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ID. MATHEMA TICS NA PHYSICS - MATEMA TIKA A FYZIKA

HOV," TO READ MATHEIVIATICAJ,;S,YllmOlS IN ENGLISH=~=========~==============~=~====================

+

~ . ,Arithmetic und Alpebra Ie riG~tikI, I reldzibraI (Aritmetika a algebra)

s/b = c/d;a:b =c:d

plus I'pla~I . - pluspositive I pozitivI - kladnyminus I'ma;naeI - minusnegative I negativI - zaporny

plus or minus I'plas 0: 'meinesIpositive or negative I'pozitiv 0:

minus or plus I'maines,o: 'plasInegativeor positive I negativ 0:

..

infinity l!n finitiI - nekone~no .infinite I lnfinitI - nekone~ny; N.B. f~nite 'I'fainaitI- kone~oya times b I'e1 'taiqJz'9i:I - a krat 9a multipl~ed by b I ei maltiplaid bai bi:la b I ei bi:l - ab .

a divided b;'t' b I'ei,di'vaididbai 'bi:Ia over b I ei ouva bi:I - a lomeno b8 by bI'ei bai 'hi:I - a deleno bthe ratio of a to b loa 'reiaiou av 'ei ta 'bi:I

equals I' i:kwalz~ - rovna seis equal to liz i:kwal tal - je rovno

,n! "pro~ortion Ip~a po:sa : a is to b as c is to d 1 ei iz ta bi:

az si: iz ta' di:I - umera a ma se ku b jako c ~u d .identical Iai'dentikalI - identicky, totoznyidentically equal to Iai'dentikal1 'i:kwal.taI - identicky rovnydoes not equal I'daz,not :t:kwaII - nerovna seis not equal to Iiz not i:k\valtal - neni roven

. , ..is approximatelyequalto Iiza proksimitli i:kwdl talpribliZne rovno

similarto I'simila tal - podoboyequivalentto Ii'kwivalanttal - ekvivalentn!must be equal to I'maat bi: 'i:kwaltal - mue! se rovnat

congruent I'ko~ruantI - kongruentn!..

greater than 1 greita oan! - veta! nezless then I'lea oan! - mens! nez

, ;not greater than I not greita oanI - neni vets! neznot less than I'not 'leaoenI - nenimene! nezgreater than or equal to I'greita~an ar '1: kwal talneborovno .

less than or equal to r"lesoan er 'i:kVlaltal' -. mens! nez neborovny

greater than, equal to qr less than l'greita ~an 'i:lQvalta 0: 'leaaanI - vets! nez, rovny nebo men~! neza a a ... to n factors l'ftEktazI:a to the nth I'ei ta ~i 'enGla na n-tou

the positive square (second) root of a ~or positive 8 :, ,')he square (second) root o~t of a l~a skwea (,sekand), ru: t . 8~t avei~ nebo: the square (second) root of a loa skwea (aekand) ru:t

av eiI - druhs odmocnina z an th root of 8 I'enG,'ru:~ av '~iI ,n th root outof a I enG ru:t autav eil

- plus nebo minus'negativI - kladny nebo zaporny; minus nebo pluspozitivI - zaporny nebo kladny

a nasobeno b

a deleno b

pomer a ku b

je

vets! nez

n-ta odmocnina z a

(/1 ,{l ~IAti i/~J tf

+ . +- I _=+= ; +

00

ab; .a. b;a x b

a/b; a of b;a : b

-+

""" ; =

00 .,

.b

=;=>-<

}

i::?:jf;

f!

j

/(

\J.I

( )

I J

< )

I J:( ; ..._~..)

e

loga;.

10g10a

log ,a; In 8;

16g~ 8

l!1ec: b! .

1

'"a

82~

,a

"8

HI.a

la I

the reciprocal ,~ri'ei~ra~alI ,of an : lIana to minus n 1 ei ta maines enI - a na ~-tou, .parentheses 1pa. ~engisi~zl ".round .brackets ,1 raund b~k1 ts1 . - kulat~ dvorkybraces (am.) Ibre1siz1

bracket~ '1 'brrekitl}!, _ .i.square br~ckets .~. akwea b~k1ts1 hranet~ z~vorky

'angular.bracketsI~~~JulQ'b~klteI - lomen~'~a~Qrky- ,.:. ,-,-

braces. I bre~$~zI . - slozen~ zlivorkybrlilC"keta t'brre1i:itsI - za:v.ork~,otevHt zlivorkuend' ~f brackets '1' end av 'bh£ldtsI - z~vorka se zavf.e

. .- . -,. .,'; " ",S + ball squBX'ed I' e1 plss"bi: 0: 1 skweadI :';",$+ b to ceH.na druhou '. . 10-garitmu. . .' . . . .

