%%HP: T(1)A(D)F(.);
DIR
  Progs
    DIR
      DMS
        « DUP IP
SWAP FP 60 * DUP IP
SWAP FP 60 * 3
LIST
        »
      Quadratic
        «  a b c
          « b SQ 4
a c * * -
            CASE
DUP 0 ==
              THEN
DROP b NEG 2 a * /
Q "Root" TAG
              END
DUP DUP SIGN 1 ==
SWAP ABS ƒ DUP IP
== *
              THEN
ƒ DUP b NEG SWAP -
2 a * / Q "Root"
TAG SWAP b NEG + 2
a * / Q "Root"
TAG
              END
DUP
              IF
SIGN -1 ==
              THEN
"i" SWAP NEG
              ELSE
"" SWAP
              END
DUP 4 / 1 + IP 1
              FOR d
DUP d SQ / DUP DUP
IP ==
IF
THEN SWAP DROP
  IF DUP 1 ‹
  THEN STR "ƒ"
SWAP + + d 1 'd'
STO
  ELSE DROP d 1 'd'
STO
  END
ELSE DROP
END -1
              STEP
DUP 1
              FOR d
DUP DUP d / IP SWAP
d / == b DUP d / IP
SWAP d / == 2 a *
DUP d / IP SWAP d /
== * *
IF
THEN d / DUP
  IF 1 ‹
  THEN STR SWAP +
  ELSE DROP
  END
  IF b 0 ‹
  THEN "±" SWAP + b
NEG d / STR SWAP +
  END DUP SIZE SWAP
DUP "" SWAP SIZE 22
SWAP - 2 / IP 1
SWAP
  FOR e " " ROT +
" " ROT +
  NEXT
  IF 2 a * d / 1 ‹
  THEN ROT "" SWAP
1 SWAP
    FOR e "-" +
    NEXT + 2 a * d
/ STR DUP SIZE 22
SWAP - 2 / IP ""
SWAP 1 SWAP
    FOR e " " +
    NEXT SWAP +
  ELSE "" ""
  END PICT PURGE {
# 0d # 0d } PVIEW 2
GROB PICT SWAP {
# 0d # 32d } SWAP
GOR 2 GROB PICT
SWAP { # 0d # 24d }
SWAP GOR 2 GROB
PICT SWAP { # 0d
# 16d } SWAP GOR 1
'd' STO
END -1
              STEP
7 FREEZE '-b+ƒ(b^2-
4*a*c)/(2*a)' EVAL
Q "Root" TAG '(-b
-ƒ(b^2-4*a*c))/(2*a
)' EVAL Q "Root"
TAG
            END
          »
        »
      Sieries
        « -1 -1 0 
A O x T
          « CLLCD 0
'n' STO
            IFERR A
NUM
            THEN 1
'n' STO
            END
DROP 0
            WHILE
DUP DUP O ‹ n 1 < +
            REPEAT
DUP 'O' STO
              IF x
1 > x 6 < *
              THEN
Q‡ƒ SWAP
              ELSE
DROP
              END
              IF x
6 ==
              THEN
'T' STO 4 LIST T
              END A
NUM + 'n' INCR
DROP DUP 1 DISP 'x'
INCR DROP
            END
DROP n 'n' PURGE
"Iterations" TAG
          »
        »
      Simpson
        «
"f(X) (in ''s)"
"''" INPUT OBJ
'EQ' STO
"Number of times"
"" INPUT OBJ 'N'
STO "Start" ""
INPUT OBJ 'A' STO
"End" "" INPUT OBJ
'B' STO B A - N /
'I' STO 0 'S' STO A
'X' STO
          WHILE X B
<
          REPEAT EQ
EVAL S + 'S' STO X
I + 'X' STO 4 EQ
EVAL * S + 'S' STO
X I + 'X' STO EQ
EVAL S + 'S' STO
          END S I 3
/ * 'S' STO CLLCD S
1 DISP 'EQ' 'X' 'N'
'A' 'B' 'S' 'I'
PURGE PURGE PURGE
PURGE PURGE PURGE
PURGE 7 FREEZE
        »
      Newton
        « CLLCD
"f(X) (in ''s)"
"''" INPUT OBJ
'EQ' STO
"1st Guess" ""
INPUT OBJ 'X' STO
1 0 0  G K E
          «
            WHILE E
0 ==
            REPEAT
G 1 + 'G' STO X EQ
NUM EQ 'X' ˆ / -
'X' STO CLLCD G 1
DISP X 2 DISP
              WHILE
KEY 0 ==
              REPEAT
              END
'K' STO
              IF
'K' 54 ==
              THEN
1 'E' STO
              END
            END
          » 'X'
'EQ' PURGE PURGE
        »
    END
  Trig
    DIR
      Coordinates
        DIR
          —. '—=ƒ(x
^2+y^2+z^2)-ƒ(r^2+z
^2)'
          r. 'r^2=x
^2+y^2'
          X. 'x=r*
COS(•)-—*SIN(ψ)*COS
(•)'
          Y. 'y=r*
SIN(•)-—*SIN(ψ)*SIN
(•)'
          Z. 'z=—*
COS(ψ)'
        END
      InvTrig
"-‡/2 ‰ ASIN(x) ‰ ‡/2
   0  ‰ ACOS(x) ‰  ‡
 -‡/2 < ATAN(x) < ‡/2"
      Functions
        DIR
          Sin
            « NUM
SIN Q‡ƒ
            »
          ASin
            « NUM
ASIN Q‡ƒ
            »
          Cos.
