* ื”ืฆื’ื” ืžื“ืขื™ืช (ื‘ืืžืฆืขื•ืช ื”ื’ื“ืจื” ื‘ืชืคืจื™ื˜)
* ืžืฆื‘ ืื—ื•ื–ื™ื
* ืฉืžื™ืจืช / ื˜ืขื™ื ืช ื”ื™ืกื˜ื•ืจื™ื”

ืžื—ืฉื‘ื•ืŸ ื’ืจืคื™
* ื’ืจืคื™ื ืขื ืคื•ื ืงืฆื™ื•ืช ืžืจื•ื‘ื•ืช
* ืคื•ื ืงืฆื™ื•ืช ืกืชื•ืžื•ืช ืขื“ ืžืขืœื” 2 (ืืœื™ืคืกื” 2x^2+3y^2=1, ื•ื›ื•')
* ื”ืฆื’ื•ืช ืคื•ืœืจื™ื•ืช / ืงื•ื˜ื‘ื™ื•ืช (r=cos2ฮธ)
* ื”ืฆื’ื•ืช ืคืจืžื˜ืจื™ื•ืช, ื”ื–ื™ื ื• ื‘ืฉื•ืจื•ืช ื ืคืจื“ื•ืช (x=cos t, y=sin t)
* ืฉื•ืจืฉื™ ืคื•ื ืงืฆื™ื” ื•ื ืงื•ื“ื•ืช ืงืจื™ื˜ื™ื•ืช ืขืœ ื”ื’ืจืฃ. ืกืžืŸ ืืช ื”ืชื™ื‘ื” ืœืฆื“ ืฉืžืืœ ืฉืœ ื”ืคื•ื ืงืฆื™ื” ืœื”ืฆื’ืช ื”ืงื•ืื•ืจื“ื™ื ื˜ื•ืช ืขืœ ื”ื’ืจืฃ. ืœื—ืฅ ืขืœ ื›ืคืชื•ืจ ื”ื’ืจืฃ ื‘ืชืคืจื™ื˜ ื”ืขืœื™ื•ืŸ ืœื”ืฆื’ืช ื”ืงื•ืื•ืจื“ื™ื ื˜ื•ืช ื‘ืจืฉื™ืžื”.
* ื ืงื•ื“ื•ืช ื—ื™ืชื•ืš ื‘ื’ืจืฃ (x^2=x+1)
* ืžืขืงื‘ ืื—ืจ ืขืจื›ื™ ื”ืคื•ื ืงืฆื™ื” ื•ืฉื™ืคื•ืขื™ื
* ื”ื’ืจืคื™ื ื ื™ืชื ื™ื ืœื’ืœื™ืœื” ื•ื”ื’ื“ืœื” / ื”ืงื˜ื ื”
* ืฆื‘ื˜ื• ืืช ื”ืžืกืš ืœืžื‘ื˜ ืงืจื•ื‘ ื™ื•ืชืจ
* ืชืฆื•ื’ืช ืžืกืš ืžืœื ื‘ืžืขื‘ืจ ื‘ืกื™ื‘ื•ื‘ ื”ืžื›ืฉื™ืจ ืœืžืฆื‘ ืžืื•ื–ืŸ
* ื˜ื‘ืœืื•ืช ืคื•ื ืงืฆื™ื•ืช
* ืฉืžื™ืจืช ื’ืจืคื™ื ื›ืชืžื•ื ื•ืช
* ืฉืžื™ืจืช ื˜ื‘ืœืื•ืช ื›ืงื‘ืฆื™ csv

ืžื—ืฉื‘ื•ืŸ ืฉื‘ืจื™ื
* ืฉื‘ืจื™ื ืคืฉื•ื˜ื™ื ื•ืžื•ืจื›ื‘ื™ื 1/2+1/3=5/6
* ืžืกืคืจื™ื ืžืขื•ืจื‘ื™ื ื•ืฉื‘ืจื™ื ืžื“ื•ืžื™ื, ื”ืฉืชืžืฉื• ื‘ืจื•ื•ื— ื›ื“ื™ ืœื”ื–ื™ืŸ ืžืกืคืจ ืžืขื•ืจื‘ 3 1/2

ืžื—ืฉื‘ื•ืŸ ืืœื’ื‘ืจื”
* ืžืฉื•ื•ืื•ืช ืœื™ื ื™ืืจื™ื•ืช x+1=2 -> x=1
* ืžืฉื•ื•ืื•ืช ืจื™ื‘ื•ืขื™ื•ืช x^2-1=0 -> x=-1,1
* ืฉื•ืจืฉื™ื ืžืฉื•ืขืจื™ื ืฉืœ ืคื•ืœื™ื ื•ืžื™ื ืžืžืขืœื” ื’ื‘ื•ื”ื” ื™ื•ืชืจ
* ืžืขืจื›ื•ืช ืžืฉื•ื•ืื•ืช ืœื™ื ื™ืืจื™ื•ืช, ื”ื–ื™ื ื• ืžืฉื•ื•ืื” ืื—ืช ื‘ื›ืœ ืฉื•ืจื”, x1+x2=1, x1-x2=2
* ื—ื™ืœื•ืง ืืจื•ืš ืฉืœ ืคื•ืœื™ื ื•ืžื™ื
* ื”ืจื—ื‘ืช ืคื•ืœื™ื ื•ื, ืคื™ืจื•ืง ืœื’ื•ืจืžื™ื