. ." ., , , ",.. -': ;~'qmmon(Brlgg81an) logar! thm of a. I koman ( brigs:l;an) 'logariQam .av,el~ . (log a.ls llsed.;forl'OglO a when the context aho-yt8'1;hat the base

is 10) - obecn1logl}r1 tmliB,a,', ..' . . '.'., 'log to the base 10 1 log ta oa.be1s ten! - log pl-i'zlikledu 10 .na't~al (Nap1ei-1im):l,ogari t~gto:t' a I' rm~ral (na' pia,~lan) ~loka.rieamBV '1:1 - pf11'"Ozentlogari"tmul)a . " . ,. -: ,., .1t1g'1;o:f;he basee. llog,teQ9. be1e 1:1 -r log pf1:f~akladu etdyo.:tlC6V~ log '," . '. .....

9E,i~U1'"a1losar1 ib of' a c~~~lex: number I' ra?~ral 'log~riQall1 aV'a"komPleks n8ll1baI - prlrqzen$ log komplexn:Cho

nCr;J~J;C(n,'rJ .

; U a " norm of ai' no\:mav ;,e1I'- norrp.a z a: 0; conj a . conjugate of a "I 'k9ndzugi t av ' eiI' _ . . . .I a conjugated Iiei kondzugeitidI', ,. cislo (komplexne) sdruzen~ a a!erg a argument Sf'a I '9:gjl,lm,mtav 'e\! -argutnent a! . amplitude.' of a I ~mp11tju:d ~v elI; -amplituda ajfl(a)j$l(ah Rela) real part of a i'iiai 'pa:'tav"eiI..,realna. Mst ~isla e.,HaJJ .7(a)'j Jf17(~) . . 1ml::lginary part of. a Ii.' ~Q~inarl' ' pa: t av 'eiI - imaglnarn!

c'st cisla a. ,., - - - . , - .-, : -,---' - - - '-x is congruent to a T eks ii.' kbMl'Uant ta eiI

~ '.'~ ...,'..., . " " .' ,.. . ,. ,., '.'uni ~ vec'tor!} along the coordinate axes. I jU11it vektaz a lop 08koli o:dnit a:ksl: zI - jedl1otkov~ vektoryleZicive smerus6uradnych~os' ' , . . '. . .

0..6 j Sahj (o.h)\, scalar; produc~of :the. Veqtors aahd b 1'skEla 'prodakt aV ~a. '.yekt~z ei and bi:I. -.sk~l~rnisoy.cin ~ektorQ a a b " ,

dot ~roduct of the vectors a and b I dot. prodakt av oa vektaz. eiand bHI .'. .' .. '. .a dot b I' et 'dot 'b1: I ; ..:. ' a skalarnen.asobel.l() b

(;1.Kb)Ya'b'j [0:61. "veCtor;prodlic~ otthe "~ct6fs. a andbI'vek\a'prodakt avoavektaz ei ,an~ bi:I ,~ vektofoyy eou~in ve1f~orl1 a a b '. ,

c;ross pr9ductofthe vectors e and b I kros', prodekt av oa vektazei and ,b1:'~ ;". . '. ...' , ,

,across b ' .1 ei 'kros 'bi:I ..:. e vektorbve n~sobeno b'- -, . -.' :.-' ,-." -".."". '-, ',., . .. '..:--> ." ,

factorial.n1~kto:X;ia,l . ~nI _ n fektori~i. n factor,lel Ie.n~k to;.~ia).I ..~. . .. ..

P(I1;rJj liP" the num~ef'9f'p~r~u1:~t19ri§'9f n 'tl)'irig~ t~k~n I' at9 time 158.' nambar~v ;pa:mju: tei~anz, av en' e19z teikn 8:r a::ta tairo!' ...

'. nf I (n -, r)! =.~ (ll';' 1) (0'- 2)... (n~' r +1) .-po~et variac! r te.. tHdy zn...prvkl1 .'

C:;~ 'the nU!1lberOf~o~binatioris,,6f J)thin~8't8ke1)r'at 8 t~meI~a .'. .nambaI'~v,:..~qmbl..n~Uanz :av . en ei9z teikn a:ratatdmI

. nl/Cr! {'d"S-~'rl!j::, ',," . ..' .