            « NUM
COS Q‡ƒ
            »
          ACos
            « NUM
ACOS Q‡ƒ
            »
          Tan.
            « NUM
TAN Q‡ƒ
            »
          ATan
            « NUM
ATAN Q‡ƒ
            »
          Csc.
            « NUM
SIN INV Q‡ƒ
            »
          ACsc
            « NUM
INV ASIN Q‡ƒ
            »
          Sec.
            « NUM
COS INV Q‡ƒ
            »
          ASec
            « NUM
INV ACOS Q‡ƒ
            »
          Cot.
            « NUM
TAN INV Q‡ƒ
            »
          ACot
            « NUM
INV ATAN Q‡ƒ
            »
        END
      Identities
        DIR
          Pathagorean
            DIR
              SinCos
"SIN² • + COS² • = 1"
              TanSec
"TAN² • + 1 = SEC² •"
              CotCsc
"COT² • + 1 = CSC² •"
            END
          Quotient
            DIR
              TAN.
'TAN(•)=SIN(•)/COS(
•)'
              COT.
'COT(•)=COS(•)/SIN(
•)'
            END
          Reciprocal
            DIR
              CSC '
CSC(•)=1/SIN(•)'
              SEC '
SEC(•)=1/COS(•)'
              COT '
COT(•)=1/TAN(•)'
            END
          Negative
            DIR
              SIN.
'SIN(-•)=-SIN(•)'
              COS.
'COS(-•)=COS(•)'
              TAN.
'TAN(-•)=-TAN(•)'
            END
          SumDifference
            DIR
              SINP
'SIN(A+B)=SIN(A)*
COS(B)+COS(A)*SIN(B
)'
              SINM
'SIN(A-B)=SIN(A)*
COS(B)-COS(A)*SIN(B
)'
              COSP
'COS(A+B)=COS(A)*
COS(B)-SIN(A)*SIN(B
)'
              COSM
'COS(A-B)=COS(A)*
COS(B)+SIN(A)*SIN(B
)'
              TANP
'TAN(A+B)=(TAN(A)+
TAN(B))/(1-TAN(A)*
TAN(B))'
              TANM
'TAN(A-B)=(TAN(A)-
TAN(B))/(1+TAN(A)*
TAN(B))'
            END
          DoubleAngle
            DIR
              SIN.
'SIN(2*A)=2*SIN(A)*
COS(A)'
              COS1
'COS(2*A)=COS(A)^2-
SIN(A)^2'
              COS2
'COS(2*A)=2*COS(A)^
2-1'
              COS3
'COS(2*A)=1-2*SIN(A
)^2'
              TAN.
