% We opened a new function m-file with the
% file menu and created sumavg.m
help SumAvg
  SumAvg(a,b) returns the sum and average
  of the input arguments a and b.

% If we do not see the documentation for
% our script, we may have to set the path,
% adding the location of the save .m file
% to the path.
path

		MATLABPATH

	C:\Users\janv\Documents\MATLAB
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\general
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\ops
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\lang
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\elmat
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\randfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\elfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\specfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\matfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\datafun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\polyfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\funfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\sparfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\scribe
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\graph2d
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\graph3d
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\specgraph
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\graphics
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\uitools
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\strfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\imagesci
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\iofun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\audiovideo
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\timefun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\datatypes
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\verctrl
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\codetools
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\helptools
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\winfun
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\winfun\NET
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\demos
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\timeseries
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\hds
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\guide
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\plottools
	C:\Program Files\MATLAB\R2009b\toolbox\local
	C:\Program Files\MATLAB\R2009b\toolbox\shared\controllib
	C:\Program Files\MATLAB\R2009b\toolbox\shared\dastudio
	C:\Program Files\MATLAB\R2009b\toolbox\matlab\datamanager
[x,y] = SumAvg(4,9)

x =

    13


y =

    6.5000

a = [3,4,5]; b = [3,9,0];
SumAvg(a,b)

ans =

     6    13     5

[x,y] = SumAvg(a,b)

x =

     6    13     5


y =

    3.0000    6.5000    2.5000

help CentDiff
  CentDiff(f,x,h) returns the central difference
    approximation for the derivative of the
    function f at x, using step size h > 0,
    with the formula (f(x+h/2) - f(x-h/2)/h).

CentDiff('sin',pi/2,0.001)

ans =

     0

% Note that we pass the function
% to the function CentDiff as a string.
CentDiff('cos',pi/2,0.001)

ans =

   -1.0000

CentDiff('cos',pi/2,0.1)

ans =

   -0.9996

f = inline('cos(x)*sin(x) + x',x)

f =

     Inline function:
     f(x,P1,P2,P3,P4,P5,P6) = cos(x)*sin(x) + x

f = inline('cos(x)*sin(x) + x','x')

f =

     Inline function:
     f(x) = cos(x)*sin(x) + x

f(8)

ans =

    7.8560

cos(8)*sin(8) + 8

ans =

    7.8560

% We inline we quickly make one line functions,
% defined by a string.
% We added a check in the CentDiff function:
CentDiff('sin',0,0)
h must be positive
ans =

     0

help bisect
  Applies the bisection method to the function f on [a,b],
  f is assumed to be continuous and f(a)*f(b) < 0.
  Stops when |f(a)| < eps or |f(b)| < eps or |b-a| < eps.
  Failure is reported (fail = 1) when the accuracy requirement
  is not satisfied in N steps; otherwise fail = 0 on return.
 
  Example :
  >> [a,b,fail] = bisect(’cos’,pi/4,2*pi/3,0.0001,100)
 

[a,b,fail] = bisect('cos',pi/4,2*pi/3,0.0001,100)
{Warning: Invalid escape sequence appears in format string. See
help sprintf for valid escape sequences.} 
> In <a href="matlab: opentoline('C:\Users\janv\Documents\bisect.m',12,1)">bisect at 12</a>
running the bisection method...
 a = 1.439897, b = 2.094395, m = 1.439897, f(m) = 0.130526
 a = 1.439897, b = 1.767146, m = 1.767146, f(m) = -0.195090
 a = 1.439897, b = 1.603521, m = 1.603521, f(m) = -0.032719
 a = 1.521709, b = 1.603521, m = 1.521709, f(m) = 0.049068
 a = 1.562615, b = 1.603521, m = 1.562615, f(m) = 0.008181
 a = 1.562615, b = 1.583068, m = 1.583068, f(m) = -0.012272
 a = 1.562615, b = 1.572842, m = 1.572842, f(m) = -0.002045
 a = 1.567728, b = 1.572842, m = 1.567728, f(m) = 0.003068
 a = 1.570285, b = 1.572842, m = 1.570285, f(m) = 0.000511
 a = 1.570285, b = 1.571563, m = 1.571563, f(m) = -0.000767
 a = 1.570285, b = 1.570924, m = 1.570924, f(m) = -0.000128
 a = 1.570605, b = 1.570924, m = 1.570605, f(m) = 0.000192
 a = 1.570764, b = 1.570924, m = 1.570764, f(m) = 0.000032
succeeded after 13 steps

a =

    1.5708


b =

    1.5709


fail =

     0

 
% Our last script prompts the user for input.
AreaCircle
Give the radius 2

ans =

   12.5664

diary off