FIC MATLAB 2017-1/Aula-13

%-- 10-04-2017 19:10:59 --% help sawtooth x = 0:0.01:10 sawtooth(x) plot(x, sawtooth(x)) plot(x, square(x)) plot(x, triang(x)) help sawtooth plot(x, sawtooth(x, 1)) plot(x, sawtooth(x, 4)) plot(x, sawtooth(x, 0.5)) plot(x, sawtooth(x, 0)) plot(x, sawtooth(x, 0.1)) plot(x, square(x, 0.5)) plot(x, square(x, 0.2)) help square plot(x, square(x, 1)) plot(x, square(x, 100)) plot(x, square(x, 80)) x = 0:0.01:10 y = 3*sin(x) plot(x, y) plot(x, min(y, 2)) plot(x, max(min(y, 2), -2)) x = 0:10 x>5 x(x>5) x(x>5) = 5 % Aula 11 edit temp.m temp a = magic(6) figure surf(a) sum(a) sum(a') sum(diag(a)) magic(3) temp clc temp x = 0:0.01:2*pi; y = 2*cos(x); plot(y, x) plot(x, y) der_x = diff(x) T = 2*pi delta = 0.01 der_x = [diff(x) 0] / delta; hold on der_y = [diff(y) 0] / delta; plot(x, der_y) x = 0:0.01:2*pi + randn(size(x)) * 0.001 x = 0:0.01:2*pi clc clear close all temp %-- 17-04-2017 19:17:16 --% factorial(52) sym('factorial(52)') sym(factorial(52)) sym('factorial(52)') sym('factorial(53)') sym('factorial(52)') sym('2^100') 2^100 sym(2^100) sym('2^200') sym(2^200) sym('2^300') sym(2^300) x = 2^300 sym(x) sym('2^200 + 1') sym(2^200 + 1) 2^200 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') x 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