'TAN(2*A)=2*TAN(A)/
(1-TAN(A)^2)'
            END
          HalfAngle
            DIR
              HSin
'SIN(•/2)*ƒ((1-COS(
•))/2)'
              HCos
'COS(•/2)*ƒ((1+COS(
•))/2)'
              HTan1
'TAN(•/2)*ƒ((1-COS(
•))/(1+COS(•)))'
              HTan2
'TAN(•/2)=SIN(•)/(1
+COS(•))'
              HTan3
'TAN(•/2)=(1-COS(•)
)/SIN(•)'
            END
          ProductFactor
            DIR
              SINM
'SIN(A)-SIN(B)=2*
COS((A+B)/2)*SIN((A
-B)/2)'
              COSP
'SIN(A)+SIN(B)=2*
SIN((A+B)/2)*COS((A
-B)/2)'
              COSM
'COS(A)-COS(B)=-2*
SIN((A+B)/2)*SIN((A
-B)/2)'
            END
        END
    END
  Dirivatives
    DIR
      Linearization
        DIR
          EQ '1-COS
(X)'
          PPAR {
(-6.5,-3.1)
(6.5,3.2) X 0 (0,0)
POLAR Y }
          IERR
.397066870644
          L 'L(x,y)
=f(x0,y0)+fx(x0,y0)
*(x-x0)+fy(x0,y0)*(
y-y0)'
          E 'E(x,y)
‰1/2*M*(ABS(x-x0)+
ABS(y-y0))^2'
        END
      Product 'ˆx(u
(x)*v(x))=v(x)*ˆx(u
(x))+ˆx(v(x))*u(x)'
      Quotient 'ˆx(
u(x)/v(x))=(v(x)*ˆx
(u(x))-ˆx(v(x))*u(x
))/v(x)^2'
      Log
        DIR
          eU 'ˆx(e^
u)=e^u'
          aU 'ˆx(a^
u)=a^u*LN(u)'
          LN. 'ˆx(
LN(u))=1/u'
          LOGa 'ˆx(
LOGa(u))=1/(u*LN(a)
)'
        END
      Trig
        DIR
          SIN. 'ˆx(
SIN(u))=COS(u)'
          COS. 'ˆx(
COS(u))=-SIN(u)'
          TAN. 'ˆx(
TAN(u))=SEC(u)^2'
          CSC 'ˆx(
CSC(u))=-CSC(u)*COT
(u)'
          SEC 'ˆx(
SEC(u))=SEC(u)*TAN(
u)'
          COT 'ˆx(
COT(u))=CSC(u)^2'
        END
      InvTrig
        DIR
          ASIN. 'ˆx
(ASIN(u))=1/ƒ(1-u^2
)'
          ACOS. 'ˆx
(ACOS(u))=-1/ƒ(1-u^
2)'
          ATAN. 'ˆx
(ATAN(u))=1/(1+u^2)
'
          ACSC 'ˆx(
ACSC(u))=-1/(ABS(u)
*ƒ(u^2-1))'
          ASEC 'ˆx(
ASEC(u))=1/(ABS(u)*
ƒ(u^2-1))'
          ACOT 'ˆx(
ACOT(u))=-1/(1+u^2)
'
        END
    END
  Intagrals
    DIR
      Polar. '„(•,•
,„(Ψ,Ψ,„(—,—,—^2*
SIN(Ψ),—),Ψ),•)'
      Applications
        DIR
          Area
            DIR
              Under
'A=„(a,b,f(x),x)'
              Btwen
'A=„(a,b,f(x)-g(x),
x)'
              Polar
'A=1/2*„(a,b,r^2,•)
'
              BtwPolar
'A=1/2*„(a,b,r1^2-
r2^2,•)'
            END
          Disk
            DIR
              XAxis
'V=‡*„(a,b,f(x)^2,x
)'
              YAxis
'V=‡*„(a,b,f(y)^2,y
)'
              Generaly
'V=‡*„(a,b,RADIUS^2
,HIGHT)'
            END
          Shells
            DIR
              XAxis
'V=2*‡*„(a,b,x*f(x)
,x)'
              YAxis
'V=2*‡*„(a,b,y*f(y)
,y)'
              Generaly
'V=2*‡*„(a,b,RADIUS
*HIGHT,WIDTH)'
            END
          ArcLen
            DIR
              XAxis
's=„(a,b,ƒ(1+ˆx(y)^
2),x)'
              YAxis
's=„(a,b,ƒ(1+ˆy(x)^
2),y)'
              Parametric
's=„(a,b,ƒ(ˆt(x)^2+
ˆt(y)^2),t)'
            END
          SurArea
            DIR
              IERR
4.14270225879E-12
              V 0
              X
1.38868454455
              EQ '0
=X^3/3-3*X^2/2+2'
              PPAR
{ (-6.5,-3.1)
(6.5,3.2) X 0 (0,0)
FUNCTION Y }
              XAxis
'SA=2*‡*„(a,b,R*ƒ(1
+ˆx(y)^2),x)'
              YAxis
