Anul 3 Semestrul 2

Anul 3/Semestrul 2/Calcul numeric/Lab2.m

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+#pkg load symbolic;
+
+#1.a
+syms x;
+
+f=exp(x)
+
+t1=taylor(f,x,0,'order',1);
+t2=taylor(f,x,0,'order',2);
+t3=taylor(f,x,0,'order',3);
+t4=taylor(f,x,0,'order',4);
+t10 = taylor(f,x,0,'order',10);
+
+#ezplot(t1)
+hold on
+ezplot(t2)
+hold on
+ezplot(t3)
+hold on
+ezplot(t4)
+xlim([-3,3])
+
+#1.b
+vpa(exp(1),7)
+
+vpa(subs(t10,x,1),7)
+
+#2.a
+
+syms x;
+f=sin(x)
+
+t3=taylor(f,x,0,'order',3);
+t5=taylor(f,x,0,'order',5);
+hold off
+ezplot(f)
+hold on
+ezplot(t3)
+hold on
+ezplot(t5)
+xlim([-pi,pi])
+ylim([-2,2])
+
+#2.b
+t10=taylor(f,x,0,'order',10);
+
+vpa(sin(pi/5),5)
+vpa(subs(t10,x,sym(pi)/5),5)
+
+vpa(sin(10*pi/3),5)
+vpa(subs(t10,x,10*sym(pi)/3),5) #it's not precise enought, increase n for Taylor series or move x0=0 to x0= 10pi/3
+
+
+#3.a
+
+syms x;
+f=log(1+x);
+t2= taylor(f,x,0,'order',2);
+t5= taylor(f,x,0,'order',5);
+
+hold off
+ezplot(f)
+hold on
+ezplot(t2)
+hold on
+ezplot(t5)
+
+xlim([-0.9,1])
+ylim([-1,1])
+t= taylor(f,x,0,'order',10);
+vpa(log(2),5)
+vpa(subs(t,x,1),5)
+
+syms x;
+g=log(1-x);
+t2 = taylor(g,x,0,'order',10)
+
+t-t2
+
+vpa(subs(t,x,sym(0.999,'f')) - subs(g,x,sym(0.999,'f')),5)