Bibliographic record
Abstract
Chapter 8 starts out with a physics motivation, as well as a mathematical statement of the problems that will be tackled in later sections. Starting from differential-equation initial-value problems, the text introduces both explicit and implicit methods, like backward Euler and the fourth-order Runge-Kutta method. Emphasis is placed on the interplay between method stability and problem conditioning (stiffness). The chapter then discusses boundary-value problems, first, via a combination of the earlier machinery on initial-value problems along with root-finding techniques and, second, via a finite-difference/matrix approach, which converts the problem to a linear system of equations. Next, the chapter tackles eigenvalue problems, again, via either rootfinding plus earlier tools, or a finite-difference approach; this time, the latter turns into a matrix eigenvalue problem. The second edition discussesfinite-difference approaches to solving the diffusion equation. The chapter is rounded out by a physics project, on Poisson’s equation in two dimensions, and a problem set. The physics project introduces and uses the two-dimensional fast Fourier transform, as part of a spectral method applied to the solution of a partial differential equation.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.050 | 0.018 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".