function [ti,wi]=euler(f,a,b,y0,N)

%Euler's method: See section 5.2.
%Solves y' = f(t,y), y(a) = y0, on the interval a <= t <= b.
%The unknown y may be a scalar or vector. (See section 5.9.)
%Time steps have a size of h = (b-a)/N.
%The output ti is a column vector of values of t.
%The output wi is a column vector or matrix, whose rows are estimated values of y.


h  = (b-a)/N;
ti = linspace(a, b, N+1);
wi(1,:) = y0(:);
for i=1:N
  k1(1,:) = h*f(ti(i), wi(i,:));
  wi(i+1,:) = wi(i,:) + k1;
end