Math Formulas and Tricks

ืžื›ื™ืœ ืžื•ื“ืขื•ืช
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ื”ื•ืจื“ื•ืช
ืกื™ื•ื•ื’ ืชื•ื›ืŸ
ื›ื•ืœื
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš
ืฆื™ืœื•ื ืžืกืš

ืžื™ื“ืข ืขืœ ื”ืืคืœื™ืงืฆื™ื” ื”ื–ื•

ื–ื”ื• ื™ื™ืฉื•ื ืžื•ืฉืœื ืžืกืคืง ืืช ื›ืœ ื”ื ื•ืกื—ืื•ืช ื”ื‘ืกื™ืกื™ื•ืช ื‘ืžืชืžื˜ื™ืงื”.

ืžืื•ื“ ื ื•ื— ืขื‘ื•ืจ ื›ืœ ื”ืชืœืžื™ื“ื™ื ื‘ื‘ื™ืช ื”ืกืคืจ, ื‘ืชื™ื›ื•ืŸ, ืื•ื ื™ื‘ืจืกื™ื˜ืช ื•ืžื”ื ื“ืกื™ื.

ื–ื” ื’ื ืฉื™ืžื•ืฉื™ ืขื‘ื•ืจ ืžื•ืจื™ื, ื”ื•ืจื™ื ื•ืื™ืฉ ืขืกืงื™ื ืœืงื—ืช ื”ืคื ื™ื” ื‘ืžืงืฆื•ืขื.

ื›ืœ Essentials ื ื•ืกื—ื” ื‘ืžืชืžื˜ื™ืงื” ืžืฉื•ื•ืื•ืช:

-> ื—ื™ืฉื•ื‘ื™ื

ืคื™ื ืช 1.

-> ืžืœื‘ืŸ
-> ืžืงื‘ื™ืœื™ืช
-> ื›ื™ื›ืจ
-> ืžืฉื•ืœืฉ
-> ืžืขื’ืœ
-> ืืงืœื™ืคืก
-> ื˜ืจืคื–

2. ื ืคื—

-> ืงื™ื•ื‘
-> ืฆื™ืœื™ื ื“ืจ
-> ื›ื“ื•ืจ
-> ืงื•ื ื™ืช
-> ืคื™ืจืžื™ื“ื”
-> ืคืจื™ื–ืžื”
-> cuboid
-> ื˜ื•ืจื•ืก

ืžืจื” 3.

-> ื›ืœ ื”ืกื•ื’ ืฉืœ ืคืจืžื˜ืจื™ื ื”ืžืจื” ื–ืžื™ืŸ

4. ืžื˜ื‘ืข (ืฉื™ืขื•ืจ ืฉื™ื—ื” ื‘ืฉื™ื“ื•ืจ ื—ื™)

ืจืฉื™ืžืช ื ื•ืกื—ืื•ืช

ื˜ึฐืจึดื™ื’ื•ึนื ื•ึนืžึถื˜ืจึดื™ึธื”

-> ื”ื’ื“ืจืช ื–ื•ื•ื™ืช ื™ืžื ื™ืช
-> ืฉื•ืœื—ืŸ ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช
-> ืฉื•ืœื—ืŸ ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช
-> ื–ื”ื•ื™ื•ืช ืžืฉื™ืงื•ืช ืžืฉื•ืชืฃ ื”ืžืฉื™ืง
-> ืคื•ืจืžื•ืœื” ื”ื‘ืกื™ืกื™ืช
-> ื ื•ืกื—ื•ืช ื–ื•ื’ื™ื•ืช / ืื™ ื–ื•ื’ื™ื•ืช
-> ื ื•ืกื—ื•ืช ื–ื•ื•ื™ืช ื–ื•ื’ื™ื•ืช
-> ื ื•ืกื—ืื•ืช Sum / Difference
-> ื ื•ืกื—ืื•ืช ื–ื”ื•ื™ื•ืช ืžื•ืฆืจื™ื
-> ื–ื”ื•ื™ื•ืช ื–ื•ื•ื™ืช ื—ืฆื™
-> ื–ื”ื•ื™ื•ืช Cofunction
-> ื–ื”ื•ื™ื•ืช ืชืงื•ืคืชื™ื•ืช

ื’ึตืื•ึนืžึถื˜ืจึดื™ึธื”

-> ืžืฉื•ืœืฉ
-> ื—ืฆื™ื•ืŸ
-> ืžืฉื•ืœืฉ ืฉื•ื•ื” ืฆืœืขื•ืช
-> ืžืฉื•ืœืฉ ื–ื•ื•ื™ืชื™ ื™ืžื ื™
-> ืžืงื‘ื™ืœื™ืช
-> ื˜ืจืคื–
-> ืžืขื’ืœ
-> ืคืœื— ืฉืœ ืžืขื’ืœ
-> ืžื’ื–ืจ ืฉืœ ืžืขื’ืœ
-> ืฉื•ื•ื” ืฆืœืขื•ืช
-> ืžืฉื•ืฉื”
-> ื›ื“ื•ืจ
-> ืฆื™ืœื™ื ื“ืจ
-> ืฉื•ื•ื™ ื›ื“ื•ืจื™ื
-> ืงื•ื ื™ืช
-> ืคื™ืจืžื™ื“ื”
-> cuboid

