Alejo

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2 years, 254 days

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These are questions asked by Alejo

Please I need help with my proc.

 

> RK2skritt:=proc(FR::procedure,xo,yo,vxo,vyo,h) local x, y, vx, vy, r, kx1, kx2, kx3, kx4, ky1, ky2, ky3, ky4, l x1, l x2, l x3, l x4, ly1, ly2, ly3, ly4, tmp; r:=sqrt(xo*xo+yo*yo); tmp:=-(h*FR(r))/(r); lx1:=h*vxo; ly1:=h*vyo; kx1:=tmp*xo; ky1:=tmp*yo; lx2:=h*(vxo+0.5*kx1); ly2:=h*(vyo+0.5 ky1); r:=sqrt((xo+0.5*lx1)^(2)+(yo+0.5*ly1)^(2)); tmp:=-(h*FR(r))/(r); kx2:=tmp*(xo+0.5*lx1); ky2:=tmp*(yo+0.5*ly1); lx3:=h*(vxo+0.5*kx2); ly3:=h*(vyo+0.5*ky2); r:=sqrt((xo+0.5*lx2)^(2)+(yo+0.5*ly2)^(2)); tmp:=-(h*FR(r))/(r); kx3:=tmp*(xo+0.5*lx2); ky3:=tmp*(yo+0.5*ly2); lx4:=h*(vxo+kx3); ly4:=h*(vyo+ky3); r:=sqrt((xo+lx3)^(2)+(yo+ly3)^(2)); tmp:=-(h*FR(r))/(r); kx4:=tmp*(xo+lx3); ky4:=tmp(yo+ly3); x:=xo+(lx1+2*lx2+2*lx3+lx4)/(6); y:=yo+(ly1+2*ly2+2*ly3+ly4)/(6); vx:=vxo+(kx1+2*kx2+2*kx3+kx4)/(6); vy:=vyo+(ky1+2*ky2+2*ky3+ky4)/(6); [x,y,vx,vy]; end proc: Error, invalid local declaration Please someone help me!!!!!!!!

Lecture 4 - Problem 2
a)
> a := -2100; b := 2100; N := 8; h := (b-a)/N; C := 4491; x := [seq(h, h = -2100 .. 2100, h)]; y := proc (x) options operator, arrow; sqrt(1+((1/2)*exp(x/C)-(1/2)*exp(-x/C))^2) end proc; evalf(y(x[1])); evalf(y(x[N+1])); L := (1/3)*h*(y(x[1])+4*(y(x[2])+y(x[4])+y(x[6])+y(x[N]))+2*(y(x[3])+y(x[5])+y(x[N-1]))+y(x[N+1])); evalf(L);
                             -2100
                              2100
                               8
                              525
                              4491
     [-2100, -1575, -1050, -525, 0, 525, 1050, 1575, 2100]
         /                           2\
         |    /1    /x\   1    /  x\\ |
x -> sqrt|1 + |- exp|-| - - exp|- -|| |
         \    \2    \C/   2    \  C// /
                          1.111332350
                          1.111332350
                                           (1/2)
         /                               2\    
         |    /1    /-700\   1    /700 \\ |    
     175 |1 + |- exp|----| - - exp|----|| |    
         \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /-175\   1    /175\\ |    
        + 700 |1 + |- exp|----| - - exp|---|| |    
              \    \2    \499 /   2    \499// /     

                                                (1/2)
              /                               2\    
              |    /1    /-175\   1    /175 \\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /175 \   1    /-175\\ |    
        + 700 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                               (1/2)
              /                              2\    
              |    /1    /175\   1    /-175\\ |    
        + 700 |1 + |- exp|---| - - exp|----|| |    
              \    \2    \499/   2    \499 // /     

                                                (1/2)     
              /                               2\          
              |    /1    /-350\   1    /350 \\ |          
        + 350 |1 + |- exp|----| - - exp|----|| |      + 350
              \    \2    \1497/   2    \1497// /           

                                                (1/2)
              /                               2\    
              |    /1    /350 \   1    /-350\\ |    
        + 350 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /     

                                                (1/2)
              /                               2\    
              |    /1    /700 \   1    /-700\\ |    
        + 175 |1 + |- exp|----| - - exp|----|| |    
              \    \2    \1497/   2    \1497// /    
                          4354.742601
> L := (1/3)*h*(y(x[1])+4*add(y(i), i = y(x[2]) .. y(x[N]), 2)+2*add(y(i), i = y(x[3]) .. y(x[N-1]), 2)+y(x[N+1])); evalf(L);
Error, invalid input: add expects 2 arguments, but received 3
                          4354.742601
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