Lectures on Partial Differential Equations
E1046818
"Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lectures on Partial Differential Equations canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T13561578 — 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: Lectures on Partial Differential Equations Context triple: [Vladimir Arnold, notableWork, Lectures on Partial Differential Equations]
-
A.
"Partial Differential Equations"
"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.
-
B.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
C.
Agmon–Douglis–Nirenberg estimates
Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.
-
D.
Lectures on Fourier Integrals
Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
-
E.
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.
- 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: Lectures on Partial Differential Equations Target entity description: "Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
-
A.
"Partial Differential Equations"
"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.
-
B.
Lectures on Cauchy’s problem in linear partial differential equations
"Lectures on Cauchy’s Problem in Linear Partial Differential Equations" is a classic mathematical treatise by Jacques Hadamard that systematically develops the theory of existence, uniqueness, and well-posedness for solutions to linear partial differential equations.
-
C.
Agmon–Douglis–Nirenberg estimates
Agmon–Douglis–Nirenberg estimates are fundamental a priori estimates in the theory of linear elliptic partial differential equations and systems, providing precise control of solution regularity in terms of data norms.
-
D.
Lectures on Fourier Integrals
Lectures on Fourier Integrals is a classic mathematical monograph by Salomon Bochner that systematically develops the theory and applications of Fourier integrals and transforms.
-
E.
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.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
nonfiction book ⓘ textbook ⓘ |
| approach |
coordinate-free methods
ⓘ
geometric theory of PDEs ⓘ use of differential geometry ⓘ |
| author |
V. I. Arnold
ⓘ
linked to:
Vladimir Arnold
Vladimir Arnold ⓘ |
| emphasis |
geometric approach
ⓘ
intuitive exposition ⓘ qualitative theory of PDEs ⓘ |
| field |
mathematical analysis
ⓘ
mathematics ⓘ partial differential equations ⓘ |
| hasReputation |
concise
ⓘ
geometrically oriented ⓘ influential ⓘ |
| hasTranslation | English edition of Lectures on Partial Differential Equations ⓘ |
| influencedBy |
classical theory of partial differential equations
ⓘ
geometric methods in analysis ⓘ |
| influentialFor |
advanced undergraduate PDE courses
ⓘ
geometric approaches to PDEs ⓘ graduate PDE courses ⓘ |
| language |
English
ⓘ
Russian ⓘ |
| originalLanguage | Russian ⓘ |
| pedagogicalStyle |
concise
ⓘ
example-driven ⓘ intuitive ⓘ |
| relatedWork |
Mathematical Methods of Classical Mechanics
ⓘ
Ordinary Differential Equations by Vladimir Arnold ⓘ
linked to:
Ordinary Differential Equations
|
| targetAudience |
advanced undergraduates in mathematics
ⓘ
graduate students in mathematics ⓘ researchers interested in geometric methods in PDEs ⓘ |
| topic |
Cauchy problem
ⓘ
Hamilton–Jacobi equations ⓘ Laplace equation ⓘ characteristics ⓘ classification of partial differential equations ⓘ elliptic equations ⓘ first-order partial differential equations ⓘ heat equation ⓘ hyperbolic equations ⓘ parabolic equations ⓘ second-order partial differential equations ⓘ wave equation ⓘ |
| usedAs |
course reference
ⓘ
university textbook ⓘ |
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: Lectures on Partial Differential Equations Description of subject: "Lectures on Partial Differential Equations" is a concise, influential textbook by Vladimir Arnold that presents the theory of partial differential equations with a strong geometric and intuitive emphasis.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.