#Dayoon Kim, 2024-2-4, HW1

#HW1. Maple Book
#Chapter 4
f:='f':
seq(f(i),i=1..6);

1$4;

L:=a+b+2*c+3*d;
op(%);
nops(L);
op(3,L);
op(L)[3];

s:=seq(i/(i+1), i=1..6);
Set:={s};
List:=[s];
List[2..4];
S:= table([(1)=A,(3)=B+C,(5)=A+B+C]);
S[3];
S;
op(S);

convert(Set,list);
?whattype

#Chapter 5
f:=(x,y)->x^2-3*x*y+5*y^2;
f(2,3);
simplify(f(sin(t),cos(t)));
g:=2*x^2+y+y^2;
unapply(g,(X,Y));
h:=x^3;
(h@@(-1))(x);
diff(f,x,y);
D(h);

readlib(extrema):
l:=x^2+y^2-1;
extrema(g,{l},{x,y},`s`)

Int(sqrt(1+x^6),x=0..1);
value(%);
evalf(%);

#with(student);
#Int(x^7/sqrt(x^16-1),x);
#G:=value(%);
#G2:=changevar(u=x^8,G,u);
#subs(u=x^8,G2);
#simplify(%);
#diff(%,x);

Int(x*cos(3*x),x);
intparts(%,x);
value(%);

rat:=(4*x^4+9*x^3+12*x^2+9*x+4)/(x+1)/(x^2+x+1)^2;
convert(rat,parfrac,x);
int(%,x);

y:=1/sqrt(1-x);
taylor(y,x=0,7);
coeff(%,x,5);