'SA=2*‡*„(a,b,R*ƒ(1
+ˆy(x)^2),y)'
              Parametric
'SA=2*‡*„(a,b,R*ƒ(ˆ
t(x)^2+ˆt(y)^2),t)'
            END
          AVAL 'AV=
1/(b-a)*„(a,b,f(x),
x)'
          VSlicing
'V=„(a,b,A(x),x)'
          Distance
            DIR
              Relative
'D=„(a,b,v(t),t)'
              Total
'D=„(a,b,ABS(v(t)),
t)'
            END
          Work
            DIR
              Work
'W=„(a,b,f(x),x)'
              Generaly
'W=„(a,b,FORCE,
ISTANCE)'
              Hookes
'F=x*k'
            END
        END
      Approximations
        DIR
          Rectangles
'…(k=1,n,f(k)*›k)'
          Trapaziod
'A=1/2*›X*(y0+2*y1+
2*y2+2*y(n-1)+yn)'
          Simpson '
A=1/3*›X*(y0+4*y1+2
*y2+4*y3+2*y4+yn)'
        END
      Fundamental.20
        DIR
          Basic
            DIR
              Associative
'„(a,b,A+B-C,u)=„(a
,b,A,u)+„(a,b,B,u)-
„(a,b,C,u)'
              Konst
'„(a,b,K,u)=K*„(a,b
,1,u)'
              du '„
(a,b,1,u)=u+C'
            END
          Exponential
            DIR
              uN '„
(a,b,u^n,u)*(u^(n+1
)/(n+1))+C'
              u1 '„
(a,b,u^-1,u)=LN(ABS
(u))+C'
              eTu '
„(a,b,e^u,u)=e^u+C'
              aTu '
„(a,b,a^u,u)=a^u/LN
(a)+C'
            END
          Trig
            DIR
              SIN.
"„(COS(u) du) = SIN(u) + C"
              COS.
"„(SIN(u) du) = -COS(u) + C"
              TAN.
"„(SEC²(u) du) = TAN(u) + C"
              COT.
"„(CSC²(u) du) = -COT(u) + C"
              SEC.
"„(SEC(u) TAN(u) du) = SEC(u) + C"
              CSC.
"„(CSC(u) * COT(u) du) = -CSC(u) + C"
              ITAN
"„(TAN(u) du) = -LN |COS(u)| + C = LN |SEC(u)| + C"
              ICOT
"„(COT(u) du) = LN |SIN(u)| + C"
              ISEC
"„(SEC(u) du) = LN |SEC(u)-TAN(u)| + C"
              ICSC
"„(CSC(u) du) = LN |CSC(u)-COT(u)| + C = -LN |CSC(u)+COT(u)| + C"
            END
          InvTrig
            DIR
              ASIN.
'„(a,b,1/ƒ(a^2-u^2)
,u)=ASIN(u/a)+C'
              ATAN.
'„(a,b,1/(a^2+u^2),
u)=1/a*ATAN(u/a)+C'
              ASEC.
'„(a,b,1/(u*ƒ(u^2-a
^2)),u)=1/a*SEC^-1*
ABS(u/a)+C'
            END
        END
      DivideConquer
"Deg. Num Š Deg. Dem"
      BreakUp 1
      CompleteSquare
'10*x-x^2-21=-(x^2-
10*x+25)-21+25'
      Parts '„(a,b,
u,v)=u*v-„(a,b,v,u)
*LIATE'
      TrigSub
"EXP       SUB
a^2-x^2    x=a*SIN(•)
a^2+x^2    x=a*TAN(•)
x^2-a^2    x=a*SEC(•)"
      PartialFractions
"Be careful of quadratics"
    END
  Series
    DIR
      Geometric 'Sn
=a1/(1-r)'
      Error.at.C '
Rx(n)=f^(n+1)*C/(n+
1)!*(x-a)^(n+1)'
      Big3
        DIR
          SIN.X 'X^
1/1!-X^3/3!+X^5/5!-
X^7/7!+(-1)^n*X^(2*
n+1)/(2*n+1)!'
          COS.X 'X^
0/0!-X^2/2!+X^4/4!-
X^6/6!+(-1)^n*X^n/(
2*n)!'
          e.x 'X^0/
0!+X/1!+X^2/2!+X^3/
3!+X^4/4!+X^n/n!'
          ATAN. 'X-
2!/3!*X^3+4!/5!*X^5
-6!/7!*X^7+(-1)^n*(
2*n)!*X^(2*n+1)/(2*
n+1)!'
        END
    END
  Vectors
    DIR
      A 155.9
      • '•=ACOS(A*B
/(ABS(A)*ABS(B)))'
      Proj 'PROJaB=
A*B/(A*A)*A'
      DIST 'd=ABS(
PS*(N/ABS(N)))'
      DST.P 'd=ABS(
PS*X*v)/ABS(v)'
      ArcLen 'L=„(a
,b,ABS(v),t)'
    END
END