Task 1
- Symbolic Algebra in Matlab
- Solving Single Variable Equation
- Solving Multi Variable Equation
- Solving Simultaneous Equation
- Using roots and polyval function
- Using expand function to expand algebraic expression
- Using simplify function to simplify algebraic expression
- using factor function to factorize algebraic expression
%Lab 6 Task 1
close all
clear
clc
a=solve('3*x-50=0');
disp(a)
b=solve('3*x^2+5*x-3=0');
pretty(b)
%Using roots function to find the roots of a polynomial
p=[3 5 -3];
roots(p)
%q(x)=5*x^4+3*x^2+5*X+9
q=[5 0 3 5 9];
roots(q)
q=[5 0 5 0 5 3 6 4 5];
roots(q)
polyval(q,3)
%5x^2+3xy+9
pretty(solve('5*x^2+3*x*y+9'))
pretty(solve('5*x^2+3*x*y+9','y'))
%2x+3y+9z=5
%3x-2y+3z=2
%5x+5y+9z=100
solu=solve('2*x+3*y+9*z=5','3*x-2*y+3*z=2','5*x+5*y+9*z=100');
disp(solu.x);
disp(solu.y);
disp(solu.z);
%Expansion, factorization and simplification
syms x y a b;
expand((x-2)*(x+5))
expand((x-2)^2*(x+5)^2)
pretty(expand((x-2)^2*(x+5)^2))
expand(cos(x+y))
expand(cos(x+y)^2)
expand(exp(a+b)^2)
factor(x^4 + 6*x^3 - 11*x^2 - 60*x + 100)
simplify((x^4 + 6*x^3 - 11*x^2 - 60*x + 100)/(x-2))
Task 2
Integration and Differentiation in Matlab
%Lab 6 Task 2 close all clear clc syms x t; f=sin(x)^2; diff(f) diff(diff(f)) diff(sin(x),52) int(sin(x), -pi, pi)
Task 3
Symbolic Fourier Transform in Matlab
%Lab 6 Task 3 close all clear clc syms a t w x; pretty(fourier(exp(-a*t)*heaviside(t))) pretty(fourier(dirac(t))) pretty(fourier(fourier(dirac(t)))) pretty(fourier(heaviside(t)))