..,p,6&etkomb~naollM I.11:s t, ;apa ba,undI . ~" supremum ,greatesti~wer' bpund' I

Kathematical:o~erations

Addi tiOD [a ' dllari ]

to add ( 8ed] - s~:!tatplus [ 'phs] - plus5 + 7 .. 12 tive plus

a + b .. c

seven equals twelveismakesareis equal to

a plus b equals c

Subtraction [sab 'tr 98k!an] - odeCSitan:(to subtract [s'ab 'tr aektJ - odeCSi1;atminus. [ ,main~s ] - m.inus9 - ,}= 6 nine minus three equals six8 - b = c a minus b equals 0Multiplication (,maltipl1 'kei!an] - nasoben:!to IIIUltipl,. ['maltiplaiJ . - nasobitx , . multiplied by, times - nasobeno, krat1 x onoe [ 'waps ]2 x twioe ['twais],} x three times (ate.)

. 5.x ,}. = 15 fi va times three is fifteenab .. c a (times) b equals 0

Division [ di'viz9n]to- div~de [di 'vaid ]: divided by

6 : 2 = ,}a:b=c

d81en1

dUit

six divided by two is threea divided by b equals c

Raising t.o the power ['rehilI t~ cf~ 'pau9] - mocnen1to .ra.iee to the P9wer of [ta 'reia ta

O~~1>lUS x, to the fitth

a plusb all to the nnus on.

a to the minus one

a to the ainus n

a to the one third

a to the miDUa one third

a to the ,one over x

a to the two thirds

[' t"' ] ",,, .L_JExtraotionot the rpot 1k8 traekien9V o~ ru:t -.odmoonovcuu

to extraot the ./nth! root ,Iout/ ot [iks'traektJ - odaocnov~tindex, mn.a. indioes ['indeks.; 'indiai:.] - odaoon1tel

, , .root [ru:t] - koren

r;. the square root ot a ['sk"~]3{& the oube ['kju:b] root ot a, a to the one third

Dall! odmooniDy se tvor! ; uraity a18n + radova a!slovka + root ot

\(a thefourthrootot anJia the nth root of a, a to the one over n~~ thexth rootof a, a to theoneoverx-~~ theminuscuberootot a, oastiji:a to thea!DD8onethird

Fractions ['fr~i9nzJ zlolllk7

a) vulgar fraotions ['valg;} 'fr98ki9JUS] ~ obeon' slo.q

numerator ['nju:mareit9] - oitate1denominator [4i 'nominei ta]- jmenovatel

fraotion line ['fr~ki9n 'lain] - .J.O'llkovaaaraI1/2 a halt, ['ha:f], one ~t1/} onethird I1/4 one quarter,one fourth

Dali! zlomky 8e hor! tak, Ie v oitateU je dd;y a8]cladJU a!alovka, ve jme-novateli radova. Je-li oitatel viti! nei 1, je jmenovatel v mnoin'm o!ale,tj. na konoi je -s. Je-U jmenovate;t.ak01108Il na jedniom, oteme jej jako

zakladn! o!slovku. U n8pravioh'~~~d oteme.p:!smenajako v abeoedi a.lomeno. jako .over" [9UV;}]. "'\ '

3/2 three halves2/5 two fifths4/10 four tenths

a/b a over b

5/21 fiTe over twenty-one .f,

b) deoimal fraotions [' desimal ' fr aelti9n. ] - de's't\tinntS810*7IListo desetinnIS ce.rky biT' tecn (deoili&1 point ['desi89l 'point] )

BIlla prado deset~ou teckQu a8 casto nep:!ie a neote. ILists sa desetinnou-'teckouse otou jednotliv8,pred d.aeti~ t~ou jako oelek.

,nought [,no:t]o (eu]zero (zi

.01

.001

.}2t

2. .1

12.5

point no~t onepoint double nought one

point three two one

two point one

twelve point tiT8

Caloulus andlanalysis ['koolkjul9S g'ngelisiz ] - matematicka analyza

Funotions ['ta~k§gna] - funkce

t(x). ; F(x), etc. funotion of x, funotion x, tx - funkce x

y = t (x) y is equal to the funotion of x, y is equal to the funotionx, y is equal to f of x - y rovna se tunkci x

,Differentiation [, ditel'enSieU9D]. - deri90van!to differentiate [,dif9'ren§ieite] ~ derivovatx to derive [di 'raiv] - odvoaovat

differential y [dif-a 'ren§gl] - diferenoi8.l ya variation in y [,.vegri'eiiignJ - variaoe y .

an inorement of y ['inkrimgnt] - pr!~stek y

y'; f'(x) ; »x y the (first) derivative [di'rivgtiv] of y

with respeot to x, wher~ y = t(x) - prvn!

