FIC MATLAB 2017-2/Aula-13
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%-- 24-10-2017 19:02:50 --%
clc
% Pacote simbólico
vitdec
help vitdec
clc
factorial(52)
format long compact
format compact
format long
factorial(52)
sym('factorial(52)')
sym(factorial(52))
expr1 = sym('x^2 + sin(x)')
expr2 = sym('a*x + b')
expr3 = sym('(a*x + b) / (c*x + d)')
pretty(expr3)
expr4 = sym('(a*x^2 + b) / (c*x + d)')
pretty(expr3)
pretty(expr4)
syms x y z a b c
x
x^2 + a*z
expr5 = x + y
expr6 = a*x == z^2
pretty(expr6)
w = 100
x + w
latex(expr6)
latex(expr4)
pretty(expr4)
subs(expr4, a, 7)
subs(expr4, {a, b}, {7, -1})
subs(expr4, {a, b, x}, {7, -1, [0, 1/2, 1]})
expr4a = subs(expr4, {a, b, x}, {7, -1, [0, 1/2, 1]})
subs(expr4a, {d, c}, {4, 17})
subs(expr4a, {'d', c}, {4, 17})
subs(expr4a, {'d', c}, {pi, 17})
expr4b = subs(expr4a, {'d', c}, {pi, 17})
clear e8
expr4b
double(expr4b)
sym('pi')
double(ans)
sym(pi)
sym(3*pi)
expr4
a = 14
subs(expr4)
b = sym('2*x')
subs(expr4)
subs(expr4, 'd', 1)
subs(expr4, 'a', 100)
expr7 = x*(x+1)
expand(expr7)
expr7a = expand(expr7)
factor(360)
factor(expr7a)
ans(1)*ans(2)
factor(expr7a)
expr7b = prod(factor(expr7a)
expr7b = prod(factor(expr7a))
expr8 = 7*x^2 + 7*(x + 1)
expr8 = x*y^2 + (1+x)*y + y^2
collect(expr8, x)
collect(expr8, y)
doc simplify
simplify(expr8)
clear all
syms x a b c
eq2grau = a*x^2 + b*x + c
solve(eq2grau, x)
sols = solve(eq2grau, x)
pretty(sols)
syms d
eq3grau = a*x^3 + b*x^2 + c*x + d
sols3 = solve(eq3grau, x)
pretty(eq2grau)
solve(eq2grau, b)
sols
subs(sols, {a,b,c}, {1, -5, 6})
subs(sols, {a,b,c}, {1, -5, 7})
double(ans)
% Limites
sin(1e-5) / (1e-5)
(1 + 1/1e5)^1e5
clear all
syms x
limit(sin(x)/x, x, 0)
limit((1 + 1/x)^x, x, inf)
double(ans)
limit('(a^x - 1)/x', x, 0)
limit('zuera', 'zuera', inf)
limit(sym('zuera'), 'zuera', inf)
% Derivadas
diff(sym('a*x^2 + sin(b*x)'), x)
diff(sym('a*x^2 + sin(b*x)'), 'a')
diff(sym('a*x^2 + sin(b*x)'), x, 2)
diff('tan(x)'), 'x')
diff(sym('tan(x)'), 'x')
e1 = diff(sym('tan(x)'), 'x')
e2 = e1 - (1/cos(x))^2
simplify(e2)
simplify(e1)
simplify(1/cos(x)^2)
exp(1)
sym('exp(1)')
syms a b c
f1 = a*x^2 + b*x + c
diff(f1, x, 3)
diff(f1, x)
diff(f1, x, 2)
diff(f1, x, 3)
% Integrais
int(x^a, x)
pretty(ans)
log(10)
log10(10)
limit((x^2 + x - 6) / (x^2 - 3*x + 2), x, 5)
limit((x^2 + x - 6) / (x^2 - 3*x + 2), x, 2)
limit((x^2 + x - 6) / (x^2 - 3*x + 2), x, 7)
limit((x^2 + x - 6) / (x^2 - 3*x + 2), x, 5/3)
ezplot((x^2 + x - 6) / (x^2 - 3*x + 2))
int('exp(-x^2)', x)
int('exp(x^2)', x)
doc erfi
int(x^2, x)
int(x^2, x, 0, 2)
int(x^2, x, a, b)
int(x^2, x, a, inf)
int(exp(-x), x, 0, inf)
int(exp(-x), x, 0, a)
int((1 / sin(x)^a, x)
int(1 / sin(x)^a, x)
int(1 / sin(x)^6, x)
int(exp(-x^2/2))
int(exp(-x^2/2), x, -inf, inf)
int(x*exp(x), x)
int(x^a, x)
assume(a > 0)
assumptions(a)
int(x^a, x)
assume(a == -1)
assumptions(a)
int(x^a, x)
assume(a, 'clear')
assumptions(a)
assume('clear') % Será que funciona?
assume((a ~= 0) & (a ~= -1))
assumptions(a)
int(x^a, x)
doc assume
sin(x*pi)
assume(x, 'integer')
sin(x*pi)
simplify*sin(x*pi))
simplify(sin(x*pi))
assume(x, 'clear')
simplify(sin(x*pi))
syms r
sum(r^x, x, 0 inf)
sum(r^x, x, 0, inf)
symsum(r^x, x, 0, inf)
pretty(ans)
symsum(x*r^x, x, 0, inf)
assume(abs(r) < 1)
symsum(r^x, x, 0, inf)
symsum(x*r^x, x, 0, inf)
symsum(x^2*r^x, x, 0, inf)
% Taylor
taylor(exp(x), x, 5)
pretty(ans)
taylor(exp(x), x, 4)
taylor(exp(x), x, 'Order', 4)
taylor(exp(x), x, 'Order', 5)
symsum(1/x, x, 1, inf)
taylor(cos(x), x, 'Order', 5)
expr = x^2 / (x^3 - 3*x + 2)
pretty(expr)
partfrac(expr, 'x')
partfrac(expr)
pretty(ans)
expr = x^2 / (x^3 - 3*x + 2)
doc fourier
doc rect
doc fourier
syms x y
f = exp(-x^2);
fourier(f, x, y)
fourier(cos(x), x, y)
assume(x, 'integer')
fourier(cos(x), x, y)
dirac(x)
clear all
syms x y z
sol = solve(3*x + 2*y == z, x^2 + y^2 == 1, x + y + 2*z == 0, x, y, z)
sol.x
sol.y
sol.z
assume(x>0)
sol = solve(3*x + 2*y == z, x^2 + y^2 == 1, x + y + 2*z == 0, x, y, z)
syms.x
sol.x
sol.y
sol.z
help dsolve
syms x(t) y(t)
z = dsolve(diff(x) == y, diff(y) == -x)
z.y
z.x
doc syms
doc laplace
clear all
syms x y
f = 1/sqrt(x);
pretty(f)
laplace(f, x, y)
divisors(sym(42))
divisors(42)
divisors(x^4 + 1)
divisors(x^4 - 1)