FIC MATLAB 2017-2/Aula-13

<syntaxhighlight lang=matlab class="mw-collapsible"> %-- 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)