% Class 10 - Root Solving
% Coded by NFR on 9.26.2019
%
% 1st Method: Graphical Approach
% Sometimes works, labor intensive
% but nice to see what's going on
cd = 0.25; % kg/m
t = 4; %s
g = 9.81; %m/s^2
ftv = @(m) sqrt(g*m/cd)*tanh(sqrt(g*cd/m)*t)-36
fplot(ftv,[130 160])
xlabel('Mass (kg)')
ylabel('Velocity (m/s)')
% Solution by inspection is 142.7
% Works for simple, one time problems
% If you need to process a lot of data or be
% more accurate, we need an alogorithm
%
% Method 2: Using Numerical Methods
% Problem 5.5 from the textbook
f1 = @(x)-12-21*x+18*x.^2-2.75*x.^3;
% (b) bisection
[r_bisect,fx,~,iter_bisect] = bisect(f1,-1,0,1);
fplot(f1,[-1 0])
hold on
plot(r_bisect,fx,'ro')
% (c) False position 
[r_fp,fx,~,iter_fp] = falsepos(f1,-1,0,1);
plot(r_fp,fx,'b+')
hold off
% Let's see if the false position method
% is more efficient
iter_fp
iter_bisect
% Example of incremental search
% Plot same function above with bigger x span
fplot(f1,[-2,6])
% There appears to be multiple roots from 
% -2 to 6, let's use incremental search
% to find them
xb = incsearch(f1,-2,6,10000)