proposition 20.7 Terminal speed and the approach to it

open in the book · parts/03-classical-mechanics/03-exp-projectile-motion.tex:455 · p. 769

Rests on

depends_on equation 20.10 eq:projectile-drag-eom ¶
depends_on theorem 9.8 Picard–Lindelöf ¶
- depends_on definition 9.4 Lipschitz condition ¶
- depends_on equation 9.3 eq:slt-ode-system ¶
- depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
  - depends_on definition 7.20 Continuity at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on equation 7.7 eq:ana-limit-left ¶
    - depends_on equation 7.5 eq:ana-limit-right ¶
  - depends_on proposition 7.47 Comparison; absolute convergence ¶
    - depends_on corollary A.46 Monotone convergence ¶
      - depends_on theorem A.40 Least-upper-bound property ¶
      - proves proof app:A-long-proofs@proof-33 ¶
    - depends_on definition 7.45 Series ¶
      - depends_on definition 7.2 Absolute value ¶ ↺
      - depends_on definition 7.4 Convergence ¶
    - depends_on theorem 7.8 Cauchy criterion ¶
      - depends_on corollary A.47 Cauchy completeness ¶
      - depends_on definition 7.4 Convergence ¶ ↺
      - proves proof ch:05-real-analysis@proof-5 ¶
    - proves proof ch:05-real-analysis@proof-28 ¶
  - proves proof ch:07-odes-sturm-liouville@proof-1 ¶
- proves proof ch:07-odes-sturm-liouville@proof-2 ¶
proves proof ch:03-exp-projectile-motion@proof-3 ¶

Supports

depends_on example 20.8 A raindrop ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	eq:projectile-drag-eom	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:474
`depends_on`	→	Picard–Lindelöf	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:474
`depends_on`	←	A raindrop	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:520
`proves`	←	ch:03-exp-projectile-motion@proof-3	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:477