17:49 08/07/06
       freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : local maximum, minimum, saddle point

                           ************

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

                   ************

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


                   ************

   c16m_a1.c  : Choose a critical point on the graph.
   c16m_a2.c  : Verify if it is a local maximum.

   c16m_a3.c  : Choose a critical point on the graph.
   c16m_a4.c  : Verify if it is a local minimum.

   c16m_a5.c  : Choose a critical point on the graph.
   c16m_a6.c  : Verify if it is a saddle point.

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c16m.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Plot f(x,y).

                           ************

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

                   ************

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

                   ************

          The functions are in the files, fa.h, fb.h, fc.h

                  Draw the function f(x,y) with Gnuplot.

          c16a_1a.c    : f : (x,y)-> 1/(x*x + y*y + 1)
          c16a_1b.c    : f : (x,y)-> cos(x*y)
          c16a_1c.c    : f : (x,y)-> cos(x)+cos(y)


                    Draw the function f(x,y) and a point.

          c16a_2a.c    : f : (x,y)-> 1/(x*x + y*y + 1)
          c16a_2b.c    : f : (x,y)-> cos(x*y)
          c16a_2c.c    : f : (x,y)-> cos(x)+cos(y)


                        Draw the function f(x,y) and
                        a list of points y = constant.

          c16a_3a.c    : f : (x,y)-> 1/(x*x + y*y + 1)
          c16a_3b.c    : f : (x,y)-> cos(x*y)
          c16a_32c.c   : f : (x,y)-> cos(x)+cos(y)


                        Draw the function f(x,y) and
                        a list of points x = constant.

          c16a_3a.c    : f : (x,y)-> 1/(x*x + y*y + 1)
          c16a_3b.c    : f : (x,y)-> cos(x*y)
          c16a_32c.c   : f : (x,y)-> cos(x)+cos(y)


                        Draw the function f(x,y) and
                        two lists of points
                         x = constant,  y = constant.

          c16a_4a.c    : f : (x,y)-> 1/(x*x + y*y + 1)
          c16a_4b.c    : f : (x,y)-> cos(x*y)
          c16a_42c.c   : f : (x,y)-> cos(x)+cos(y)

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c16a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus :Curvature.

                   ************

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

                   ************

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

                   ************

          c15d_1a.c fa.h
          c15d_1b.c fb.h


  If a smooth curve C is the graph of y = f(x),

  then the curvature K at P(x,y) is


   K = |y''| / [1 + (y')^2]^(3/2)



  Find the curvature K of the curve at P(+1.00,+0.00) with


  f : x-> 1-x**2


  At the point P(+1.00,+0.00) K = +0.18

                   ************

          c15d_2d.c fd.h
          c15d_2e.c fe.h


  If a plane curve C has a parametrization

  x = f(t), y = g(t) and if f'' and g'' exist,


   then the curvature K at P(x,y) is


   K = |f' g'' - g' f''| / [ (f')^2 - (g')^2 ]^(3/2)



  Find the curvature K of the curve at P(+0.50,+0.25) with


  f : t-> t**2
  g : t-> t**3

  At the point P(+0.25,+0.13) K = +0.768


                   ************

          c15d_3g.c fd.h
          c15d_3h.c fe.h


  If P(x,y) is a point on the graph of y = f(x)
  at which K != 0. The point M(h,k) is the center
  of the cuvature for P if


  h = x - y'[1 + y'^2] / y''

  k = y +   [1 + y'^2] / y''


                   ************

          c15d_4j.c fj.h
          c15d_4k.c fk.h


  The position vector of a moving point at time t is

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

  With

  f : t-> t
  g : t-> t**2
  h : t-> t**3

  t = +4.00

  Find the tangential component of acceleration at time t. (aT)

  Find the normal     component of acceleration at time t. (aN)

  Find the curvature K at time t.


