FIX CODE SO IT RUNS ON MATLAB!!!

function S$0=$ S$0\_$func$($x$)$

S$0=1-2*$x $-$ x$^3$;

end

function S$1=$ S$1\_$func$($x$,$ b$,$ c$,$ d$)\%$ Fixed: Added missing parameters

S$1=2+$ b$*($x $-1)+$ c$*($x $-1)^2+$ d$*($x $-1)^3$;

end

$\%$ Enforce C$1$ continuity at x $=1$

S$0\_$prime $=$ diff$($S$0\_$func$($x$),1)$; $\%$ Fixed: Used correct syntax for differentiation

S$1\_$prime $=$ diff$($@$($x$)$ S$1\_$func$($x$,$ b$,$ c$,$ d$),1)$; $\%$ Fixed: Used correct syntax for differentiation

eqn$1=$ S$0\_$prime $==$ S$1\_$prime;

$\%$ Enforce C$2$ continuity at x $=1$

S$0\_$secondPrime $=$ diff$($S$0\_$func, $2)$; $\%$ Fixed: Used correct syntax for differentiation

S$1\_$secondPrime $=$ diff$($@$($x$)$ S$1\_$func$($x$,$ b$,$ c$,$ d$),2)$; $\%$ Fixed: Used correct syntax for differentiation

eqn$2=$ S$0\_$secondPrime $==$ S$1\_$secondPrime;

$\%$ Enforce natural spline condition at x $=0($second derivative $=0)$

eqn$3=$ diff$($diff$($S$0\_$func$),1)==0$; $\%$ Fixed: Used correct syntax for differentiation

$\%$ Solve for unknowns $($b$,$ c$,$ and d$)$

syms b c d;

sol $=$ solve$([$eqn$1,$ eqn$2,$ eqn$3],[$b$,$ c$,$ d$])$;

b$\_$val $=$ double$($sol$.$b$)$;

c$\_$val $=$ double$($sol$.$c$)$;

d$\_$val $=$ double$($sol$.$d$)$;

$\%$ Define S$1$ with the solved coefficients

function S$1\_$complete $=$ S$1\_$func$($x$)$

S$1\_$complete $=2+$ b$\_$val$*($x $-1)+$ c$\_$val$*($x $-1)^2+$ d$\_$val$*($x $-1)^3$;

end