1. ^ffc^ffc^GD Bft<^7 (How to read equations) HiB (Notations) / mzMM [ ] m^x-^m 1 Hift^iftjtfDnJC^^T (How to read equations) 1.1 ift (numbers) 100] a [one] hundred (one, a^r^tl^V^ t ) 10,000 ten thousand 628,000 six hundred and twenty-eight thousand 12,000,000 twelve million 2,000,000,000 two billion 2,000,000,000,000 two trillion [3.55 J three point five five [0.32] zero point three two [0.333 • • • J zero point three recurring [0.35848484 • • • ] zero point three five eighty-four recurring [20 — 30 ] twenty to thirty 4 x 105J four times ten to the fifth/ four times ten to the fifth power/ four times ten to the power of five 6.5 x 10 3J six point five times ten to the minus three 1. ^ffc^ffc^GD Bft<^7 (How to read equations) 1.2 B#fe1 (ffi) (years, time, etc.) [l995J nineteen ninety-five [l800j eighteen hundred [2000] two thousand [2006] two thousand six/twenty oh six [7 : 00a.m.] seven am/ seven in the morning1 [2 : 30] two thirty/ half past two/ two half (Br.) [10 : 18] ten eighteen/ eighteen past (after) ten [9 : 45] nine forty-five/ a quarter to (of) ten $35.80J thirty-five dollars and eighty cents [l cent] a penny [5 cents] a nickel [10 cents] a dime [25 cents] a quarter 1.3 a/b ftWi (fractions) a over b ab/cd a times b over c times d 1/n one nth/ one over n 1/2 one half/one-half/a half 1/3 one third/one-third/a third 1/4 one quarter/one-quarter/a quarter 3/4 three quarters/three-quarters (1/5 one fifth/one-fifth/a fifth Vclock (io^&V^ 1. ^ffc^ffc^GD Bft<^7 (How to read equations) 2/3 two-thirds 4/3 four over three/four thirds/four-thirds 1/10 one tenth /a tenth/one-tenth 3/7 three sevenths/three-sevenths 112/303 a [one] hundred (and) twelve over three hundred (and) three five (and) two-fifths twenty-one over three hundred (and) eleven 21 311 1.4 ^K.^ (suffices), Hit( powers, roots) —x] minus [negative] x [x'\ x prime2 (W) x bar {&} x hat/ x wedge [x~j\ x sub i x super i 7 J seven squared 53J five cubed / five to the third power x squared x cubed/ x to the third power xn\ x to the nth power/ x to the nth/ x to the powemfo/ x to the 72 x to the minus 72th power/ x to the power minus n/ x to the minus 72 x to (the) half power/ the square root of x the cube root of x the nXh root of x a/2 a/3 a/n 2 a; dash £ t> e"5 #s dash It-OfSt fo5 0 1. ^ffc^ffc^GD Bft<^7 (How to read equations) \/2 the square root of two \/2 the cube root of two the nth root of x yjx + y the square root of the sum of x plus y 1.5 JP/i" JUgBi" fH/£" ffe) ( addition, subtraction, multiplication, division, etc.) x — y x minus y x + y x plus y x ± y x plus minus y/ x plus or minus y x^fy x minus or plus y xy, x x y x times y / x multiplied by y [x • y] x dot y x -T- y x divided by y x/y \ x over y [x : y] the ratio of x to y [re!J 72 factorial / factorial 72 binomial 72 over a / binominal coefficient n over a n choose a 1 • • • 5) one to five one plus three plus five dot dot dot 1+3+5+ x(y + z) x times the sum of y plus z / x open parenthesis y plus z close parenthesis3 (x + y)z open parenthesis x plus y close parenthesis multiplied by zj (initial) parenthesis x plus y (final) parenthesis multiplied by z 3 V =¥y xM%~ete parenthesis bracket SrfflWS „ ffi$&b parentheses, brackets 11» English for Science and Engineering 1. ^ffc^ffc^GD Bft<^7 (How to read equations) x in brackets \{x[y + (z — w)]} one half times open brace x open bracket y plus open parenthesis z minus w close parenthesis close bracket close brace x'y" x prime times y double prime/ x prime times y second prime modulus of zj absolute value of z Z A angle A [lAJ right angle A 1.6 s***} h Jls, ^T^'J, vectors, matrices, functions) x, x vector x \x • y] x dot y 4 x x y x cross y ( au ai2 Ö13 ^ ß21 Ö22 Ö23 y a3i a32 ß33 / matrix with the diagonal a sub one one to a sub three three [detAJ determinant A f(x) function of xj f of x f (x) inverse of the function / of xj f of x to the power minus one exp(x) e to the xth power/ e to the power x exp(kc) e to the power ix [\nx\ the natural log of x logx the log of x log10 x the common log of x log2 x the binary log of x/ the log of x to the base two 4 f*3fi!S(i dot [scalar, inner] product, ^SKi cross [vector, outer] product0 Outer product l~t^\-W.SX^\-(DM^< EVE English for Science and Engineering 1. ^ffc^ffc^GD Bft<^7 (How to read equations) lim^^oo f(x) the limit of the function / of x as x goes to [approaches] infinity sins sme x cos a; cosine x [tanx] tangent x [cosec x) cosecant x [secx) secant x cot a;, ctg a;, etna; cotangent x [sinhxj sinch x/ shine x/ hyperbolic sine x [cosha;J kosh xj hyperbolic cosine x [ tanh x J than x/ tanch x/ hyperbolic tangent x [cosechxj kosetch x j hyperbolic cosecant x [sechxj setch x f hyperbolic secant x [cothsj koth x/ hyperbolic cotangent x [arcsinx] arc sine x/ the angle whose sine is x [arccosxj arc cosine xj the angle whose cosine is x [arctana:] arc tan xj the angle whose tangent is x [arccosecx] arc cosec xj the angle whose cosecant is x [arcsecx] arc sec xj the angle whose secant is x arccot x, arcctn x\ arc cot x/ the angle whose cotangent is x inverse cosine xj cos minus one x inverse sine xj sine minus one x cos 1 x sin 1 x tan-1 x\ inverse tangent x/ tangent minus one x cot-1 x\ inverse cotangent x/ cotangent minus one x inverse secant xj secant minus one x sec 1 x cosh 1 x j inverse kosh xj inverse hyperbolic cosine xj kosh minus one x sinh 1 x J inverse shine xj inverse hyperbolic sine xj shine minus one x 1. ^ffc^ffc^GD Bft<^7 (How to read equations) tanh 1 x J inverse than xj inverse hyperbolic tangent xj than minus one x sech 1x\ inverse setch x/ inverse hyperbolic secant x/ setch minus one x 1.7 fft^, $&fP (derivatives, differentials, integrals, sums) A/1 delta // finite difference of / [dx J differential of x dfdx d / of x d x da; d/(z) da; dx dif / to dif xj the partial derivative of / with respect to x/ round / round Dxf D sub x of // the derivative of / with respect to x Sf(x) small difference in the function / of x la f(x)^x the integral from a to b of / of x with respect to x ff double integral fff triple integral circuital integral / integral round a closed circuit Yli=i ai the sum from i equals one to n of a sub ij the sum of all terms of a sub i from i equals one to i equals n n^Li ai the product from i equals one to n of a sub ij the product of all terms of a sub i from i equals one to i equals n 1.8 Hit, ^^lit (equations, inequality) [20 + 12 = 32 Twenty plus twelve equals thirty-two. [50 — 16 = 341 Fifty minus sixteen equals thirty-four. [7 x 5 = 35J Seven times five is [equals, is equal to] thirty-five. 1. ^ffc^ffc^GD Bft<^7 (How to read equations) 15 -j- 5 = 3 Fifteen divided by five equals three. 18/2 = 9 Eighteen over two is nine. 10/20 = 1/2 Ten-twentieths is reduced to one half [one-half] 31 -j- 7 = 4r3 Thirty-one divided by seven is four with a remainder of three. 4.1 — 8.3 = — 4.2 Four point one minus eight point three equals minus [negative] four point two. 22 = 4j Two squared is four. 23 = 8J Two cubed is eight. [2 : 3 = 4 : 6J Two is to three as four is to six. [x = y] x equals y.j x is equal to y. x [I y x is parallel to y. .'. x = y Therefore x equals y. x = y since x equals y. [x : y = z : w] x is to y as z is to w. 3x + 2x = 5x J Three x plus two x equals five x. y = —5x2 + 2x + 4 y equals minus [negative] five x squared plus two x plus four. (x + y)2 = x2 + 2xy + y1 The quantity x plus y squared is x squared plus two xy plus y squared.5/ Open parenthesis x plus y close parenthesis squared is x squared plus two xy plus y squared.3 (x + y)(x - y) = x2 - y1 The quantity x plus y times the quantity x minus y equals x squared minus y squared.6 Open parenthesis x plus y close parenthesis, open parenthesis x minus y close parenthesis, is equal to x squared minus y squared.3 x2 + y2 = z2 x squared plus y squared equals z squared. 