function y_2 = odeStep_euler(x_1,y_1,h,deriv)
%y_2 = odeStep_euler(x_1,y_1,h,deriv);
% A self-starting, simple, single Euler step function
%  x_1 --> initial independent variable (scalar, typically time)
%  y_1 --> initial dependent variable (vector)
%    h --> step size in x
%deriv --> function handle for derivative function (may be annonymous call
%          if derivatives are functions of parameters other than x & y)
%  y_2 <== final dependent variable; i.e., y(x_n+h) 

% (c) 2007, 2008 Curt A. L. Szuberla
% University of Alaska Fairbanks, all rights reserved

% ver 1.01
% 2 February 2008

% implementation of standard Euler formula
k_1 = h * deriv(x_1,y_1);    % use slope at start
y_2 = y_1 + k_1;           % to estimate final point

% some things to note here:
% the function to take a single Euler-type step has 4 inputs and delivers
% one output (we don't need to output x_2, since it's simply x_1 + h)
% notice how the function handle to our derivative function is passed in as
% input WITHOUT arguments, but when it is called in the function it is
% called with the two generic input arguments, the independent variable 
% (x_n) and the independent variable (y_n)
%
% we'll soon see that the Euler method is too error prone for oscillating
% sysems and taht a simple modification will do much better -- but the way
% we've constructed this function lends itself to the improved versions,
% since they will take EXACTLY the same input arguments and deliver the
% same output

return