clear all
close all

dx=.1
x=0:dx:2*pi;
y=sin(x);
n=length(x);
figure(1)
plot(x,y)

%fwd difference scheme
for i=1:n-1
    dy(i)=(y(i+1)-y(i))/dx;
end
dy(n)=(y(n)-y(n-1))/dx; %must use bwd scheme at right endpt

hold on
plot(x,dy,'r')

%bwd difference scheme
for i=2:n
    dyb(i)=(y(i)-y(i-1))/dx;
end
dyb(1)=(y(2)-y(1))/dx; %must use fwd scheme at left endpt

plot(x,dyb,'g')

%center difference scheme--second order accurate
for i=2:n-1
    dyc(i)=(y(i+1)-y(i-1))/(2*dx);
end
%use second order accurate diff schemes at endpts
dyc(n)=(3*y(n)-4*y(n-1)+y(n-2))/(2*dx); %must use bwd scheme at right endpt
dyc(1)=(-3*y(1)+4*y(2)-y(3))/(2*dx); %must use fwd scheme at left endpt

plot(x,dyc,'k')

%c=cos(x);
%plot(x,c,'b--')


load bears.dat
yr=bears(:,1);
win=bears(:,2);
figure(2)
plot(yr,win,'o--')
m=length(yr);
db=(yr(end)-yr(1))/m;
%fwd difference scheme
for i=1:m-1
    dw(i)=(win(i+1)-win(i))/db;
end
dw(m)=(win(m)-win(m-1))/db; %must use bwd scheme at right endpt

hold on
plot(yr,dw,'r*:')

dbs=.1;
xp=yr(1):dbs:yr(end);
xpm=length(xp);
bearspline=spline(yr,win,xp);
plot(xp,bearspline,'m')

%fwd difference scheme
for i=1:xpm-1
    dws(i)=(bearspline(i+1)-bearspline(i))/dbs;
end
dws(xpm)=(bearspline(xpm)-bearspline(xpm-1))/dbs; %must use bwd scheme at right endpt
plot(xp,dws,'k')