Assignment 2 Problem 1

108 days ago by emi3489

#To show that f(z)+f'(z)dz is an acceptable approximation for f(z+dz) we show a variety of examples. 
       
f=x^2; g=derivative(f,x); z=1+I; dz=.01+.01*I; print(f(z)+g(z)*dz); print(f(z+dz)); 
        
2.04000000000000*I
2.04020000000000*I
2.04000000000000*I
2.04020000000000*I
f=4*x^3+x; g=derivative(f,x); z=3+4*I; dz=.01+.01*I; print(f(z)+g(z)*dz); print(f(z+dz)); 
        
-468.710000000000 + 182.050000000000*I
-468.719608000000 + 182.057208000000*I
-468.710000000000 + 182.050000000000*I
-468.719608000000 + 182.057208000000*I
f=sin(x); g=derivative(f,x); z=1+4*I; dz=-.01+.02*I; print(f(z)+g(z)*dz); print(f(z+dz)); 
        
sin(4*I + 1) - (0.0100000000000000 - 0.0200000000000000*I)*cos(4*I + 1)
23.2912903265301 + 15.2763906902575*I
sin(4*I + 1) - (0.0100000000000000 - 0.0200000000000000*I)*cos(4*I + 1)
23.2912903265301 + 15.2763906902575*I
f=1/(x); g=derivative(f,x); z=5+2*I; dz=.04-.03*I; print(f(z)+g(z)*dz); print(f(z+dz)); 
        
0.172128418549346 - 0.0672651605231867*I
0.172116451805686 - 0.0672756765986511*I
0.172128418549346 - 0.0672651605231867*I
0.172116451805686 - 0.0672756765986511*I