%% LAB 3  FUNCTIONS and FILES

%% A function is created as in the following example
%
% function [x,y]=func(a,b)
% % Simple function 
% x=a^b;
% y=cos(b);
%
% a and b are the parameters (input data)  of the function and  x and y are
% the output data. 
% Usually a function is stored in a separate m-file with the same name as
% the function.
% The first comment of the function is displayed if one types "help func"
%--------------------------------------------------------------------------
%% Write the function in an m-file and execute it for a=1.5 and b=3.6


%--------------------------------------------------------------------------
%% Write a function that implements the expression y=sin(x²). Make sure
% that it works also when x is a vector. 

%--------------------------------------------------------------------------
%% Write a function polyn that evaluates the polynomial
% p(x)=c(1)+c(2)*x+c(3)*x^2+...+c(n+1)*x^n
% The function should have two parameters: a vector c with the coefficients
% and a scalar x. The output is the value of the polynomial for x. Make
% sure that it functions also for x being a vector. Use your function to
% plot the polynmial p(x)=3-2x+x² over the interval [0,2].

%--------------------------------------------------------------------------
%% Write a function that computes the square root of a non-negative number
% a. Use the iteration 
%    x(1)=1,  x(n+1)==.5*(x(n)+a/x(n)),  n=1,2,...
% Terminate when |x(n)^2 - a| < tol. 
% Your function should have two parameters, a and tol. Check your function
% using sqrt(a).

%--------------------------------------------------------------------------
%% FILES
% The functions "save" and "load"  can be used to handle data stored on
% disk. (help save, help load)
%
%--------------------------------------------------------------------------
%% Create a random 5x5  matrix with normally distributed  entries (help randn), 
% and compute its SVD.  Store the SVD in a file svda, clear the workspace
% and check that it is empty of variables (help who, help clear). Load the
% file and check that the variables are back in the workspace. 

%--------------------------------------------------------------------------
%% END