Differentiable function of several variables
Summary
A function of several variables is differentiable at a point when, near that point, it is close to a linear function plus a constant. The error is small compared with the distance to the point. The linear function is the total derivative of the function at the point.
Reading path
To understand this page from the ground up, read these 5 pages in order. The foundations come first.
Show the path as a graph
- no evidence level
- Euclidean space object
- Function concept
- Total derivative concept
- Function of several variables concept
- Differentiable function of several variables concept
Where this leads
233 pages build on this one.
- Tangent plane to a graph
- Mean value theorem in several variables
- Lagrange multiplier with one constraint
- Poincaré lemma for one-forms on convex sets
- Chain rule for a composition with a curve
- Gradient
- Stokes' theorem
- Path independence of line integrals
- Harmonic function
- Laplacian
- Curl-free field that is not conservative
- Del operator
- Scalar potential
- Generalised Stokes theorem
- Vector calculus identities
- Saddle point
- Diffeomorphism
- Conservative vector field
- Gradient theorem
- Partial derivatives do not imply differentiability
- Gradient is orthogonal to level sets
- Linear approximation
- Homotopy invariance of line integrals of closed forms
- Liouville's equation
- Conformal invariance of harmonic functions
- Shell theorem
- Green's function for the Laplacian
- Phragmén–Lindelöf principle for subharmonic functions
- Harmonic functions on Riemannian manifolds
- Weyl's law
- Pluriharmonic function
- Quaternionic analysis
- Cheng–Yau gradient estimate
- Removable singularities for harmonic functions
- Minimum principle for harmonic functions
- Minimal surface equation
- Hamiltonian Monte Carlo
- Superharmonic function
- Schrödinger equation
- Hamilton–Jacobi equation
- Zaremba's punctured ball
- Harmonic at a point
- Newtonian potential
- h-cobordism theorem
- Nonlinear Schrödinger equation
- Takens's theorem
- Stokes flow
- Krylov–Safonov estimate
- Neumann problem
- Schwarz integral formula
- Yamabe problem
- Harmonic majorant
- Circle map
- Harnack inequality for parabolic equations
- Ehresmann's fibration theorem
- Reaction–diffusion system
- Sphere theorem
- KdV equation as an integrable system
- Log-modulus of a holomorphic function is subharmonic
- Moser's trick
- Single layer potential
- Gradient flow on a manifold
- Mutual absolute continuity of harmonic measures
- Lusin area integral
- Dirichlet problem
- Positive harmonic function
- Isometry of Riemannian manifolds
- Weyl's lemma
- Ginzburg–Landau equation
- Cahn–Hilliard equation
- Harmonic function on a ball
- Brelot space
- Maximum principle for subharmonic functions
- Fundamental solution of the Laplacian
- Herglotz representation theorem
- Euler equations
- Poisson–Jensen formula
- Subharmonic function
- Poisson's equation
- Collar neighbourhood theorem
- Newtonian kernel
- Porous medium equation
- Ebin's slice theorem
- Smoothness and analyticity of harmonic functions
- Spectral geometry
- Gaussian free field
- Soul theorem
- Sub-mean value property
- Riesz decomposition theorem
- Kakutani's solution of the Dirichlet problem
- Clifford analysis
- Keller–Segel model
- Boundary integral equation for the Neumann problem
- Numerical continuation
- Converse of the mean value property
- Gross–Pitaevskii equation
- Local existence of harmonic conjugates
- Brenier's theorem
- Feedback linearization
- Polyharmonic spline
- Boundary integral method for the Dirichlet problem
- Earnshaw's theorem
- Five-point stencil
- p-Laplacian
- Logarithmic kernel
- Spherical harmonics
- Dirichlet-to-Neumann operator
- Plateau's problem
- Darcy's law
- s-cobordism theorem
- Convex functions of subharmonic functions
- Injectivity radius