                   ************

          c15d_5j.c fj.h


  The position vector of a moving point at time t is

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

  With

  f : t-> t
  g : t-> t**2
  h : t-> t**3

    1 < t < 5

  Find the tangential component of acceleration at time t. (aT)

  Find the normal     component of acceleration at time t. (aN)

  Find the curvature K at time t.


                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c15d.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Curvilinear Motion.

                   ************

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

                   ************

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

                   ************

          c15a_1a.c  fa.h
          c15a_1b.c  fb.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 velocity and accelerator vectors at the point P(f(t),g(t)),

open the file "a_my.plt" with Gnuplot.

                   ************

          c15a_2c.c  fc.h
          c15a_2d.c  fd.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 velocity and accelerator vectors at the point P,

  open the file "a_my.plt" with Gnuplot.


                   ************

          c15a_3e.c  fe.h
          c15a_3f.c  ff.h

  If

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

  is the position vector of a moving point
  P, find its velocity, acceleration, and
  speed at the given time t.

  With

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

  t = +1.57

  r' (+1.57) =   v(+1.571)   = -4.810i  +4.810j +4.810k

  The speed  = ||v(+1.571)|| =  +8.332

  r''(+1.57) =   a(+1.571)   = -9.621i  -0.000j  +4.810k

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c15c.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Vector-Valued Functions, and space curves.

                   ************

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

                   ************

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

                   ************

          c15a_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

  To see the graph of the curve, and the vector r(t),

  open the file "a_my.plt" with Gnuplot.


                   ************

          c15a_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

  To see the graph of the curve, and the vector r(t),

  open the file "a_my.plt" with Gnuplot.


                     ************

          c15a_2f.c ff.h   :

  If a curve C has a smooth parametrization

       x = f(t), y = g(t)

  And if C does not intersect itself,
  except possibly for t= a and t = b,
  then the length L of C is

      / b
     |
     |    [f_t^2+g_t^2]^1/2 dt = 8.000
     |
    /   a

   With

    f : t-> t-sin(t)
    g : t-> 1-cos(t)

   +0.00 < t < +6.28


                     ************

          c15a_2g.c fg.h   :

  If a curve C has a smooth parametrization

       x = f(t), y = g(t)

  And if C does not intersect itself,
  except possibly for t= a and t = b,
  then the length L of C is

      / b
     |
     |    [f_t^2+g_t^2]^1/2 dt = 15.683
     |
    /   a

  With

  f : t-> exp(sin(3*t))
  g : t-> exp(-cos(t))
  +0.00 < t < +6.28

                     ************

          c15a_2g.c fg.h   :

  If a curve C has a smooth parametrization

       x = f(t), y = g(t), z = h(t)

  And if C does not intersect itself,
  except possibly for t= a and t = b,
  then the length L of C is

      / b
     |
     |    [f_t^2+g_t^2+h_t^2]^1/2 dt = 22.356
     |
    /   a

  With

  f : t-> exp(sin(3*t)**2)
  g : t-> exp(-cos(t))
  h : t-> sin(t)

  +0.00 < t < +6.28

                     ************

          c15a_2i.c fi.h   :


If a curve C has a smooth parametrization

      x = f(t), y = g(t), z = h(t)

And if C does not intersect itself,
except possibly for t= a and t = b,
then the length L of C is

     / b
    |
    |    [f_t^2+g_t^2+h_t^2]^1/2 dt = 925.767
    |
   /   a

  With

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

  +0.00 < t < +6.28


                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c15a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Sketch the graph of polar equation.

                   ************

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

                   ************

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

                   ************

          c13c_1a.c fa.h   r = 2 + 2*cos(k)
          c13c_1b.c fb.h   r = sin(k)
          c13c_1c.c fc.h   r = 1./k
          c13c_1d.c fd.h   r = k

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c13c.zip

freeware  http://groups.yahoo.com/group/mathc/

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

                   ************

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

                   ************

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

                   ************

          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.

                   ************

          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.