derivaoe y die x, kde y = t(x)

the (first) derivative of f at Xo - prvn1 de-

rivaoe t(x) dle x v bod~ Xo

the nth derivative of y = f(x) with respect

to x - n-ta derivace y podle x 2

d to the nth y by dx to the nth (e.g.~

d squared y by dx squared; H.B.. is dx

pronounced much longer than in dx above)

the partie.1. derivative ['pa:!l di 'riv'CItiv Jof u = f(x,y) with respect to x - parc18.ln1derivace u dle x

partial ~ by partial dxthe first partial derivative of f(x, y) with

respect to x at (xo ' Yo) - prvn1 parci8.ln!

derivaoe t(x, y) podle x v bcid~ xo' Yo

the second partial derivative of u = f(x, y),

(taken first) with respect to x and then with

respect to y - druba paroi8.ln1 derivace

u = t(x,y) podle x a y

partie.1.d squared u by partial dy dx

cl /Mvf (L, l'lj-. d ~Jfintegrove! (j

dt(x)CiX

tx(x,y) ; Dx(u)

t~ (x,y)

Uxy ; fxy( X,1)

Dy (Dxu)

Integration [,inti 'gre1!an] -to integrate ['intigreit]integrand ['intigr~ntJintegral ['intigrgl]

~b . the intearal of from a to b - integral .. od a do b:.-a

i1itegrovat.integrandintegr8.l

double integra1 - dvoJni integral 'the integra1 ot t(%) with respeot to. % - integral tl%' -, dx

the (detinite) integral. ot t( %) trolL a to be - integrtU t{ %) dxod a do b '

Limits ['limits J - limitylim limit - limita~ tends [ ,tendz ] to, approaches [ ~'prQuCSb ] - bl:U1 selim t(%) = b the limit ot t(%) where % tends to a is equal to. b%~ a limita tl% - pro % bl1!1c1'se a rOTna ,se blim [t( %) + g( %)] =s + t the l1mi t ot t( %) p'lus ef..%) as % tends to a is% ~ a equal to s plus t

Trigonometry [, triga .' nomltri] - trigonometrie[' ,

sin % saln eks ,1 ,sine % [sain eks][' ,

cos % kos eks J, ,ooslne % [k'ausaln eks]

tan % [' t aen ' eka] , ,tangent % [t oondzgnt eka], ,

cot %;ctn % [kot eks] " ,cotangent % [k'au t oondz-ant eks], ,

aec % secant x: [si :k'Jn1;, eka J[

, " ']csc %;cosec % cosecant % k~u sl:~~n~ eks

sin %

ooe. %

tg %

ctg x:

sec'x:cosecx

Gr,ee).:a\Lphabet [' grl;k aelt9bet]

,A 0

E x e r cis e s

e) 2/}, -4/7, 1/2, 3/4, 1/10, 5/100, 3/1000, 6/21, 4/3, 5/22 .

a/b, b Ie, o(../y, 'J[/2, 1/x, x/2, 1/ vx , c+d/c- d

.r-- 3,- ~~ nr- -2r -?J~ 11myx, va, yx+1, vy, va, "X, va-. a

m.r;;.n= ( v-a)n .. an/fA, nJ 1/a = 1/V--;' = a1/nn 17 11, nr:- n~ nrr;:- nr:V ab = 1/a . Vb, a V b = Va-b, V 0 .. 0

2. Read the following 819M:

o ; + ; - ; ! ; a.b; a:b ; x:y .. a:b ; a: ; :=;~ ; -::::::;==; a >b~ ,-- 'If - == *it " ,a -r b ; Y

c,:;;:".LATIN' ABBREVIA~IONS IN .'cOMMONUSE "IN ENGLISH

,.,):',/>:,'.;.iI .' ,=~,:::~,==~===~===~~,~,=,~,~:~~'~~=~:;'~==.~~~========".Abbreviaiion: / . 't~'oin~the .Latin :- ":;:~~!~~.iij;.:th~~f~~;itJ?ipi~gi;"! "

l f. i,ba~clem]:";i:~?'~L. in9 e~.:~'B8i~"':p~e ia] .i

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; '" ".

..""...;';':,:;.

C" i ':, .'f t"

h" . .::-, .--~'" ...

.:'.

'.;.:.'

..:t

.

h.

....:~.em"... ',," " n e ,same au.' 0..,

~~i*W~emJ. " .'::;j;;~i::~;fi;~~~::;,.i.e.,-,,-;that is '

~tt.~:~:';. .. ::.+;~¥)f( ~~'a~~~~M.:~:. ~o ~Y:';(izJloco' H tato"',';';':)hloc.qi t~

1..1nthe "place

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