2

Alpha

Beta

Gamma

Delta

Epsilon

Z Zeta

H Eta

Theta

I Iota

K Kappa

Lambda

M Mu

N Nu

Xi

O Omicron

Pi

Rho

Sigma

Tau

Upsilon

Phi

Chi

Psi

Omega

3

x y x y Less than equal a b a b Greater than

equal

3 4< Less than < 3 2> Greater than > 1.99997 2 ABC A B C

)(

Approximately

Congruent

F x F kx = Proportional

5 1(mod 2)

Is congruent to

Modulo

3 2 Not equal 2 1 1x x= = Plus-minus

( ) & ( )a b b c a c= = = Equal = 2 3 6 =

x y zA a i a j a k= + +

x y zB b i b j b k= + +

x y z

x y z

i j kA B a a a

b b b

=

Times, cross

2 3 5+ = Plus + 2 3 1 = Minus -

4

noisiviD = 2 3 6 yb dediviD

/ :

% tnecreP %05

00 0500 dnasuoht reP

00

. toD = B A B Asoc ! lairotcaF = =021 5 4 3 2 1 !5

=2 4 =3 72 3

m n

toor erauqS

T

== b A Baji ij AT esopsnarT

= = = y y x6 6.5 & 5 3.5] [ ] [21 11

22 12

a aa a

tekcarB

xirtaM

] [

) ( sesehtneraP = +51 ))1 4( 2(3

secarB teS

ecneuqeS } {

02,01] [0,1) (

lavretni esolc

lavretni-nepo ,] [ ,) (

5

( ]5, 2 [ )10,13

close-open

open-close

[ ),

( ],

{ } { } { }( )* ( ) ( ) ( )F g x f x F g x F f x= Convolution

, 0, 0

x xx

x x>=

6

222

11

1 1 3(4 1)2 2 2

xdx x= = = Integral ( , )f x y dxdy Double integral

( , , )g x y z dxdydz Triple integral C

dlv Line integral Contour integral v A

dw Surface integral w V

dx Volume integral x Therefore Because ,a b a b Exist

,a b / a b Not exist / ,a b a b For all

( )p p= Propositional p q

p rq r

if then

7

p qp q

q p

if and only if

iff

{ }, ,A a b c= , a A

Membership

Element of

{ }, ,A a b c= , d A

Not member

{ }, ,A a b c= , { },B a d= { }, , ,A B a b c d=

Union

{ }A B a= Intersection { }C a= , C A (proper) Subset

superset B/ Not subset { } = M =

Empty set

2( )f x x= , 2df xdx

= ( ) 2f x x =

x Derivation to x ' XD

ddx

2( )f x x= , 2f xx =

Paritial

derivation

3( )f x x= , 2

2 6df xdx

= n Derivation n order

nth , nth

n

n

ddx

8

3( )f x x= , 2

2 6f xx =

n

Partial

derivation n

order nth

n

nx

x y z = + +

Nabla

Laplace

operator (Nabla)

2 2 22

2 2 2x y z = + +

) (

Square Lap. Op.

Laplacian

2

Line segmentAB

)( Ray AB

Infinity lineAB

ABC , ABC Triangle ABC , ABC ) ( Angle

) ( Right angle

Square , Parallelogram . Circle AB AC Perpendicular AB AC& Parallel & ABC A B C Similar ABC A B C Congruent

ABC Arc

9

52 51 03" '

eergeD

etuniM

dnoceS

' "

7.5,1) (

)2,0,4.1(

) 52,9(

naisetraC

etanidrooC

.ooC ecapS

.ooC raloP

y x) , (

z y x) , , (

r) , (

BA

rotceV

W V W V1

n

iiX X

= =

mus tceriD

1

n

iiX X

= =

tcudorp tceriD

q p q p T T T

F F T

F T F

F F F

( )

dna

eurT

eslaF

T

F

q p q p T T T

T F T

T T F

F F F

ro

01

!) ( ) (!nk

nnk

n == Pk

n k

nk) ( noitatumrePn Pk

kn knk ! !!) (nn

== Ck

n k

Ckn kn) ( noitanibmoC

= i1

yranigamI

rebmun i

= e...4828182817.2

sreipaN

tnatsnoc

rebmun sreluE

e

iP = ...56295141.3 oitar nedloG = 889330816.1

1

n

nnx

xn

=

= x naem

0

1 milnisx

xx

mil timil =

1

mil1+x x1 + =

ytinifnI

` =,4,3,2,1} {

larutaN

srebmun `

` =,4,3,2,1,0 0} { 0

`0 0 htiw larurtaN

11

] =,2,1,0,1 ,2 ,} {

] srebmun regetnI

n n m m0 , , :n

] _ =

lanoitaR

srebmun _

( )

\ srebmun laeR

.

laeR evitisoP

srebmum

\+

+yi x

xelpmoC

srebmun ^

no os dna

=x f y) ( :

edis dnah tfeL

yb denifed si

dnah thgir eht

edis

=:

xam} { mumixaM = xam4 2,4,3,1} { nim} { muminiM = nim1 2,4,3,1} {

03nis12

nis eniS =

06soc12

soc enisoC =

nat tnegnaT = 1 54 nat

12

cot 45 1 = Cotangent cot 1sec

cos =

Secant sec

1cscsin

= Cosecant csc

1 302

sinArc = Arc sine sinArc

Radian : 45 ( )4

rad = 2 45 ( )

2 4cos radArc ==

Arc cosine cosArc

Arc tangent tanArc Arc cotangent cotArc Arc secant secArc Arc cosecant cscArc

sinh2

x xe ex=

)(

Hyperbolic sine sinh sh

cosh2

x xe ex+=

)(

Hyperbolic

cosine cosh

ch 2sec x xhx e e

= +

)(

Hyperbolic

secant sech

2c x xcs hx e e =

)(

Hyperbolic

cosevantccs h

31

2

2

hnat11

x

x

xee

+ =

()

cilobrepyH

tnegnat hnat

ht2

2

htoc11

x

x

xee

=+

()

cilobrepyH

tnegnatoc hnatoc htoc

()

cilobrepyh crA

enis crAhnis

()

cilobrepyh crA

enisoc crAhsoc

,1ji,0j ij i

== atled rehcenorK

+ =T T Tj j ji2 1 = i2,1 Tkji k j i

rosneT Tji

i Tkj

)1 (n2

Sn ecneuqeS + + + +n 3 2 1 =+ Sn n

b goLa mhtiragoL = =goL goL2 001 00101 larutaN =x x goLenl

mhtiragol nl

an n rewop a n a =001 012 B A B A P) (

x0

f=+ x

ytilibaborP

noitcnuF

|

41

O noitisopmoC x g f x g f)) ( ( ) (0 ,1

0 ,0 ngs0 ,1

xx x

x

< = =>

x ngs noitcnuf ngis

6 ot dneT 6 x nwod dednuoR pu dednuoR k j iF F F F Fdarg

z y x + + = =

darg tneidarG

FvidF F F Fz y x

+ + = = GG

vid ecnegreviD

z y x

k j i

F Flrucz y xF F F

= = G G

lruc noitatoR

.

8002