# MATLAB MATLAB max(x) x x [y, i] =

MATLAB MATLAB

max(x) x x [y, i] = max(x) x y i x min(x), [y, i] = min(x)

max(A) i A i [y, u] = max(A) y u y A u max(A, [], dim) dim 1 max(A) dim 2 i A i min(A), [y,u] = min(A), min(A, [], dim)

x prod(x) x sum(A) i A i prod(A) i i sum(A, dim) prod(A, dim) dim = 1 sum(A) prod(A) dim = 2 sum(x)

n 1 x xi n i 1 1 n 2 1 ( xi x ) n 1 i 1 1 n 2 ( xi x ) 2 n i 1

mean(x) x std(x) x y=mean(A,dim)

dim = 1: y i A i dim = 2: y i A i y=std(A,flag,dim) dim = 1: dim = 2: flag = 0: flag = 1:

1 2 r=corrcoef(x,y) x [ x1 , x2 ,..., xn ] y [ y1 , y2 ,..., yn ]

n ( x x )( y i r i y) i 1 n (x x) i

i 1 2 n (y i 1 i y) 2

x y [y,i] = sort(x) x y i y x y=sort(x) n n+1

0 n n p( x) a1 x a2 x n 1 ... an x an 1 MATLAB p(x) p=[a1,a2, ,an,an+1]

conv(p1,p2) p1, p2 [q, r] = deconv(p1, p2) p1 p=polyder(p1,p2) p1 p2 [p,q] = polyder(p1,p2) p1 p2

p q p=polyder(p1) y=polyval(p, x) x x

x=roots(p) p=poly(x) x z=fzero(fname,x0) x0

fminbnd: x=fminbnd(fname,x1,x2) x1,x2: fminsearch: x=fminsearch(fname,x0) x0:

-f(x)f(x) MATLAB sym sym a=sym(a) a a MATLAB

a=sym(a); b=sym(b); % a,b x=3; y=4; % x,y w=a*a+b*b % w=x*x+y*y % whos MATLAB p1=sym(pi); a=sym(3); b=sym(4); %

p2=pi; x=3; y=4;% sin(p1/3) % sin(p2/3) % cos((a+b)^2) sin(pi/4) cos((x+y)^2) sin(pi/4) MATLAB syms syms syms var1 var2 varn var1,var2,,varn

(') MATLAB : y=1/sqrt(2*x) sym z = sym(3*x^2-f(x)5*y+2*x*y+6) A= sym([a,b;c,d]) syms x y;

z= 3*x^2-f(x)5*y+2*x*y+6 MATLAB findsym(s) s syms a b x y; % c=sym(3); % s=3*x+y; findsym(s) findsym(5*x+2) findsym(a*x+b*y+c)

MATLAB symadd symsub symmul symdiv sympow

MATLAB factor(s) expand(s) collect(s) collect(s,v) s

s s s v MATLAB sym sym(1.5) eval x=(1+sqrt(5))/2 eval(x) y=3/2 eval(y)

MATLAB limit limit(f,x,a) limit limit(f,x,a,'right') limit(f,x,a,'left') MATLAB

MATLAB diff(f,x,n) diff f x n x limit limit n 1 MATLAB MATLAB int

int(f,x) int f x x diff int(f,x,a,b) MATLAB symsum(s,x,n,m) s x n m

2.13 MATLAB taylor(f, x, n, a) f x n a f x=a MATLAB

x=solve(s,x) s x [x1,x2,,xn] = solve(s1,s2,,sn,x1,x2,,xn) s1,s2,,sn x1,x2,,xn. MATLAB D Dyy, D2yy dsolve

dsolve(e,c,x) e, c x c dsolve(e1,e2,,en, c1,c2,,cn,x1,x2,,xn)

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