The LaTeX Workshop: Typesetting Mathematics in LaTeX

8/13/2019 The LaTeX Workshop: Typesetting Mathematics in LaTeX

1/17

Casogs ]ypfsfttodl Nate roge tacbfs

]ypfsfttodl Natefnatogs od Ba]fULfttodl yjur eadms morty

Wummeaseffb Lejse

1Mfpartnfdt j` Govob FdlodffrodlNLNs Kawaearbab Dferu Fdlodffrodl Gjbbflf,

Auradlacam, NE

3NLN - Odstotutf j` Cojsgofdgfs adm ]fgedjbjly

Auradlacam, NE

]ef Ba]fU wjrhsejp

seume Natefnatogs
http://find/


2/17


Jutbodf

1 Yrfbonodary gjnnadms

3 Odbodf adm mospbay nateWfttodl up fquatojdsWtfp-wosf `udgtojds jr gasf casfm `udgtojdsNatrogfs adm mftfrnodadts

7 Nate roge tacbfs

seume Natefnatogs
http://find/http://goback/


3/17


Jutbodf



7 Nate roge tacbfs

seume Natefnatogs
http://find/


4/17


Yrfancbf sfttodlsDfgfssary rfquorfnfdt `jr typfsfttodl nate

Od tef prfancbf, sft tef `jbbjwodlRusfpaghalf{anssync, ansnate}

seume Natefnatogs
http://find/


5/17


Casog gjnnadms

Ot os dfgfssary tj fdgbjsf abb nate cy tef $ sold.

$RsunZ{o>1}Td

aZd xTd > 9$

$RprjmZ{o>1}Td

aZd xTd > 1$

$Rodt xTd mx >

R`rag{xT{d+1}}{d+1}$

$RodtZ9TRod`ty xTd mx >R`rag{1}{d+1} Rbf`tX

xT{d+1}Rrolet^Z9TRod`ty$

${=}Rgejjsf{3}$

do>1

adxd>9

d

o>1

adxd>1

xdmx >

xd+1

d + 1

9 x

d

mx > 1

d + 1xd+1

9=

3

seume Natefnatogs

e e cb
http://find/


6/17


Jur lrffhy `rofdms

]ef snabb jdfs;

Rabpea, Rcfta, Rlanna, Rmjts, Rgeo, Rpo, Rpeo, Rpso, Rxo

prjvomf;,,, . . . , ,,,,

Jd tef jtefr eadm, tef gapotab jdfs;A, C, Rlanna, Rmjts, U, Rpo, Rpeo, Rpso, Rxo

prjvomf;A,C, , . . . ,U,,,,

seume Natefnatogs

C o ] tto N te o e t cb
http://find/


7/17


Jur wjdmfr`ub rjjts

]ef Fugbomfad mostadgf cftwffd twj pjodts $Rnatec`{p}

(xZ1, yZ1)$ adm $Rnatec`{q}(xZ3,yZ3)$ os lovfd cy;$$ m(Rnatec`{p}, Rnatec`{q}) > Rsqrt{(xZ1-xZ3)T3

+ (yZ1 - yZ3)T3}$$

adm tef Nodhjwshos mostadgf wote tef $p$-djrn os lovfd as

$$mZp(Rnatec`{p}, Rnatec`{q}) > RsqrtXp^{Rvfrt xZ1-xZ3

Rvfrt Tp + Rvfrt yZ1 - yZ3 Rvfrt Tp}$$

prjmugfs;

]ef Fugbomfad mostadgf cftwffd twj pjodtsp(x1,y1) admq(x3,y3) os lovfd cy;

m(p,q) >

(x1 x3)3 + (y1y3)3

adm tef Nodhjwshos mostadgf wote tefp-djrn os lovfd as

mp(p,q) > p

|x1 x3|p + |y1y3|p

seume Natefnatogs

C o ] tto N te o e t cb
http://find/


8/17


Wyncjbs wf bjvf

Rpn Rnp

R`jrabb Rod Rsupsft Rsucsft

Rbf Rdbfq

Rlf Rdlfq

Rson Rapprjx

Rdson Rdapprjx

Rfquov Rdfquov

Rgap Rgup

Rtonfs Rmov

Rbb Rll

Rroletarrjw RSoletarrjw

Rbf`tarrjw RBf`tarrjwx Rcar{x} x Rvfg{x}

Abb syncjbs rfquorf nate njmf. ]ef nate fxprfssojds nust

cf surrjudmfm cy tef $ sold jd cjte somfs.

seume Natefnatogs

http://find/


9/17


]eats tef bonot !

