Advanced Mathematical Methods for Scientists and Engineers¶
Bender, C. M., & Orszag, S. A. (1978). Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.
Cited by¶
2 citations across 2 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Asymptotic Behavior
- In physical modelling it drops transient modes that decay faster than the slowest.
This sourceDevelops asymptotic expansions, dominant balance, and the regime-validity range — leading-order plus successively smaller corrections, and retaining the slowest-decaying mode.
Supported in partVerified against the publisher's abstract
Canonical asymptotics textbook; its abstract confirms coverage of asymptotics and perturbation series, backing the order-hierarchy frame, but states nothing about successive smaller-order corrections.
“This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations.”
- In physical modelling it drops transient modes that decay faster than the slowest.
- Perturbation Theory
- Perturbation Theory is the technical framework in which (1) an intractable problem with Hamiltonian, Lagrangian, or operator H is decomposed as H = H₀ + λV where H₀ is exactly solvable and V is the perturbation with a small dimensionless coupling λ, (2) quantities of interest (eigenvalues, eigenstates, cross-sections, correlation functions) are expanded as power series in λ: E_n = E_n^(0) + λE_n^(1) + λ²E_n^(2) + ..., with explicit formulas
This sourceComprehensive pedagogical treatment of perturbation theory, asymptotic methods, and matched asymptotic expansions; standard reference for boundary-layer problems and singular perturbation.
Supported in partVerified against the publisher's abstract
Abstract confirms the book covers perturbation theory and perturbation series, but not the Hamiltonian decomposition or eigenstate expansions in the claim.
“This book gives a self-contained presentation of the methods of asymptotics and perturbation theory, methods useful for obtaining approximate analytical solutions to differential and difference equations.”
- Perturbation Theory is the technical framework in which (1) an intractable problem with Hamiltonian, Lagrangian, or operator H is decomposed as H = H₀ + λV where H₀ is exactly solvable and V is the perturbation with a small dimensionless coupling λ, (2) quantities of interest (eigenvalues, eigenstates, cross-sections, correlation functions) are expanded as power series in λ: E_n = E_n^(0) + λE_n^(1) + λ²E_n^(2) + ..., with explicit formulas
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 2 of 2 citations: 2 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:3ab4e4f994ed · see in the full table