5quantity x plus y y x is greater [more] than y. x < y a is less [smaller] than b. x > y x is greater [more] than or equal to y.j x is equal to y or greater [more]. x < y x is less [smaller] than or equal to y./ x is equal to y or less [smaller]. [x y] x is much greater than y. x <^y\ x is much less [smaller] than y. x + y> z x plus y is greater than z. 2x + y < z Two x plus y is less than or equal to z.j Two x plus y is equal to z or less. x^y x tends to y.j x approaches y. [x ~ y] x is nearly equal to y./x is approximately equal to y. [x = y] x is identical with [to] y. x^y x is not identical with [to] y. x II y x .Ly x is perpendicular to y. x is parallel to y. [x ~ y] x is asymptotic to y. [x oc y] x is proportional to y./ x is in proportion to y. x oc 1/y x varies inversely with y.j x is inversely proportional to y. [/A = ZB] Capital a has the same angle as capital b.j The angle A is equal to the angle B. [ABC = DEF\ All capital abc coincides with all capital def. 3cf. 7i/w-©Hit-Sa, Fermat's last theorem English for Science and Engineering 2. Glossary 10 2 Glossary 2.1 Basic terms J£"t~ plus 31 "n minus 30>tt<5 times, MULtiplied by ts><5 over, deVIDed by AXiom ^» defiNItion ^ffl THEorem ^ CORollary fiEK proof ftffc ALgebra geOMetry ffltir aNALysis INteger, INtegral NUMber ^ilfc prime NUMber CARdinal NUMber Ff%L ORdinal NUMber ffiffc Even NUMber odd NUMber MtJ^^ffl^k. greatest COMmon diVIsor ft/Jv&fgifc least COMmon MULtiple H#: FACtor ^Hffc prime FACtor Hifc^Ä? factoriZAtion ^Hffc9"Ä? factoriZAtion in prime NUMbers /hf& DECimal FRACtion deNOMinator ^^f*" Numerator H^SA round off §39 ±tf round up W) round down HIS: REal NUMber älffc iMAGinary NUMber comPLEX NUMber/ COMplex NUMber itM proPORtion Ex.) A is proPORtional to B./ A is in proPORtion to B. lEitM diRECT proPORtion MitM INverse proPORtion Ex.) A is INversely proPORtional to B. ^ eQUAtion 1 VÖjU^ SIMple eQUAtion BMJj&Z LINear eQUAtion 2 ^C^"©^: quaDRAtic eQUAtion 3 dÖjW^ CUbic eQUAtion n rcth-deGREE eQUAtion EVE English for Science and Engineering 2. Glossary 11 WÄJjU^ differENtial eQUAtion MWfrJiUä: PARtial differENtial eQUAtion simulTAneous eQUAtion m%L FUNCtion 1 &M%L Linear FUNCtion 2 IkmWL quaDRATic FUNCtion Wti differENtial Wt$& differentiAtion m^Wc deRIVative H# INtegral WM£ inteGRAtion -^IrI conGRUence/ conGRUent /CONgru-ence / CONgruent fäfö simiLARity/ SIMilar Mfä SYMmetry If ipg width flue* height &?T# depth length 1S$ weight ARea VOLume f&jH base Mti VERtex 9^ =¥y ^ ^ff-ett trapezoid # 3n face ffflffi LATeralface a (HÄ^) side R circle HR elLIPSE / Oval ¥@ RAdius ias diAMeter TRIangle %fa=.faM(DTä leg/ hyPOTenuseadjacent r^32HÄ^ iSOSceles TRIangle ÜL^IHÄ^ right TRIangle IE = Ä^ equiLAteral TRIangle ^32HÄ^ scaLENE [SCAlene] TRIangle quadriLAteral, QUADrangle ( m , quadRANgle(^) opposite ¥fflOT^ paralLELogram TRAPezoid ^32032^ traPEzium9 JEjjfö square gjjfö RECtangle oblon9 Wfo RHOMbus = diamond PENtagon HEXagon Aftm OCtagon POLygon trapezium ißisfö EVE English for Science and Engineering 2. Glossary fh&fate con VEX POLygon B&ftM conCAVE POLygon prism PYRamid Rft CYLinder R$t cone 2.2 ^ h Jl/fiW (vector analysis) W,gradV| NABla CAPital V / GRAdient CAPital V V -E,6ivE\ diVERgence of VECtor field CAPital E Vx£, rot£ roTAtion of VECtor field CAPital E AV LaPLACian CAPital V 2.3 ^-fi (units) 53 grams, 2 centimeters (DX. 5 fcWt&M&t 5 o L , gs, cms E><£ 5 , g, cm (D (mj MEter fern) CENTImeter reCIProcal CENTImeter/ per CENTImeter cm -l mol"1 ] per mole (3S1H3 mom h ISf) (sj SECond (g) gram [kg] KILOgram (n) NEWton [JJ joule jergj erg (A) AMpere (C) COUlomb O ohm (ISWf* oum) (s) SIEmens (T) TESla [Pa] pasCAL [Wbj WEber [KJ KELvin ^C| deGREE CENtigrade/ deGREES CELsius10 \Mj MEGa- 106 (GJ GIGa- 109 (t) TERa- 1012 (PJ PETa- 1015 (EJ EXa- 1018 (ZJ ZETta- 1021 (mj MILli- 10-3 Micro- 10-6 (n) NAno- KT9 (p) Pico- 10-12 (fj FEMto- 10-15 (a) ATto- 10-18 (z) ZEPto- 10-21 Iftfi FAHrenheit, Sft = (^ft - 32) * 5/9