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* Calculus : Vector-valued function : Derivative and Integral.

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Windows : Dev-C++ 4
Linux : gcc abc.c -lm Return
a.out Return

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* You can compile the *.c files directly without create a project.

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c15b_1a.c fa.h :

r(t) = f(t)i + g(t)j

With

f : t-> 2*t
g : t-> 8 - 2*t**2

t = +1.00

Draw the tangent vectors to C at P(f(t),g(t)),

open the file "a_my.plt" with Gnuplot.

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c15b_1b.c fb.h :


r(t) = f(t)i + g(t)j + h(t)k

With

f : t-> cos(t)
g : t-> sin(t)
h : t-> t

t = +6.00

Draw the tangent vectors to C at P(f(t),g(t),h(t)),

open the file "a_my.plt" with Gnuplot.


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c15b_2f.c ff.h
c15b_2g.c fg.h


Evaluate the integral

/ b / b
| |
| r(t) dt = | f(t)i + g(t)j + h(t)k dt
| |
/ a / a

/ b / b / b / b
| | | |
| r(t) dt = (| f(t)dt)I + (| g(t)dt)J + (| h(t)dt)K =
| | | |
/ a / a / a / a

With

f : t-> 6*t**2
g : t-> -4*t
h : t-> +3

+0.00 < t < +2.00


/ b
|
| r(t) dt = +16.00i -8.00j +6.00k
|
/ a


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c15b_3a.c fa.h
c15b_3b.c fb.h

If

r(t) = f(t)i + g(t)j


and f, g are differentiable, then

r'(t) = f'(t)i + g'(t)j


If f, g are two time differentiable, then

r''(t) = f''(t)i + g''(t)j

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The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c15b.zip