TI-89 Programs: Calculus
Functions
- Volume of a parallelepiped
- Angle between 2 vectors
- Project vector u onto vector v
- Line Integral
- Tangent line
- Arclength of a vector valued function
- Make basis program
Volume of a parallelepiped
ppv(a,b,c)
Func
@a,b,c
Return dotP(crossP(a,b),c)
EndFunc
Func
@a,b,c
Return dotP(crossP(a,b),c)
EndFunc
Angle between 2 vectors
vangle(u,v)
Func
@u,v
Return cos-1(dotP(u,v)/(norm(u)*
norm(v)))
EndFunc
Func
@u,v
Return cos-1(dotP(u,v)/(norm(u)*
norm(v)))
EndFunc
Project vector u onto vector v
vproj(u,v)
Func
@u,v
Return dotP(u,v)/norm(v)^2*v
EndFunc
Func
@u,v
Return dotP(u,v)/norm(v)^2*v
EndFunc
Line integral
flinint(f,rti,rtj,rtk,l,u)
Func
@f,rti,rtj,rtk,l,u
Return ∫((f|x=rti and y=rtj and z=rtk)*norm(
d([[rti,rtj,rtk]],t)),t,l,u)
EndFunc
Func
@f,rti,rtj,rtk,l,u
Return ∫((f|x=rti and y=rtj and z=rtk)*norm(
d([[rti,rtj,rtk]],t)),t,l,u)
EndFunc
Tangent line
tline(rt,t,a)
Func
@rt,t,a
Return (rt|t=a)+(d(rt,t)|t=a)*t
EndFunc
Func
@rt,t,a
Return (rt|t=a)+(d(rt,t)|t=a)*t
EndFunc
Arclength of a vector valued function
varclen(rt,a,b)
Func
@rt,a,b
Return ∫(norm(d(rt,t)),t,a,b)
EndFunc
Func
@rt,a,b
Return ∫(norm(d(rt,t)),t,a,b)
EndFunc
Make basis program
mbbs(rt,a)
Prgm
@rt,a
ClrIO
d(rt,t)→vt
norm(vt)→dsdt
vt/dsdt→tt
d(tt,t)/dsdt|t=a→ka
norm(ka)→ksa
If ksa=0 Then
[[0,0,0]]→na
Else
ka/ksa→na
EndIf
crossP(tt|t=a,na)→ba
[["rt: ",string(rt)]
["Point: ",string(a)]
["vt: ",string(vt)]
["dsdt: ",string(dsdt)]
["tt: ",string(tt)]
["ka: ",string(ka)]
["ksa: ",string(ksa)]
["na: ",string(na)]
["ba: ",string(ba)]]→mbbsa
Pause mbbsa
EndPrgm
Prgm
@rt,a
ClrIO
d(rt,t)→vt
norm(vt)→dsdt
vt/dsdt→tt
d(tt,t)/dsdt|t=a→ka
norm(ka)→ksa
If ksa=0 Then
[[0,0,0]]→na
Else
ka/ksa→na
EndIf
crossP(tt|t=a,na)→ba
[["rt: ",string(rt)]
["Point: ",string(a)]
["vt: ",string(vt)]
["dsdt: ",string(dsdt)]
["tt: ",string(tt)]
["ka: ",string(ka)]
["ksa: ",string(ksa)]
["na: ",string(na)]
["ba: ",string(ba)]]→mbbsa
Pause mbbsa
EndPrgm