Version, citation, and corrections
Advanced Methods for Linear ODEs is an evolving graduate-level guide and reference on connection problems, exact WKB, and spectral applications. Its main scope is second-order complex linear equations and rank-two systems. The revision described here is dated 7 September 2026. The source identity record lists the actual source-file hashes; its base Git commit alone does not describe any additional working changes included in that revision.
Cite the page and revision
Section titled “Cite the page and revision”For the whole resource, a title-first citation is:
Advanced Methods for Linear ODEs: A Guide to Connection Problems, Exact WKB, and Spectral Applications. Revision 7 September 2026. heun.xyz/advanced-ode/.
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What the review establishes
Section titled “What the review establishes”The guide has internal mathematical, physical, pedagogical, and computational checks, including computer-assisted review. These checks are scoped: selected derivations, example calculations, normalization and sign tests, adverse-input tests, structural validation, and rendered-page checks address different questions. The numerical records state the actual checks and their limits.
The content field status: reviewed records an internal editorial state. It
does not mean that an external specialist has certified every theorem or
that readers have demonstrated the intended learning outcomes. The word
exact describes a mathematical relation under its stated hypotheses; it
does not convert a finite numerical approximation into a proof.
No completed external specialist sign-offs or graduate-reader pilots are claimed for this revision. Whole-route scholarly review and measured reader trials remain necessary before making those stronger claims. Session lengths in the study routes are planning estimates, not measured completion times.
Corrections and additions
Section titled “Corrections and additions”| Date | Change | Consequence |
|---|---|---|
| 7 September 2026 | Corrected the exact-WKB pole-order hypotheses to use positive pole order, distinct from signed divisor order | A third-order pole can no longer satisfy a printed bound intended to allow at most a second-order pole |
| 7 September 2026 | Added explicitly sufficient regular Sturm–Liouville hypotheses | The stated regular problem has a usable coefficient and operator-domain formulation |
| 7 September 2026 | Repaired the Heun checker | Unsupported overlap points are rejected; verification checks both determinants and full matrix drift, with nonzero failure exits |
| 7 September 2026 | Added two starters, focused study routes, and progressive help at 18 exercise bottlenecks | Readers can complete a first connection or spectral problem before taking a longer route |
| 7 September 2026 | Packaged selected numerical laboratories | Commands, environments, comparison methods, adverse cases, and saved outputs are available together |
| 7 September 2026 | Adopted the guide label and cleaned the scholarly source map and mathematical search indexing | Existing chapter routes remain usable; search excludes duplicate visual and source-TeX copies while retaining MathML |
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