FIC MATLAB 2017-1/Aula-13

factorial(52)
sym('factorial(52)')
sym(factorial(52))
sym('2^200 + 1')
sym(2^200 + 1)
e = sym('x^2 + sin(x)')
e = sym('a*x + b')
e = sym('(a*x + b) / (c*y + d)')
pretty(e)
e = sym('(x^2 + a*x + b) / (c*y + d)')
pretty(e)
syms x y a b
x
e2 = x^2 + a*x + b
eq1 = sym('x^2 = y')
eq2 = x^2 == y
eq1 = sym('x^2 == y')
eq1 = sym('x^2 = y')
syms x y a b
eq2 = x^2 = y
eq2 = x^2 == y
pretty(eq2)
latex(eq2)
expr = x/a + sin(x) + int(x^2, x, 0, 1)
latex('x/a + sin(x) + int(x^2, x, 0, 1)')
expr = 'x/a + sin(x) + int(x^2, f(x), 0, 1)'
sym(expr)
latex(expr)
latex(sym(expr))
expr = 'x/a + sin(x) + int(x^2, x, 0, c)'
expr = x/a + sin(x) + int(x^2, x, 0, b)
expr
latex(expr)
expr
subs(expr, b, 2)
expr
subs(expr, {a, b}, {9, 2})
subs(expr, {a, b, x}, {9, 2, [0 1 2]})
vet = subs(expr, {a, b, x}, {9, 2, [0 1 2]})
sin(1)
vet
double(vet)
% Simplificações
x
x*(x + 1)
expr = x*(x+1)
expand(expr)
expr2 = expand(expr)
expr
expr2
factor(expr2)
prod(factor(expr2))
solve(x^2 - 1 == 0, x)
solve(x^2 - 2 == 0, x)
syms a b c
solve(a*x^2 + b*x + c == 0, x)
pretty(ans)
sol = solve(a*x^2 + b*x + c == 0, x)
sol(1)
sol(2)
a = 10
b = 0.25
c = 0
subs(sol)
expr3 = x*y^2 + (1 + x)*y + y^2
collect(expr3, x)
collect(expr3, y)
simplify(expr3)
doc simplify
clc
mupad
clc
clear all
% Cálculo
x = linspace(-10, 10, 1000);
plot(x, sin(x)./x)
sin(0) / 0
syms x
limit(sin(x) / x, x, 0)
limit((1 + 1/x)^x, x, Inf)
double(ans)
(1 + 1/1000)^1000
exp(1)
sym('exp(1)')
sym('e')
x = 1:1000;
plot(x, (1 + 1./x).^x)
limit((1 + 1/x)^x, x, 0)
syms x
limit((1 + 1/x)^x, x, 0)
x = -1:0.0001:1;
plot(x, (1 + 1./x).^x)
x = -0.9:0.0001:4;
plot(x, (1 + 1./x).^x)
f = sym('a*x^2 + sin(b*x) + c')
diff(f, x)
diff(f, 'x')
syms x
diff(f, x)
diff(f, c)
diff(f, 'c')
diff(f, 'b')
f
int(f, x)
int(f, x, 0, 2)
a = 10
b = 5
subs(int(f, x, 0, 2))
c = 7
subs(int(f, x, 0, 2))
double(ans)
syms a
int(x^a, x)
pretty(ans)
assume(a ~= -1)
assumptions(a)
assumptions(x)
int(x^a, x)
assume(a ~= 0)
assumptions(x)
assumptions(a)
assume(a ~= 0, a =~ -1)
assume(a ~= 0, a ~= -1)
assume((a ~= 0) & (a ~= -1))
assumptions(a)
ans
ans(0)
assumptions(a)
ans(1)
assumptions(a)
ans(2)
assume([a ~= 0, a ~= -1])
assumptions(a)
assume((a ~= 0) | (a ~= -1))
assumptions(a)
int(x^a, x)
assume(a == -1)
assumptions(a)
int(x^a, x)
help assume
sin(pi*x)
assume(x, 'integer')
sin(pi*x)
simplify(sin(pi*x))
assumptions(x)
assume(x, 'clear')
assumptions(x)
simplify(sin(pi*x))
diff(x^3 + 2*x^2 + 7*x - 9, x)
diff(x^3 + 2*x^2 + 7*x - 9, x, 2)
diff(x^3 + 2*x^2 + 7*x - 9, x, 3)
diff(x^3 + 2*x^2 + 7*x - 9, x, 4)
doc int
help taylor
taylor(exp(x), x, 'Order', 5)
taylor(exp(x), x, 'Order', 7)
taylor(exp(x), x, 'Order', 7, 'ExpansionPoint', 3)
symsum(sym('r^n'), 'n')
syms r n
symsum(r^n, n)
symsum(r^n, n, 0, Inf)
lookfor fractions
doc syms
doc taylor
doc partfrac
expr4 = x^2/(x^3 - 3*x + 2)
pretty(expr4)
partfrac(expr4)
pretty(partfrac(expr4))
% Outros: dsolve, fourier, laplace, ...
doc dsolve
syms a x(t)
dsolve(diff(x) == -a*x)
clear all
syms R C v(t)
dsolve(R*C*diff(v) + v == 0, v(0) == 10)
pretty(ans)
R = 1
C = 1
sol = dsolve(R*C*diff(v) + v == 0, v(0) == 10)
ezplot(sol, [0, 10])
ylim([0 10])
syms R C L v(t)
sol = dsolve(C*L*diff(v, 2) + R*C*diff(v) + v == 0, v(0) == 10)
C9 = 5
sol
R = 2
C = 1
L = 1
sol = subs(sol)
syms R C L v(t)
sol = dsolve(C*L*diff(v, 2) + R*C*diff(v) + v == 0, v(0) == 10)
C9 = 1
R = 1/100
C = 1
L = 2
sol = dsolve(C*L*diff(v, 2) + R*C*diff(v) + v == 0, v(0) == 10)
c13 = 2
C13 = 2
sol = subs(sol)
ezplot(sol, [0, 10])
ezplot(sol, [0, 1000])
ezplot(sol, [0, 100])
doc ezplot
doc solve
clear
syms x y z
solve(3*x + 2*y == z, x^2 + y^2 == 1, x + y + 2*z == 0, 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)
sol.x
doc dsolve
syms x(t) y(t)
z = dsolve(diff(x) == y, diff(y) == -x)
z.y
z.x