ืžื—ืฉื‘ื•ืŸ ืžื˜ืจื™ืฆื•ืช
* ืคืขื•ืœื•ืช ืขืœ ืžื˜ืจื™ืฆื•ืช ื•ื•ืงื˜ื•ืจื™ื
* ืžื›ืคืœื” ืกืงืœืจื™ืช (ืœื—ื™ืฆื” ืžืžื•ืฉื›ืช ืขืœ *), ืžื›ืคืœื” ื•ืงื˜ื•ืจื™ืช
* ื“ื˜ืจืžื™ื ื ื˜ื”, ืžื˜ืจื™ืฆื” ื”ืคื•ื›ื”, ื ื•ืจืžื”, ืฉื—ืœื•ืฃ, ืขืงื‘ื”

ืกืคืจื™ื”
* ื”ื’ื“ืจืช ืงื‘ื•ืขื™ื ื•ืคื•ื ืงืฆื™ื•ืช ื‘ื™ื“ื™ ื”ืžืฉืชืžืฉ
* ืฉืžื™ืจืช / ื˜ืขื™ื ืช ื‘ื™ื˜ื•ื™ื™ื
ืขื“ื›ื•ืŸ ืื—ืจื•ืŸ ื‘ืชืืจื™ืš
11 ื‘ืื•ืงืณ 2025

ืื‘ื˜ื—ืช ื ืชื•ื ื™ื

ื›ื“ื™ ืœืฉืžื•ืจ ืขืœ ื”ื‘ื˜ื™ื—ื•ืช ืฆืจื™ืš ืงื•ื“ื ื›ืœ ืœื”ื‘ื™ืŸ ืื™ืš ื”ืžืคืชื—ื™ื ืื•ืกืคื™ื ื•ืžืฉืชืคื™ื ืืช ื”ื ืชื•ื ื™ื ืฉืœืš. ื ื•ื”ืœื™ ืคืจื˜ื™ื•ืช ื”ื ืชื•ื ื™ื ื•ืื‘ื˜ื—ืช ื”ื ืชื•ื ื™ื ืขืฉื•ื™ื™ื ืœื”ืฉืชื ื•ืช ื‘ื”ืชืื ืœืฉื™ืžื•ืฉ, ืœืื–ื•ืจ ื•ืœื’ื™ืœ ื”ืžืฉืชืžืฉ. ื”ืžืคืชื— ืกื™ืคืง ืืช ื”ืžื™ื“ืข ื”ื–ื” ื•ื”ื•ื ืขืฉื•ื™ ืœืขื“ื›ืŸ ืื•ืชื• ืžื“ื™ ืคืขื.
ื”ืืคืœื™ืงืฆื™ื” ื”ื–ืืช ืขืฉื•ื™ื” ืœืฉืชืฃ ืืช ืกื•ื’ื™ ื”ื ืชื•ื ื™ื ื”ืืœื” ืขื ืฆื“ื“ื™ื ืฉืœื™ืฉื™ื™ื
ืžื–ื”ื” ื”ืžื›ืฉื™ืจ ืื• ืžื–ื”ื™ื ืื—ืจื™ื
ื”ืืคืœื™ืงืฆื™ื” ื”ื–ืืช ืขืฉื•ื™ื” ืœืืกื•ืฃ ืืช ืกื•ื’ื™ ื”ื ืชื•ื ื™ื ื”ืืœื”
ืคืขื™ืœื•ืช ื‘ืืคืœื™ืงืฆื™ื•ืช, ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื•ื‘ื™ืฆื•ืขื™ ื”ืืคืœื™ืงืฆื™ื” ื•ืžื–ื”ื” ื”ืžื›ืฉื™ืจ ืื• ืžื–ื”ื™ื ืื—ืจื™ื
ื”ื ืชื•ื ื™ื ืžื•ืฆืคื ื™ื ื‘ื–ืžืŸ ื”ื”ืขื‘ืจื”
ืื™ ืืคืฉืจ ืœืžื—ื•ืง ืืช ื”ื ืชื•ื ื™ื

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ืžืฆื•ื™ื™ืŸ ืชื•ื“ื” ืžืจืืฉ ื™ืœืื• ืžื ื™ื’ืกื˜ื• ืื—ืœื” ืืคืœื™ืงืฆื™ื”
ื”ื‘ื™ืงื•ืจืช ื”ื–ื• ื”ื•ืขื™ืœื” ืœืื“ื ืื—ื“.
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