                   ************

          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


                   ************

          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

                   ************

The members can try these links :

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

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Cubic bezier curve.

                   ************

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

                   ************

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

                   ************

          c13b_1a.c    :  a curve.
          c13b_1b.c    :  2

          c13b_2c.c    :  step 1
          c13b_2d.c    :  step 2
          c13b_2e.c    :  step 3
          c13b_2f.c    :  r

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c13b.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Curve.

                   ************

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

                   ************

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

                   ************

          c13a_1a.c fa.h
          c13a_1b.c fb.h
          c13a_1c.c fc.h
          c13a_1d.c fd.h
          c13a_1e.c fe.h

  ex :

  Let C be the curve consisting of all ordered pairs (f(t),g(t)).

  With

   f : t-> (a+b)*cos(t)-b*cos((a+b/b)*t)

   g : t-> (a+b)*sin(t)-b*sin((a+b/b)*t)

  To see the curve C, open the file "a_main.plt" with Gnuplot.


                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c13a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Vectors 2d 3d.

                   ************

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

                   ************

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

                   ************

          c14a_1a.c    : Magnitude, Unit vector. (2d)
          c14a_1b.c    :                         (3d)

          c14a_2a.c    : Vector PQ. (2d)
          c14a_2b.c    :            (3d)

          c14a_3a.c    : Draw the vector u.      (2d)
          c14a_3b.c    :                         (3d)

          c14a_4a.c    : Draw the vector PQ.     (2d)
          c14a_4b.c    :                         (3d)

          c14a_5a.c    : Draw the vectors u, v.  (2d)
          c14a_5b.c    :                         (3d)

          c14a_6a.c    : The dot product u.v.    (2d)
          c14a_6b.c    :                         (3d)

          c14a_7b.c    : The vector product u x v.

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c14a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Area in polar coordinate.

                   ************

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

                   ************

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

                   ************

  If f is continuous and f(k) >= 0 on [a,b],

         where 0 <= a  < b <= 2Pi,

  then the area A of the region bounded by the
  graphs of r = f(k) with k = a and k = b is

        / b                   / b
       |                     |
  A =  |   1/2 f(k)^2 dk  =  |   1/2 r^2 dk
       |                     |
      /   a                 /   a

                   ************

  c13d_1a.c fa.h   : r= 2+2cos(k)
  c13d_1b.c fb.h   : r= 2cos(k)
  c13d_1c.c fd.h   : r= exp(k)

  c13d_2d.c fd.h   : r= 2+2sin(k)
  c13d_2e.c fe.h   : r= sin(2k)


                   ************

  The area A of the region bounded by the graph of
  two polar equations r = f(k) and r = g(k) and
  the line  k = a and k = b is

        / b                   / b
       |                     |
  A =  |   1/2 f(k)^2 dk  -  |   1/2 g(k)^2 dk
       |                     |
      /   a                 /   a

                   ************

  c13d_3g.c fg.h   : r=2+2cos(k); r=3;
  c13d_3h.c fh.h   : r=4*cos(2k); r=2;


                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c13d.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Laplace transform.

                   ************

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

                   ************

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

                   ************

      Verify the laplace transform with some examples.

          c10j_1a.c  fa.h  :   without parameter.
          c10j_1b.c  fb.h
          c10j_1c.c  fc.h


          c10j_2f.c  fa.h  :   with one parameter.
          c10j_2g.c  fb.h

          c10j_3j.c  fa.h  :   with two parameters.


example :


      / oo
     |
     |    exp(-st) F(t) dt = 0.230769226920
     |
    /  0

                  f(+5.000) = 0.230769230769

  With


  F(t) t-> exp(P2*t) * cos(P1*t)

  f(s) s-> (s-P2) / ((s-P2)^2 + P1^2)   (Laplace transform of F(t))


                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c10j.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Integral Solids of revolution by using cylindrical
shells.

                   ************

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

                   ************

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

                   ************

           Compute the volume of a solid of revolution,
           generated by revolving R about the y-axis,
           by using cylindrical shells.

