A boundary term is an endpoint or boundary integral left when derivatives are transferred by integration by parts. It vanishes under some boundary conditions and otherwise supplies natural boundary conditions, conserved charges, or physical surface forces.
Ancestors (6)
Incoming links (510)
- Absolute Fourier convergence from a square-integrable derivative
- Adjoint eigenfunction
- Amplitude of an oscillatory integral
- Balanced shallow-water energy as a signed potential-vorticity pairing
- Boundary expression for transverse filament thrust
- Boundary term
- Boundary-term shift of canonical field momenta
- Complete boundary-jet condition for formal adjoints
- Conserved first moment of a draining porous current
- Contour-shift proof of the Paley–Wiener–Schwartz theorem
- Cowling energy principle for a rotating barotropic star
- Derivative-antighost gauge-fixing fermion
- Derivative expansion of a four-point vertex
- Diffeomorphism Noether identity for a scalar field
- Direct spherical-shell H2 estimate
- Dirichlet boundary-forcing heat-kernel formula
- Discrete integration by parts
- Discrete L2 inner product
- Distributional derivative of the logarithmic modulus
- Distributional divergence
- Divergence-forcing interior H1 estimate
- Divergence form
- Divergence of a Riemannian vector field
- Energy conservation for semidiscrete Galerkin advection
- Energy dissipation identity for Model H
- Energy square completion for long-wave convection
- Entropy dissipation identity for Ornstein-Uhlenbeck flow
- Fluctuation-dissipation relation for a conserved flux
- Folded sine approximation to a Dirac delta
- Formal adjoint
- Formal transpose of a differential operator
- Fourier decay from a derivative jump
- Fourier decay in a bounded complex strip
- Fourier derivative identities for distributions
- Full-film eccentric journal-bearing rotation
- Ghost vertex in scalar-dependent gauge fixing
- Graph estimate for the harmonic oscillator
- Ground-state transform for a weighted Dirichlet energy
- Growth-rate solvability for conducting-square Darcy convection
- Heat equation energy identity
- High-frequency reciprocal parametrix kernel
- Holomorphic derivative of a quadrant Dirichlet solution
- Joint path probability of an order parameter and its flux
- KdV mass and energy conservation
- Location score
- Logarithmic expansion of a symmetric exponential integral
- Neumann boundary-forcing formula
- Nonstationary oscillatory integral
- Novikov's theorem
- Operator basis in effective field theory
- Ornstein-Uhlenbeck moment equations
- Orthogonality of Sturm-Liouville eigenfunctions
- Overdamped relaxation of a clamped--free filament
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- Photon angular temperature moments
- Photon energy density
- Pohozaev identity
- Power-transformed Taylor–Goldstein energy identity
- Quadratic density derivative functional
- Radial quadratic oscillation defect in two dimensions
- Reversible stress of a polar liquid crystal
- Scalar variance
- Schwartz seminorm
- Schwarz integral formula
- Scorer Hi function
- Self-adjoint endpoint conditions for filament bending
- Skew-symmetry of incompressible transport
- Stationary-direction bound for singular support
- Stationary phase endpoint cancellation in a half-strip contour
- Stieltjes bilinear functional under a variation constraint
- Strict monotonicity of Fermi gas entropy per particle
- Uniform half-line Schrodinger representation by boundary lifting
- Uniqueness of Sobolev weak solutions of a wave equation
- Van der Corput sum-integral lemma
- Vanishing boundary condition
- Vanishing harmonic function by level-set integration
- Wave energy estimate
- Wave map energy
- Weak convergence of bounded-variation integrators
- Weak formulation
- Weak-star convergence in BV
- Weighted identity for Howard's semicircle theorem
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Integration by parts is a technique used in calculus to integrate the product of two functions. It's based on the product rule for differentiation and is particularly useful when dealing with integrals of the form \( \int u \, dv \), where \( u \) and \( dv \) are functions that we can choose strategically to simplify the integration process.