- Finite determinacy theorem
- Harmonic measure
- Superharmonic potential
- Resolutivity of boundary functions
- Lamé equations of elasticity
- Pólya's conjecture on Laplacian eigenvalues
- Minimal harmonic function
- Riesz measure of a subharmonic function
- Normal coordinates
- Martin kernel
- Klein–Gordon equation
- Calderón projector
- Action-angle coordinates
- Tubular neighborhood theorem
- Fractional Laplacian
- Morin singularities
- Obstacle problem
- Geometric optics
- Energy method
- Schiffer's conjecture
- Double layer potential
- Jump relations for layer potentials
- Discrete harmonic function
- Stefan problem as a variational inequality
- Stable map
- Zimmer's conjecture
- Open embedding theorem for Hilbert manifolds
- Fischer decomposition
- Navier–Stokes equations
- Douglas–Radó solution of Plateau's problem
- Koebe's theorem on the mean value property
- Area-minimizing current
- Turing pattern
- Level-set method
- Bessel potential
- Perron method
- Compactness of families of harmonic functions
- Polyharmonic function
- Boltzmann equation
- Gradient estimates for harmonic functions
- Shadowing lemma
- Fefferman's theorem on extension of biholomorphisms
- p-harmonic function
- Kelvin transform
- Harnack's principle
- Smooth four-dimensional Poincaré conjecture
- Poisson integral formula
- Displacement convexity
- Noether's second theorem
- Littlewood subordination theorem
- Biharmonic equation
- Dahlberg's theorem on harmonic measure
- Boundary Harnack principle
- Denjoy theorem on rotation number
- Green's identities
- Least harmonic majorant
- Liouville's theorem for harmonic functions
- Symplectomorphism
- Removable sets for bounded harmonic functions
- Transport equation
- Calderón problem
- Dirichlet's principle
- Harmonic functions on Riemann surfaces
- Calderón–Zygmund estimates
- Mean-field game
- Hardy spaces of harmonic functions
- Wave equation
- Herglotz–Riesz kernel
- Martin boundary
- Laplace's equation
- Whitney's theorem on folds and cusps
- Caloric function
- Liouville's theorem for planar harmonic functions
- Gauss's law for potentials
- Zimmer program
- Green's function of the ball
- Maximum principle for harmonic functions
- Steklov eigenvalue problem
- Differential game
- Hadamard three-circle theorem for subharmonic functions
- Lindelöf's maximum principle
- Condenser capacity
- Pesin theory
- Heat equation
- Slice theorem
- Lie pseudogroup
- Helmholtz equation
- Poisson kernel
- Schrödinger operator
- Sinai–Ruelle–Bowen measure
- Differential dynamic programming
- Harmonic measure as exit distribution
- Bateman transform
- Envelope theorem
- Diffeomorphism group
- Method of steepest descent
- Parabolic and hyperbolic Riemann surfaces
- Poisson integral for the half-space
- Hearing the shape of a drum
- Eikonal equation
- Adjoint state method
- Logarithmic potential
- Harmonic space
- Harmonic polynomial
- Hadamard's two-constants theorem
- Noether's theorem
- Schwarz reflection principle for harmonic functions
- Method of fundamental solutions
- Conformal geometry
- Bôcher's theorem
- Vlasov equation
- Dirichlet eigenvalue
- Harnack's inequality
- Free boundary problem
- Expansion in spherical harmonics
- Monogenic function
- Allen–Cahn equation
- Hartogs lemma for subharmonic functions
- Dirac operator
- Boundary integral equation for the Dirichlet problem
- Lane–Emden equation
Further reading
- Web https://en.wikipedia.org/wiki/Differentiable_function, Differentiability in higher dimensions
About this page
| Tag | 0HHHDCXZV4 |
|---|---|
| URI | m2://0HHHDCXZV4 |
| Aliases | differentiable-map, totally-differentiable-function |
| Kind | concept |
| Writing | W0 stub |
| MSC | 26B05 |
| Specializes | Differentiable function |
| Uses | Total derivative, Function of several variables |
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