           Draw the region R bounded by the graph of f,
           the x-axis,  x = a and x = b (0 <= a <= b)

         c05c1A.c  : f : x->   sqrt(x)
         c05c1B.c  : f : x->   2*x - x**2
         c05c1C.c  : f : x->   sqrt(x-2)
         c05c1D.c  : f : x->   cos(x)


           Compute the volume of a solid of revolution,
           generated by revolving R about the y-axis,
           by using cylindrical shells.

           Draw the region R bounded by the graph of f,
           the graph of g,and x = a and x = b

         c05c2A.c  : g : x->  sqrt(x)       h : x->   x**2
         c05c2B.c  : g : x->  x + 4         h : x->   x**2 + 1
         c05c2C.c  : g : x->  sin(x)+2      h : x->   cos(x)+2
         c05c2D.c  : g : x->  2*x - x**2    h : x->   0
         c05c2E.c  : g : x->  2*x - x**2    h : x->   .5

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c05c.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Integral Length and sufaces of revolution.

                   ************

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

                   ************

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

                   ************

         * The arc length of the graph of f from A(a,f(a)) to B(b,f(b))

         c05d1A.c  : f : x->   x + 1
         c05d1B.c  : f : x->   x**2
         c05d1C.c  : f : x->   sin(x)
         c05d1D.c  : f : x->   log(x)
         c05d1E.c  : f : x->   exp(x)


         * The area S of the surface generated by revolving
           the graph of f about the x-axis is (ONLY A GIFT GRAPH).


         c05d2A.c  : g : x->  sqrt(x)
         c05d2B.c  : g : x->  x**(2)
         c05d2C.c  : g : x->  sin(x)
         c05d2D.c  : g : x->  exp

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c05d.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Integral. Area.

                   ************

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

                   ************

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

                   ************

      Compute the area A of the region bounded by
      the graph of f, the x axis, x = a and x= b.

         c05a1A.c  : f : x->   sqrt(x)
         c05a1B.c  : f : x-> 1/sqrt(x)
         c05a1C.c  : f : x->   sin(x)
         c05a1D.c  : f : x->   exp(x)
         c05a1E.c  : f : x->   log(x)


      Compute the area A of the region bounded by
      the graph of g, the graph of h, x = a and x= b.


         c05a2A.c  : g : x-> sqrt(x)      ;   h : x->  x**2
         c05a2B.c  : g : x-> 6.-x**2      ;   h : x->  3-2*x
         c05a2C.c  : g : x-> x + 3        ;   h : x->  x**2 + 1
         c05a2D.c  : g : x-> x - 1        ;   h : x->  x**2 + 1
         c05a2E.c  : g : x-> 1/(x**2)     ;   h : x-> -x**2
         c05a2F.c  : g : x-> cos(x)       ;   h : x->  x**2
         c05a2G.c  : g : x-> cos(x)       ;   h : x->  sin(x)
         c05a2H.c  : g : x-> exp(x)       ;   h : x->  log(x)

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c05a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Solids of revolution.

                   ************

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

                   ************

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

                   ************


        Compute the volume V of the solid of revolution
        generated by revolving R about the x-axis.
        The region R bounded by the graph of f, the x-axis,
        and the vertical lines x = a and x = b


         c05b1A.c  : f : x->   x**2 + 2
         c05b1B.c  : f : x->   sin(x)
         c05b1C.c  : f : x->   1/x
         c05b1D.c  : f : x->   exp(x)
         c05b1E.c  : f : x->   log(x)


        Compute the volume V of the solid of revolution
        generated by revolving R about the x-axis.
        The region R bounded by the graph of f, the graph g,
        and the vertical lines x = a and x = b


         c05b2A.c  : g : x->   x**2 + 2    ;   h : x->   x/2  + 1
         c05b2B.c  : g : x->-2*x**2 + 2    ;   h : x->  -x**2 + 1
         c05b2C.c  : g : x->  sin(x)       ;   h : x->   x**2
         c05b2D.c  : g : x->  sqrt(x)      ;   h : x->   x**2
         c05b2E.c  : g : x->  exp(x)       ;   h : x->   cos(x)
         c05b2F.c  : g : x->  exp(x)       ;   h : x->   log(x)

                    ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c05b.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Derivative Tangent.