ืึทืœื’ึถื‘ึผืจึธื”

-> ืคื•ืœื™ื ื•ื
-> ืžืขืจื™ื›ื™ื
-> ืฉื‘ืจื™ื
-> ื–ื”ื•ืช
-> ืฉื•ืจืฉื™ื
-> ืคื•ืจืžื•ืœื” ื”ื ื“ื™ืจ
-> ืžืกืคืจื™ื ืžืจื•ื›ื‘ื™ื
-> ืกื™ื›ื•ืžื™ื
-> ืœื•ื’ืจื™ืชื
-> ืขืฉืจื•ื ื™ ืœื•ื’ืจื™ืชื
-> ืœื•ื’ืจื™ืชื ื˜ื‘ืขื™

ืžืฉื•ื•ืื•ืช

-> Linear ืžืฉื•ื•ืื”
-> ืžืขืจื›ืช ืฉืœ ืฉืชื™ ืžืฉื•ื•ืื•ืช ืœื™ื ื™ืืจื™ื•ืช
-> ืžืฉื•ื•ืื” ืจื™ื‘ื•ืขื™ืช
-> ืžืขืจื™ื›ื™ ืžืฉื•ื•ืื”
-> ืžืฉื•ื•ืื” ืœื•ื’ืจื™ืชืžื™ืช
-> ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช ืžืฉื•ื•ืื”
-> ืฉื•ื•ื™ื•ืŸ ืœื™ื ืืจื™
-> ืฉื•ื•ื™ื•ืŸ ืจื™ื‘ื•ืขื™ืช
-> ืฉื•ื•ื™ื•ืŸ ืžืขืจื™ื›ื™ื
-> ืฉื•ื•ื™ื•ืŸ ืœื•ื’ืจื™ืชืžื™
-> ืฉื•ื•ื™ื•ืŸ ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช
-> Constant
-> Absolute
-> ืฉื•ืจืฉ ืจื™ื‘ื•ืขื™
-> Parabolic
-> ืžืขื•ืงื‘
-> ื’ื•ืžืœื™ืŸ
-> Sec
-> Cosec

ื’ึดื–ืจึธื”

-> ื”ื’ื‘ืœ
-> ื ื’ื–ืจ
-> ื‘ื™ื“ื•ืœ

ืฉื™ืœื•ื‘

-> ืกืชืžื™ ืื™ื ื˜ื’ืจืœื™ื
-> ื ืžืจืฅ integrals
-> ืฉื•ืจืฉื™ ืขื™ืจื•ื‘
-> ืฉื‘ืจื™ื ื—ืœืงื™ื™ื
-> ื˜ืจื ืกืคื•ืจืžืฆื™ื”
-> ืคื•ื ืงืฆื™ื•ืช ื˜ืจื™ื’ื•ื ื•ืžื˜ืจื™ื•ืช

ืึฒื ึทืืœึดื™ื˜ึดื™

-> ืคื•ื™ื ื˜
-> ืžืฉื•ืœืฉ
-> ืžืฉื•ื•ืื” ืžืขื’ืœืช
-> ืžืฉื•ื•ืืช ืงื•

ืกื˜ึธื˜ึดื™ืกื˜ึดื™ืงึธื”

-> Set
-> ืชืช-ืงื‘ื•ืฆื”
-> ืฆื•ืžืช
-> ืื™ื—ื•ื“
-> ืžืฉืœื™ื ื™ื—ืกื™ืช
-> ืžืฉืœื™ื Absolute
-> ืคืขื•ืœื•ืช ืขืœ ืงื‘ื•ืฆื•ืช
-> ืฉื™ืœื•ื‘ื™ื
-> ืฆื™ืจื•ืคื™ื
-> ื”ืกืชื‘ืจื•ืช

ื˜ืจื™ืงื™ื

-> ืชื•ืกืคืช
-> ื—ื™ืกื•ืจ
-> ื›ืคืœ
-> ืื’ืฃ
-> ืžืชื™ื™ืฉื‘
ืขื“ื›ื•ืŸ ืื—ืจื•ืŸ ื‘ืชืืจื™ืš
14 ื‘ื™ื•ืœื™ 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.
ืœื ืžืชื‘ืฆืข ืฉื™ืชื•ืฃ ื ืชื•ื ื™ื ืขื ืฆื“ื“ื™ื ืฉืœื™ืฉื™ื™ื
ื”ื ืชื•ื ื™ื ืžื•ืฆืคื ื™ื ื‘ื–ืžืŸ ื”ื”ืขื‘ืจื”
ืื™ ืืคืฉืจ ืœืžื—ื•ืง ืืช ื”ื ืชื•ื ื™ื

ืžื” ื—ื“ืฉ?

Minor Bug Fixes.