lemma A.126 Cartesian coordinates and scale factors

open in the book · appendices/A-long-proofs.tex:7097 · p. 2854

Rests on

depends_on definition A.125 Ellipsoidal coordinates ¶
- depends_on definition A.116 Orthogonal curvilinear coordinates; scale factors ¶
  - depends_on definition 7.98 Functions of class $C^{1}$ ¶
    - depends_on definition 7.20 Continuity at a point ¶
      - depends_on definition 7.16 Limit ¶
      - depends_on equation 7.7 eq:ana-limit-left ¶
      - depends_on equation 7.5 eq:ana-limit-right ¶
    - depends_on definition 7.97 Partial derivative; gradient ¶
      - depends_on definition 7.26 Derivative of a function at a point ¶
      - depends_on definition 5.15 Basis ¶
  - depends_on equation 10.25 eq:pde-helmholtz-equation ¶
depends_on equation A.263 eq:app-stackel-orthogonality ¶
proves proof app:A-long-proofs@proof-78 ¶

Supports

depends_on proposition A.128 The ellipsoidal system separates ¶
- depends_on proposition A.132 The count ¶

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`	→	Ellipsoidal coordinates	declared	appendices/A-long-proofs.tex:7111
`depends_on`	→	eq:app-stackel-orthogonality	declared	appendices/A-long-proofs.tex:7111
`depends_on`	←	The ellipsoidal system separates	declared	appendices/A-long-proofs.tex:7232
`proves`	←	app:A-long-proofs@proof-78	declared	appendices/A-long-proofs.tex:7114