Stationary phase and critical manifolds
A complete lesson on nonstationary cancellation, quadratic and parameter stationary phase, differentiated symbol estimates, and clean critical manifolds with their normal densities. Three examples and five solved exercises accompany the full proofs.
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Prerequisite lessons
The proofs are included here. Free source citations support their construction; they do not replace a programme proof. The proof index gives the exact dependency order.
- Gaussian regularization and quadratic stationary phase
- Completing the finite-dimensional prerequisites
- A smooth quadratic reduction with parameters
- Completing the elementary inputs actually used
- Completing the algebra and differentiation inputs
- Mixed derivatives and the compact-interval integral
- Exponentials, circle coordinates and the Gaussian branch
- Rectangle integrals, tails and the interchanges used in stationary phase
- Completing the change-of-variables prerequisites
105 selected human prerequisite proofs, from 33 sections of Jiří Lebl’s freely accessible Basic Analysis, version 6.3, accompany the local completions. The selection preserves the mathematical passages and their figures, with explicitly recorded reference routing, optional-note omissions, and one shared-proof deduplication.
Sources and rights
The lesson and its companions contain their exact free reading references and component notices. Lebl’s selected statements, proofs and figures are used under CC BY-SA 4.0, with the original dual-licence notice retained. The selected editable HTML/TeX and adaptation records are in the source selection.
The receiving edition and local prerequisite adaptations are CC BY-SA 4.0; retained original Sol-authored CC0 text keeps its terms. The included CSS and fonts retain KaTeX’s MIT notice. The read-only author PDFs consulted for mathematical comparison are linked from the lessons; they are not included in this edition. The machine-readable proof index contains the scopes, exact local locators and prerequisite edges.
Review status
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