$RbonZ{x Rroletarrjw 6} R`rag{xT3 - 36}{x - 6} > 19$

prjmugfs;

bonx6

x3 36

x 6 >19

seume Natefnatogs

Casogs ]ypfsfttodl Nate roge tacbfs Fquatojds Gasfs Natrogfs adm mftfrnodadts
http://find/


10/17


Jutbodf



7 Nate roge tacbfs

seume Natefnatogs

http://find/


11/17


]ypfsfttodl nateOdbodf adm mospbay njmfs

]ef fquatojd j` a straolet bodf os lovfd cy $y > n x + g$, wefrf $n$mfdjtfs tef sbjpf, adm $g$ mfdjtfs tef $y$-odtfrgfpt.

prjmugfs;]ef fquatojd j` a straolet bodf os lovfd cy y >nx + g, wefrfnmfdjtfs tef sbjpf, admgmfdjtfs tefy-odtfrgfpt.

]ef @jurofr trads`jrn j` a `udgtojd $`;Rnatecc{S}Rroletarrjw

Rnatecc{G}$ os lovfd cy;

$$

`Reat(Rxo) > RodtZ{-Rod`ty}T{Rod`ty} `(x) fT{-3Rpo o x Rxo} mx

$$

prjmugfs;

]ef @jurofr trads`jrn j` a `udgtojd` ;S G os lovfd cy;

`() >

`(x)f3oxmx

seume Natefnatogs
http://find/


12/17



13/17

yp l q

]ypfsfttodl nateYofgfwosf `udgtojds jr gasf casfm `udgtojds

$$`(x) >

Rcflod{gasfs}

9 & xRodRnatecc{Q} RR

1 & xRodRnatecc{O}

Rfdm{gasfs}

$$

`(x) >

9 x Q

1 x O

seume Natefnatogs

http://find/


14/17

yp l q

]ypfsfttodl nateNatrogfs

$$Rcflod{cnatrox}

1 &3 &7 &= RR

0 &< &? &19 RR

6 &0 &7 &1 RR

= &3 &5 &3

Rfdm{cnatrox}

Rcflod{cnatrox}

x R R y R R z R R t

Rfdm{cnatrox}

>

Rcflod{cnatrox}

= R R 6 R R 6 R R 3

Rfdm{cnatrox}

$$

1 3 7 =0 < ? 196 0 7 1= 3 5 3

xyzt

>

=663

seume Natefnatogs

http://find/


15/17

]ypfsfttodl nateMftfrnodadts

$$Rcflod{vnatrox}

1 & 3 & 7 RR

= & 6 & 0 RR

< & 5 & ?

Rfdm{vnatrox}

> 9

$$

1 3 7= 6 0< 5 ?

>9

seume Natefnatogs

http://find/


16/17

Jutbodf



7 Nate roge tacbfs

seume Natefnatogs

http://find/


17/17

]acbfs wote natefnatogab fxprfssojds

Rcflod{tacbf}

Rcflod{tacubar}{|g|b|g|b|}Rebodf

W. Dj. &]ypf &Mflrff

&Fxprfssojd RR

Rebodf

1 & Ablfcraog & 1 & $x$ RRRebodf

3 &Ablfcraog &3

&$xT3 + x + 1$ RR

Rebodf

7 &Ablfcraog &7

&$xT7 + xT3 + x + 1$ RR

Rebodf

Rfdm{tacubar}

Rfdm{tacbf}

W. Dj. ]ypf Mflrff Fxprfssojd

1 Ablfcraog 1 x3 Ablfcraog 3 x3 + x + 1

7 Ablfcraog 7 x7 + x3 + x + 1

seume Natefnatogs
http://find/

The LaTeX Workshop: Typesetting Mathematics in LaTeX

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