Applied Functional Analysis
E483187
Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Applied Functional Analysis canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T4966482 — 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: Applied Functional Analysis Context triple: [J. Tinsley Oden, notableWork, Applied Functional Analysis]
-
A.
"Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
-
B.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
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C.
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.
-
D.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
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E.
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.
- 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: Applied Functional Analysis Target entity description: Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
-
A.
"Functional Analysis"
Functional Analysis is a branch of mathematical analysis that studies vector spaces with additional structure (such as norms and inner products) and the linear operators acting on them, with deep applications across pure and applied mathematics.
-
B.
Sobolev spaces
Sobolev spaces are function spaces that incorporate both functions and their weak derivatives, providing a fundamental framework for studying partial differential equations and variational problems.
-
C.
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.
-
D.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
E.
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.
- F. None of above. chosen
Statements (36)
| Predicate | Object |
|---|---|
| instanceOf |
functional analysis textbook
ⓘ
mathematics book ⓘ textbook ⓘ |
| author | J. Tinsley Oden ⓘ |
| covers |
Banach spaces
ⓘ
Hilbert spaces ⓘ Sobolev spaces ⓘ eigenvalue problems ⓘ linear operators ⓘ operator equations ⓘ spectral theory ⓘ variational methods ⓘ weak formulations of boundary value problems ⓘ |
| emphasizes |
connection between abstract theory and applications
ⓘ
rigorous mathematical foundations for engineering models ⓘ |
| field |
applied mathematics
ⓘ
differential equations ⓘ engineering mathematics ⓘ functional analysis ⓘ |
| focusesOn |
applications to differential equations
ⓘ
applications to engineering problems ⓘ |
| hasAudience |
engineers
ⓘ
graduate students ⓘ researchers in applied mathematics ⓘ |
| isKnownFor |
application-oriented presentation of functional analysis
ⓘ
integration of theory and engineering examples ⓘ |
| language | English ⓘ |
| provides |
functional analytic tools for modeling physical systems
ⓘ
theoretical background for numerical methods ⓘ |
| relatedTo |
continuum mechanics
ⓘ
finite element methods ⓘ numerical analysis ⓘ partial differential equations ⓘ |
| usedIn |
graduate courses in applied mathematics
ⓘ
graduate courses in engineering ⓘ graduate courses in functional analysis ⓘ |
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: Applied Functional Analysis Description of subject: Applied Functional Analysis is a foundational textbook by J. Tinsley Oden that introduces and develops the tools of functional analysis with a strong emphasis on applications to differential equations and engineering problems.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.