                   ************

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

                   ************

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

                   ************

  c03a1A.c  : Draw    the tangent.
  c03a1B.c  : Animate the tangent.
  c03a1C.c  : Find the intersection points of the tangent with the x-y
axis.
  c03a1D.c  : Find PA, the length of the tangent from P to the x axis.
  c03a1E.c  : Find PB, the length of the tangent from P to the y axis.
  c03a1F.c  : Find AM, the length of the under tangent.


  c03a2A.c  : Draw    the tangent.
  c03a2B.c  : Animate the tangent.
  c03a2C.c  : Find the intersection points of the tangent with the x-y
axis.
  c03a2D.c  : Find PA, the length of the tangent from P to the x axis.
  c03a2E.c  : Find PB, the length of the tangent from P to the y axis.
  c03a2F.c  : Find AM, the length of the under tangent.


  c03a3A.c  : Draw    the tangent.
  c03a3B.c  : Animate the tangent.
  c03a3C.c  : Find the intersection points of the tangent with the x-y
axis.
  c03a3D.c  : Find PA, the length of the tangent from P to the x axis.
  c03a3E.c  : Find PB, the length of the tangent from P to the y axis.
  c03a3F.c  : Find AM, the length of the under tangent.


  c03a4A.c  : Draw    the tangent.
  c03a4B.c  : Animate the tangent.
  c03a4C.c  : Find the intersection points of the tangent with the x-y
axis.
  c03a4D.c  : Find PA, the length of the tangent from P to the x axis.
  c03a4E.c  : Find PB, the length of the tangent from P to the y axis.
  c03a4F.c  : Find AM, the length of the under tangent.

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c03a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Mean Value.

                   ************

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

                   ************

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

                   ************

         Find a number c in (r,s) that satisfies

         the mean value theorem for :


         c03e2A.c  : f : x-> x**2          +  1
         c03e2B.c  : f : x-> x**2 + 2*x    - 11
         c03e2C.c  : f : x-> x**4 -   x**3 -  1

         c03e2E.c  : f : x-> x    + 4/x
         c03e2F.c  : f : x-> x**2 + 4/x

         c03e2H.c  : f : x-> exp(x)
         c03e2I.c  : f : x-> exp(x) + x**2
         c03e2J.c  : f : x-> exp(x) + sin(x)
         c03e2K.c  : f : x-> exp(x) + 1/x

         c03e2M.c  : f : x-> sin(x)
         c03e2N.c  : f : x-> cos(x)

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c03e.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Derivative:Newton2's method.

                   ************

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

                   ************

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

                   ************

  c03g_1A.c  : Compute sqrt(7).
  c03g_2A.c  : Compute sqrt(5).
  c03g_3A.c  : Compute sqrt(11).



  c03g_4A.c  : Find and draw the largest  positive real root of "x**3 -
  3x + 1"
  c03g_4B.c  :               the smallest negative
  c03g_4C.c  :               the intermediate

  c03g_5A.c  : Find and draw the largest positive  real root of "x**4 -
  x**2 + x - 2"
  c03g_5B.c  :               the smallest



  c03g_6A.c  : Find and draw the intersection point of "x" and "cos(x)"

  c03g_7A.c  : Find and draw the first intersection point of "x**2"
and "cos(x)"
  c03g_7B.c  :               the second

  c03g_8A.c  : Find and draw the intersection point of "sin(x)"
and "cos(x)"
  c03g_8B.c  :           Another intersection point

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c03g.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus :  Integral: trapezoidal, Simpson's rule.

