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Everything about Gradient theorem
Evaluates a line integral through a gradient field using the original scalar field
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a gradient field can be evaluated by evaluating the original scalar field at the endpoints of the curve. The theorem is a generalization of the second fundamental theorem of calculus to any curve in a plane or space rather than just the real line. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Gradient theoremA 5-minute orientation
- Skim a recent paper: On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continuaInfluential work since 2022
- Pick up a classic book: Introduction à l'analyse numérique matricielle et à l'optimisationThe most-reprinted book on the subject
- Read the landmark paper: SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDSCited 175 times
- Go sideways: Line integralA closely related topic
- Go sideways: Conservative vector fieldA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
SHARP GRADIENT ESTIMATE AND YAU'S LIOUVILLE THEOREM FOR THE HEAT EQUATION ON NONCOMPACT MANIFOLDS
A gradient bound and a liouville theorem for nonlinear poisson equations
A gradient estimate in the Calabi–Yau theorem
A novel spatial–temporal nonlocal strain gradient theorem for wave dispersion characteristics of FGM nanoplates
Theorem for the local volume average of a gradient revised
A reciprocity theorem in linear gradient elasticity and the corresponding Saint-Venant principle
A theorem on elliptic differential inequalities with an application to gradient bounds
A Liouville-Type Theorem for an Elliptic Equation with Superquadratic Growth in the Gradient
🆕 Influential since 2022
On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continua
Local central limit theorem for gradient field models
Does the conventional reciprocal theorem break down in strain gradient elasticity?
Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics
Splitting theorem of gradient $$\rho $$-Einstein solitons
📚 Books worth reading
Introduction à l'analyse numérique matricielle et à l'optimisationPhilippe G. Ciarlet · 1985
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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