(data set_34 1 10 15 21 29 30 34 39)
(pick 3 set_34)
;; (30 1 10)

(new-plot)
(contour-points 21)
(spin-points 21)

(message "
 #1 p. 34: contours are lines, evenly spaced as z changes by a constant amount.
")
(func f(x y) x + y)
(contour f)

(message "
 #10 p. 34: contours are ellipses, which grow closer together as z changes by a
constant amount.
")
(func f(x y) x ^ 2 + 2 * y ^ 2)
(contour f)

(message "
 #30 p. 34: this is the way I read it:
")
(data surfaces "a" "b" "c" "d" "e")
(data contours 3 1 5 2 4)
surfaces
contours


(data set_48 1 2 3 4 5 6 7 8 12 15 20 25)
(pick 3 set_48)
;; (25 8 15)

(message "
#8, page 48: z = c + mx + ny

f(0,0) = 1 => c=1
f(1,0) - f(0,0) = 2 => m = 2
f(0,1) - f(0,0) = -.5 => n = -.5

z = 1 + 2x - y/2
")

(message "
#15, page 48: z = z_0 + m(x - x_0) + n(y - y_0)

Change of 1 in y  and  change of 200 in z  => n = 200
Change of 100 in x  and  change of 600 in z  => m = 6
f(150,0) = 1000

z = 1000 + 6(x - 150) + 200(y - 0)
z = 100 + 6x + 200y
")

(message "
#25, page 48: z = .003x + .8y - 4
")
(func f(x y) .003 * x + .8 * y - 4)
(f 1050 3)
;; no: 1.5500000000000007
(f 1600 0)
;; no: 0.7999999999999998
(f 0 4.3)
;; no: -0.5600000000000001
(domain 400 1600)
(range 0 4.3)
(spin-domain 400 1600 0 4.3)
(contour f)
(func g(x y) heaviside (.003 * x + .8 * y - 4 - 2.5))
(contour g)

(calc (f 800 0) - (f 700 0))
(calc (f 0 3.0) - (f 0 2.5))
;; the .5 on the grade point is worth more.


(data set_73 1 2 3 4 12 13 14 15 16 21 26 36 37 40)
(pick 3 set_73)
;; (1 40 16)

(message "
#1, page 73:

p -> 2w
q -> -u
r -> u + w
s -> 2w - u
t -> u - w
")

(message "
#16, page 73:
")
(def a (vector 1 3))
(def b (vector 3 2))
(def v (vector -2 -2))
(def w (vector -1 2))
a b v w

(message "
#40, page 73:
")
(vector (calc 2 * cos (pi / 4)) (calc 2 * sin (pi / 4)))
(vector (calc cos (pi / 6)) 0 (calc sin (pi / 6)))