                   ************

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

                   ************

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

                   ************

       Approximate the definite integral by using the trapezoidal's
rule.

         c04g_1A.c  : f : x->   sqrt(x)
         c04g_1B.c  : f : x-> 1/sqrt(x)
         c04g_1C.c  : f : x->   sin(x)
         c04g_1D.c  : f : x->   exp(x)
         c04g_1E.c  : f : x->   log(x)


        Approximate the definite integral by using the Simpson's rule.

         c04g_2A.c  : f : x->   sqrt(x)
         c04g_2B.c  : f : x-> 1/sqrt(x)
         c04g_2C.c  : f : x->   sin(x)
         c04g_2D.c  : f : x->   exp(x)
         c04g_2E.c  : f : x->   log(x)

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c04g.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Numerical Derivatives.

                   ************

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

                   ************

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

                   ************

         Numerical Derivatives.

  c03f_1a.c  : first.
  c03f_1b.c  :
  c03f_1c.c  :

  c03f_2a.c  : second.
  c03f_2b.c  :
  c03f_2c.c  :


  I have used :

  f'(a) = f(a+h) - f(a-h)
           -------------
               2h


  f''(a) = f(a+h) - 2 f(a) + f(a-h)
            ----------------------
                      h**2

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c03f.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Derivative Newton's method.

                   ************

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

                   ************

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

                   ************

  c03c1A.c  : Compute sqrt(7).
  c03c2A.c  : Compute sqrt(5).
  c03c3A.c  : Compute sqrt(11).



  c03c4A.c  : Find and draw the largest  positive real root of "x**3 -
3x + 1"
  c03c4B.c  :               the smallest negative
  c03c4C.c  :               the intermediate

  c03c5A.c  : Find and draw the largest positive  real root of "x**4 -
x**2 + x - 2"
  c03c5B.c  :               the smallest




  c03c6A.c  : Find and draw the intersection point of "x" and "cos(x)"

  c03c7A.c  : Find and draw the first intersection point of "x**2"
and "cos(x)"
  c03c7B.c  :               the second

  c03c8A.c  : Find and draw the intersection point of "sin(x)" and "cos
(x)"
  c03c8B.c  :           Another intersection point

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c03c.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Derivative Normal.

                   ************

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

                   ************

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

                   ************

  c03b1A.c  : Draw    the normal.
  c03b1B.c  : Animate the normal.
  c03b1C.c  : Find the intersection points of the normal with the x-y
axis.
  c03b1D.c  : Find PA, the length of the normal from P to the x axis.
  c03b1E.c  : Find PB, the length of the normal from P to the y axis.
  c03b1F.c  : Find AM, the length of the under normal.


  c03b2A.c  : Draw    the normal.
  c03b2B.c  : Animate the normal.
  c03b2C.c  : Find the intersection points of the normal with the x-y
axis.
  c03b2D.c  : Find PA, the length of the normal from P to the x axis.
  c03b2E.c  : Find PB, the length of the normal from P to the y axis.
  c03b2F.c  : Find AM, the length of the under normal.


  c03b3A.c  : Draw    the normal.
  c03b3B.c  : Animate the normal.
  c03b3C.c  : Find the intersection points of the normal with the x-y
axis.
  c03b3D.c  : Find PA, the length of the normal from P to the x axis.
  c03b3E.c  : Find PB, the length of the normal from P to the y axis.
  c03b3F.c  : Find AM, the length of the under normal.


  c03b4A.c  : Draw    the normal.
  c03b4B.c  : Animate the normal.
  c03b4C.c  : Find the intersection points of the normal with the x-y
axis.
  c03b4D.c  : Find PA, the length of the normal from P to the x axis.
  c03b4E.c  : Find PB, the length of the normal from P to the y axis.
  c03b4F.c  : Find AM, the length of the under normal.

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c03b.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Approximate the definite single integral with
parameters.

