theorem 10.36 Solution of the heat problem on an interval

open in the book · parts/02-mathematical-methods/08-pdes.tex:1000 · p. 350

Rests on

depends_on proposition 10.29 Time separation reduces the canonical equations to Helmholtz ¶
- depends_on equation 10.25 eq:pde-helmholtz-equation ¶
- depends_on lemma 10.28 The separation constant ¶
  - depends_on definition 10.2 Linear, semilinear, quasilinear ¶
    - depends_on definition 10.1 Partial differential equation; order ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 6.2 Open set ¶
  - proves proof ch:08-pdes@proof-9 ¶
- proves proof ch:08-pdes@proof-10 ¶
depends_on remark 9.53 rem:slt-parseval-completeness ¶
proves proof ch:08-pdes@proof-11 ¶

Supports

Nothing declares a dependency on this node yet.

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`	→	Time separation reduces the canonical equations to Helmholtz	declared	parts/02-mathematical-methods/08-pdes.tex:1017
`depends_on`	→	rem:slt-parseval-completeness	declared	parts/02-mathematical-methods/08-pdes.tex:1017
`proves`	←	ch:08-pdes@proof-11	declared	parts/02-mathematical-methods/08-pdes.tex:1020