Advanced Mathematics for Engineering (Essay Sample)

ADVANCED MATHEMATICS FOR ENGINEERING
by Student’s Name
Code + Course Name
Professor’s Name
University Name
City, State
Date
Task 1
1
*
For Cosx the series will be 1-x22!+x44!-x66!+…
For x-3the series will be 1-x-62!+x-124!-x-186!+…
* ln1+x2=Ln1+x2=n=1„(1n+1/nx^n))+1/nx^n
=n=1„(1n+1/nx^n))+1/nx^n
=n=1„22nx2n=n=1„11nx2n
Task 2
2.
ddxln1+x2=2x1+x2=1?91+x)
=1-x+x2-x3+..=11+x2
=1-x2+x4-x6+…=2x1+x2
=2x-2x3+2x5-2x7+…
=ln1+x2=x2-x42+x63-x84+..
Task 3
3,
y(0)=1;
;
H=0.1;
for h=1:H
t(h+1)=t(h)+h;
t(h+1)=y(h)+h*x(h);
t(h+1)=t(h)+h*(-2*t(h)-y(h)+t(h));
t(h+1)=t(h)+h*(t(h)+t(h+1) )/2;
t(h+1)=t(h)+h*( -2*t(h)-y(h)+t(h) -2*t(h+1)-t(h+1)+t(h+1))/2;
end
hold off
plot(t,y,'h)
1 The recurrence formula for the method will be
Yn+1=Yn+hT4(Xn,Yn, h)
dVdt=t+2V
=1t0
=0t-1
=-1t-2
=2t-3
Using the method
V4+0.2t-3)
Task 4
5.
* dtdCt=Ct-Lt
* dt0dCt=Ct-Lt=250,
Task 5
6.