"Partial Differential Equations"
E305926
"Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
All labels observed (2)
| Label | Occurrences |
|---|---|
| "Partial Differential Equations" canonical | 1 |
| Partial Differential Equations of Parabolic Type | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2866510 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: "Partial Differential Equations" Context triple: [Princeton Mathematical Series, workIncluded, "Partial Differential Equations"]
-
A.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
B.
Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
-
C.
Generalized Functions (multi-volume series)
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
-
D.
"Invariante Variationsprobleme"
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: "Partial Differential Equations" Target entity description: "Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
-
A.
Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
-
B.
Asymptotic Methods in Analysis
Asymptotic Methods in Analysis is a classic mathematical monograph by N. G. de Bruijn that systematically develops techniques for approximating functions and integrals in limiting regimes, widely used in analysis and number theory.
-
C.
Generalized Functions (multi-volume series)
Generalized Functions (multi-volume series) is a foundational multi-volume work in functional analysis and distribution theory that systematically develops the theory of generalized functions and its applications to differential equations and mathematical physics.
-
D.
"Invariante Variationsprobleme"
"Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
-
E.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
- F. None of above. chosen
Statements (39)
| Predicate | Object |
|---|---|
| instanceOf |
foundational text
ⓘ
mathematics textbook ⓘ |
| aim |
introduction to analytical techniques for PDEs
ⓘ
systematic development of PDE theory ⓘ |
| audience |
advanced undergraduates
ⓘ
graduate students ⓘ |
| covers |
Fourier series methods
ⓘ
Fourier transform methods ⓘ Green's functions ⓘ Laplace equation ⓘ Laplace transform methods ⓘ Poisson equation ⓘ Sobolev spaces ⓘ boundary value problems ⓘ classification of partial differential equations ⓘ distribution theory ⓘ eigenvalue problems ⓘ elliptic partial differential equations ⓘ energy methods ⓘ fundamental solutions ⓘ heat equation ⓘ hyperbolic partial differential equations ⓘ initial value problems ⓘ maximum principles ⓘ parabolic partial differential equations ⓘ separation of variables ⓘ variational methods ⓘ wave equation ⓘ weak solutions ⓘ |
| field | partial differential equations ⓘ |
| focus |
methods for solving partial differential equations
ⓘ
theory of partial differential equations ⓘ |
| language | English ⓘ |
| topic |
equations involving multivariable functions
ⓘ
partial derivatives ⓘ |
| usedIn |
applied mathematics
ⓘ
engineering ⓘ physics ⓘ quantitative finance ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: "Partial Differential Equations" Description of subject: "Partial Differential Equations" is a foundational mathematical text that systematically develops the theory and methods for analyzing equations involving multivariable functions and their partial derivatives.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: "Partial Differential Equations"