Phrasebook

Now that you know all the names for mathematical symbols, it's high time to use them to build up longer phrases! Click on the name of the folder of your interest to read and listen to complex phrases from all areas of mathematics..

Słowniczek Wyrażeń

Teraz gdy już znasz wyrazy opisujące matematyczne symbole, nadszedł czas na składanie ich w dłuższe wypowiedzi! Kliknij na tytuł katalogu który Cię interesuje, żeby czytać i słuchać skomplikowanych wyrażeń z różnych dziedzin matematyki.

$a=b$

a is equal to b
a equals

$a\neq b$

 a is not equal to b
 a doesn't equal b

$a<b$

 a is less than b

$a\leq b$

 a is less than or equal to b

$a>b$

 a is greater than b

$a\geq b$

 a is greater than or equal to b

$a+b=c$

 a plus b is c
 a plus b is equal to c
 a plus b equals c
 a plus b makes c

$a+b<c$

 a plus b is less than c

$a-b=c$

 a minus b is c
 a minus b is equal to c
 a minus b equals c
 a minus b makes c

$a\cdot b=c$

 a times b is c
 a by b is equal to c
 a multiplied by b equals c
 a times b makes c

$\dfrac{a}{b}=c$

 a divided by b equals c
 a over b makes c

$(2a-3b)$

 open bracket, two a minus three b, close bracket

$\dfrac{a\cdot b^2}{b}=ab$

 a times b square over b equals a times b

$\dfrac{a+b^2}{c}$

 a plus b square all divided by c

$\dfrac{\sqrt{a+b^2}}{c}$

 the square root of a plus b square all divided by c

$(a+b)^2=c$

 a plus b all square equals c

$\dfrac{a}{\infty }=0$

 a divided by infinity equals zero

 

$y=f(x)$

 y is a function of x
 y equals f of x

$y=\sin x $

 y equals sine of x

$y=\cos x $

 y equals cosine of x

$y=\tan x $

 y equals tangent of x

$y={\rm ctan}\; x $

 y equals cotangent of x

$y=\arcsin x$

 y equals arcus sine of x

$y=\arccos x$

 y equals arcus cosine of x

$y=\arctan x$

 y equals arcus tangent of x

$y=e^x$

 y is an exponent of x

$y=\log x$

 y equals the logarithm of x

$y=log_3 x$

 y equals the logarithm of x to the third base

$y=\ln x$

 y equals the natural logarithm of x

$\displaystyle\lim_{x\rightarrow \infty}f(x)=5$

 the limit of f, as x approaches infinity, is equal to 5
 f of x converges to 5 as x tends to infinity

$\displaystyle\lim_{x\rightarrow \pi }\sin x=0$

 as x approaches pi, the sine function approaches zero

$\displaystyle\lim_{x\rightarrow 7^{+}}f(x)=3$

 function f has a right-hand-side limit 3 as x approaches 7
 f approaches 3 as x approaches 7 from the right-hand-side

$\displaystyle\lim_{x\rightarrow 2^{-}}f(x)=1$

 function f has a left-hand-side limit 1 as x approaches 2
 f approaches 1 as x approaches 2 from the left-hand-side

 

$f'(x)$

 f prime of x
 the first derivative of f

$f''(x)$

 f double prime of x
 the second derivative of f

$\dfrac{dy}{dx}$

 dy over dx
 the first derivative of (function) y with respect to (variable) x

$\dfrac{d^2y}{dx^2}$

 d two y over dx squared
 the second derivative of y with respect to x

$\dfrac{d^ny}{dx^n}$

 the n'th derivative of y with respect to x

$\dfrac{\partial ^2z}{\partial x^2}+\dfrac{\partial ^2z}{\partial y^2}=0$

 partial d two z over partial dx square plus partial d two z over partial dy square equals zero

$\displaystyle\int f(x)dx$

 integral of f of x times dx

$\displaystyle\int_{a}^{b} f(x)dx$

 integral from a to b of f of x dx

$\displaystyle\int_{a}^{b} \dfrac{dy}{\sqrt{1-y^2}}$

 integral of dy divided by the square root of one minus y square

$\displaystyle\iint_{D} f(x,y)dxdy$

 double integral of f of x and y dx, dy, over domain D
 double integral on D of f of x and y with respect to x first

$\displaystyle\iiint_{T} f(x,y,z)dxdydz$

 tripple integral on T of f of x, y and z with respect to x first and y second

 

$V=u \sqrt{\sin ^2 i+\cos ^2 i}=u$

 capital V equals u square root of sine square i plus cosine square i equals u

$4c+W_3+2n_1a'R_n=33\dfrac{1}{3}$

 four c plus capital W third plus two n first a prime capital R sub n equals thirty three and one third

$P_{cr}=\dfrac{\pi ^2E_l}{4l^2}$

 capital P sub c r equals pi square times capital E sub l all over four l square

$\left[\left( x+a\right)^p-\sqrt[r]{x}\right]^{-q}-s=0$

 x plus a in round brackets to the power p minus the r'th root of x all in square brackets to the power of minus q minus s equals zero

$(D-r_1)[(D-r_2)y]=(D-r_2)[(D-r_1)y]$

 open round brackets, capital D minus r first, close the round brackets, open square and round brackets, capital D minus r second, close round brackets, by y, close square brackets, equals, open round brackets, capital D minus r second, close the round brackets, open square and round brackets, capital D minus r first, close the round brackets, times y, close the square brackets

$u=\int f_1(x)dx+\int f_2(y)dy$

 u is equal to the integral of f sub one of x multiplied by dx plus the integral of f sub two of x multiplied by dy

$a_v=\dfrac{m\omega \omega ^2\alpha ^2}{[rp^2m^2+R_2(R_1+\frac{\omega ^2\alpha ^2}{rp})]}$

 a sub v is equal to m omega, omega square alpha square divided by square brackets, r, p square m square plus capital R second, round brackets opened, capital R first plus omega square alpha square divided by r p, round and square brackets closed

$K=\displaystyle\max_{j}\sum_{i=1}^{n} |a_{ij}(t)|\quad (t\in [a,b];j=1,2,\ldots ,n)$

 capital K is equal to the maximum over j of the sum from i equals one to n of the modulus of a sub i j of t, where t lies in the closed interval a b and where j runs from one to n

$\displaystyle\lim_{n\rightarrow \infty }\int_{\tau }^{t}\{f[s,\psi_n(s)]+\Delta _n(s)\}ds=\int_{\tau }^{t}f[s,\psi (s)]ds$

 the limit, as n becomes infinite, of the integral of f of s and psi sub n of s plus delta n of s with respect to s, from tau to t, is equal to the integral of f of s and psi of s, with respect to s, from tau to t

$f(z)=\widehat{\psi }+\Theta |z|^{-1}\quad (|z|\rightarrow \infty , arg z=\gamma )$

 f of z is equal to psi hat plus capital theta times the modulus of z to minus first power, as the absolute value of z becomes infinite, with the argument of z equal to gamma

$D_{n-1}=\displaystyle\prod_{s=0}^n(1-x^2_s)^{\epsilon-1}$

 D sub n minus one of x equals the product fom s equal to zero to n of, parenthesis, one minus x sub s squared, close parenthesis, to the power of epsilon minus one