                   ************

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

                   ************

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

                   ************

  c04h_1a.c; fa.h; c1simp.h; f : x->      sqrt(P1*x)

  c04h_2b.c; fb.h; c2simp.h; f : x-> P2 * sqrt(P1*x)

  c04h_3c.c; fc.h; c3simp.h; f : x-> P2 * sqrt(P1*x) + P3

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c04h.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Piecewise-defined functions.

                   ************

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

                   ************

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

                   ************

          c01a_1a.c  fa.h  :  With two functions.
          c01a_1b.c  fb.h
          c01a_1c.c  fc.h

          c01a_2a.c  fa.h  :  With three functions.
          c01a_2b.c  fb.h
          c01a_2c.c  fc.h

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c01a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Compute some limits.

                   ************

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

                   ************

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

                   ************

  c02a1A.c : Does lim x->0 sin(x)/x
exist ?

  c02a1B.c : Does lim x->0 (sin(x)-7*x) / (x*cos(x))
exist ?

  c02a1C.c : Does lim x->0 (1+x)**(1/x)
exist ?

  c02a1D.c : Does lim x->0 ((4.**|x| + 9.**|x|) /2.) ** (1./|x|)
exist ?

  c02a1E.c : Does lim x->0 |x|**(x)
exist ?

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c02a.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Exponential Functions.

                   ************

        hfile_c.zip : Download this package first.

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

                   ************

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

                   ************

                    Exponential Functions.

  c01d_1a.c : a**x  (  a>1)
  c01d_2a.c : a**x  (0<a<1)

  c01d_2b.c : -2**x
  c01d_2c.c : 3*(2**x)
  c01d_2d.c : 2**(x+3)
  c01d_2e.c : 2**x+3
  c01d_2f.c : 2**(x-3)
  c01d_2g.c : 2**x-3
  c01d_2h.c : 2**(-x)
  c01d_2i.c : (1/2)**x
  c01d_2i.c : 2**(3-x)


                 Natural Exponential Function.

  c01d_3a.c : e**x

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c01d.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus :  Logarithmic Functions.

                   ************

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

                   ************

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

                   ************

  c01e_1a.c :  loga(x) with a = 2.
  c01e_1b.c :  loga(x) with x > 0.
  c01e_1b.c :  if x < 0, loga(x) is undefined.

  c01e_2b.c :  -log2(x  )
  c01e_2c.c : 3*log2(x  )
  c01e_2d.c :   log2(x+3)
  c01e_2e.c :   log2(x  )+3
  c01e_2f.c :   log2(x-3)
  c01e_2g.c :   log2(x  )-3
  c01e_2h.c :   log2(-x )
  c01e_2i.c :   log1/2(x)
  c01e_2i.c :   log2(3-x)

  c01e_3a.c :    ln(x)

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c01e.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : The synthetic division. (Horner method)

                   ************

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

                   ************

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

                   ************

    c01c_1*.c   : Compute p(a).

    c01c_2*.c   : Verify if r is a root of p(x).

    c01c_3*.c   : Find an upper bound for the zeros of p(x).

    c01c_4*.c   : Find a  lower bound for the zeros of p(x).

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c01c.zip

freeware  http://groups.yahoo.com/group/mathc/

     * Calculus : Root of Polynomial functions. (graphic solution)

                   ************

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

                   ************

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

                   ************

   * Find all the values of k such that, a is a root of f(x).

  c01a_1a.txt : example 1.
  c01a_1b.c   :
  c01a_1c.c   :
  c01a_1d.c   :
      f1 .h   :

  c01a_2a.txt : example 2.
  c01a_2b.c   :
  c01a_2c.c   :
  c01a_2d.c   :
      f2 .h   :

  c01a_3a.txt : example 3.
  c01a_3b.c   :
  c01a_3c.c   :
  c01a_3d.c   :
      f3 .h   :

                   ************

The members can try these links :

http://groups.yahoo.com/group/mathc/files/C/D/c01b.zip