Bibliographic record
Abstract
This is a textbook for an introductory course on linear partial differential equations (PDEs) and initial/boundary value problems (I/BVPs). It also provides a mathematically rigorous introduction to Fourier analysis (Chapters 7, 8, 9, 10, and 19), which is the main tool used to solve linear PDEs in Cartesian coordinates. Finally, it introduces basic functional analysis (Chapter 6) and complex analysis (Chapter 18). The first is necessary to characterize rigorously the convergence of Fourier series, and also to discuss eigenfunctions for linear differential operators. The second provides powerful techniques to transform domains and compute integrals, and also offers additional insight into Fourier series. This book is not intended to be comprehensive or encyclopaedic. It is designed for a one-semester course (i.e. 36–40 hours of lectures), and it is therefore strictly limited in scope. First, it deals mainly with linear PDEs with constant coefficients. Thus, there is no discussion of characteristics, conservation laws, shocks, variational techniques, or perturbation methods, which would be germane to other types of PDEs. Second, the book focuses mainly on concrete solution methods to specific PDEs (e.g. the Laplace, Poisson, heat, wave, and Schrödinger equations) on specific domains (e.g. line segments, boxes, disks, annuli, spheres), and spends rather little time on qualitative results about entire classes of PDEs (e.g. elliptic, parabolic, hyperbolic) on general domains.
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.470 | 0.317 |
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".