% complex_convergence checks for the radius of convergence of a   
%  Taylor series by plotting the modulus of the sum for a fixed value 
%  of z (supplied by the user) as a function of the number of terms
%  in the sum.  It is expected that z is entered as a complex
%  number (e.g., 0.5 + 0.2*i).

% Programmer: Dick Furnstahl  furnstahl.1@osu.edu
%
% Revision history:
%   20-Apr-2005 -- original version for Physics 263 based on
%                   test_convergence.m.
%

clear;    % this sets variables to zero, so we start with a clean slate

z = input('enter a test value of z: ');   % get a value of z to try
N = 500;               % maximum number of terms in the series to sum

% We'll create two vectors, nvec and my_sum.  The i'th elements of the
%  vectors are referenced by nvec(i) and my_sum(i), with i starting at 1.
nvec(1) = 1;            % first element of the vector nvec = (1,2,3,...,N) 
my_sum(1) = 1 - z;      % start with the sum of the z^0 and z^1 terms

for n = 2:N            % now add in the rest, i.e., n = 2, 3, 4, 5, ..., N
    nvec(n) = n;       % build the nvec vector (1,2,3,4,...,N) entry by entry 
    my_sum(n) = my_sum(n-1) +  (-1)^n * (z)^n;   % add the n'th term to the sum 
end

% now make a plot of the modulus of the sum vs. the number of terms
plot(nvec,abs(my_sum));     % plot(x_vector,y_vector) plots one line
xlabel('n');     % add the x-axis label
ylabel('sum');   % add the y-axis label