(message "
(pick 3 '(1 7 23 27 34 36 37 41 42))
(pick 3 '(3 4 20 21))
(pick 3 (combine '(1 3 10) (iseq 15 26)))
;; selected problems:
13.5: (27 34 23)
13.6: (3 4 21)
13.7: (10 25 26)
")

(message "
13.5: 23
(func f(x y) sqrt (tan x + y))
(gradient f fgrad)
(fgrad 0 1)

")
(func f(x y) sqrt (tan x + y))
(gradient f fgrad)
(fgrad 0 1)

(func f(x y) sqrt (tan (x + y)))
(gradient f fgrad)
(fgrad 0 1)

(message "
13.5: 27

(func f(x y) x ^ 2 * exp y)
(gradient f fgrad)

(def v (vector 4 3))
(def u (/ v (norm v)))

(dot (fgrad 1 0) u)
")
(func f(x y) x ^ 2 * exp y)
(gradient f fgrad)

(def v (vector 4 3))
(def u (/ v (norm v)))

(dot (fgrad 1 0) u)

(message "
13.5: 34

(func f(x y z) x ^ 2 + y ^ 4 + x ^ 2 * z ^ 2)
(diff f x fx)
(diff f y fy)
(diff f z fz)
(def gradf (vector (fx -1 1 1) (fy -1 1 1) (fz -1 1 1)))
(calc 4 * (norm gradf))
")
(func f(x y z) x ^ 2 + y ^ 4 + x ^ 2 * z ^ 2)
(diff f x fx)
(diff f y fy)
(diff f z fz)
(def gradf (vector (fx -1 1 1) (fy -1 1 1) (fz -1 1 1)))
(calc 4 * (norm gradf))

(message "
13.6: 3
(gradient (func g(x y) ln (x ^ 2 + y ^ 2)) ggrad)
(def xt (calc 1 / (rseq 1 10 100)))
(def yt (calc sqrt (rseq 1 10 100)))
(plot (ggrad xt yt))
")

(message "
13.6: 4
")

(message "
13.6: 21
")

(message "
13.7: 10
")

(message "
13.7: 25
")

(message "
13.7: 26
")