Mathe-pronun.pdf

Universit´e Louis Pasteur - Strasbourg I UFR Maths-Info Anglais Scientifique 2006-2007 Licence

Reading Mathematical Expressions (A. Oancea, S. Maillot, C. Mitschi) Note: Some groups of letters are underlined in order to draw one’s attention to their pronunciation. Basics a+b a−b a·b a , a/b b 1 1 1 1 , , , ..., 2 3 4 10 5 2 7 , , ..., 2 3 10 a=b a = b ab a≥b

a plus b a minus b ab, a times b a over b, a divided by b one half, one third, one fourth, ... , one tenth five halves, two thirds, ... , seven tenths a a a a a a

equals b, a is equal to b different from b, a not equal to b (strictly) less than b less than or equal to b (strictly) bigger than b, a greater than b greater than or equal to b

Powers and roots ab a to the b, a to the b-th (power) [if b is a positive integer] 2 x x squared x3 x cubed −1 x√ x inverse n √ t n-th root of t t square root of t √ 3 t cubic root of t 1

Sets ∅ A∪B A∩B Ac A\B A×B x∈A

(the) empty set A union B A intersected with B the complement of A A minus B A times B x in A, x belongs to A, x belonging to A

Miscellaneous 5% 30◦ xk j x i n 2 k=1 k n

2k+1 k=1 2k+2

n! partie enti`ere de x |x| |z| Re(z), Im(z)

x

v, w cos sin tan etc. ηθξ πσχψ R2 , R3 , Rn (blablabla) · (blbl) blablabla blbl x 1 , . . . , xn

five percent thirty degrees xk x i j [if j is an index, not an exponent!] sum k equals 1 to n of k 2 , sum for k (running) from 1 to n of k 2 , summation k from 1 to n of k 2 product k equals 1 to n of 2k + 1 over 2k + 2 product for k (running) from 1 to n of 2k + 1 over 2k + 2 n factorial integer part of x absolute value of x (if x is a real number) modulus of z (if z is a complex number) real part of z, imaginary part of z norm of x scalar product of v and w cosine/cosinus sine/sinus tangent etc. eta [´ıta] theta [th´ıta] xi [ks´ai] pi [p´ai] sigma [z´ıgma] chi [k´ai] psi [s´ai] R 2, R 3, R n blablabla, the whole times blbl blablabla, the whole divided by blbl x1 up to xn

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Calculus f

f prime, f dashed d by dx df by dx d x f , partial derivative of f with respect to x

d dx df , ∂f dx ∂x

∂ f x b

f (s)ds  a  , D

±∞ lim f (x)

integral from a to b (of) f (s) ds double integral, triple integral over the domain D D

x→a

log(x), loga x exp(x), ex

plus/minus infinity (the) limit of f (x) as x tends/goes to a, (the) limit of f of x as x tends/goes to a logarithm of x, logarithm in base a of x exponential of x, e to the x

Functions f :U →V f (x) x → f (x) of class C k of class C ∞ the Lebesgue spaces Lp , L∞ the Sobolev spaces H k , W k,p

f from U to V f of x x maps to f (x) of class C k of class C infinity the Lebesgue spaces L p, L infinity the S´obolev spaces H k, W k p

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