Interval
Summary
An interval is a set of real numbers that contains each real number between two of its elements. Examples are , , and itself.
Where this leads
190 pages build on this one.
- Picard–Lindelöf theorem in integral form
- Non-uniqueness for a non-Lipschitz equation
- Exponential growth and decay
- Picard operator
- Lotka–Volterra equations
- Integral equation form of an initial value problem
- Maximal solution
- Periodic orbit
- Integrating factor
- Uniqueness of solutions for Lipschitz vector fields
- Flow of a vector field
- Newton's law of cooling
- Reduction of order
- C^1 vector fields satisfy the Picard–Lindelöf hypotheses
- Lyapunov function
- Solution of an ordinary differential equation
- Phase plane
- Asymptotic stability
- LaSalle's invariance principle
- Solution formula for linear first-order equations
- Initial value problem
- Autonomous system
- Grönwall's inequality
- Phase line
- Power series solution
- An iterate of the Picard operator is a contraction
- Eigenvalue method for linear systems
- Lyapunov stability
- Peano existence theorem
- Liouville's formula
- Linearisation at an equilibrium
- Linear equation with constant coefficients
- System of linear differential equations
- Solutions for complex conjugate roots
- Global existence for globally Lipschitz vector fields
- Trajectory
- Hamiltonian system
- Hyperbolic equilibrium point
- Logistic equation
- Integrating factor for a non-exact equation
- Singular solution
- Riccati equation
- Blow-up in finite time
- Exact equation
- Limit cycle
- Homogeneous linear equation
- Poincaré–Bendixson theorem
- Superposition principle
- Grönwall bound
- Continuous dependence on initial data
- Equilibrium point
- General solution of an inhomogeneous linear equation
- Solution space of a homogeneous linear equation has dimension n
- Fundamental system of solutions
- Solutions for distinct real roots
- Solutions for repeated roots
- Lyapunov's stability theorem
- Picard–Lindelöf hypotheses
- Euler method
- Underdamped
- Estimate for approximate solutions
- Solving initial value problems with the Laplace transform
- Homogeneous first-order equation
- Wronskian test for linear independence of solutions
- Fundamental matrix
- Test for exactness
- Classification of equilibria of planar linear systems
- Discrete Grönwall inequality
- Picard–Lindelöf theorem
- Linear differential equation of order n
- Characteristic equation
- Picard iteration
- Slope field
- Damped harmonic oscillator
- Variation of constants formula for linear systems
- Hartman–Grobman theorem
- Pendulum equation
- Stability of linear systems via eigenvalues
- General solution and particular solution
- First integral
- Phase portrait
- Clairaut's equation
- Reduction of a higher-order equation to a first-order system
- Separable equation
- Abel's identity
- Homogeneous linear system with constant coefficients
- Time translation of solutions of an autonomous system
- Cauchy–Euler equation
- Nullcline
- Forced oscillation and resonance
- Method of undetermined coefficients
- Variation of parameters
- Matrix exponential as the solution of a linear system
- Harmonic oscillator
- Linear first-order equation
- Bernoulli equation
- Liénard's theorem
- Hopf bifurcation
- Transcritical bifurcation
- O-minimal theory
- Osgood uniqueness criterion
- Darboux's theorem on additive functions bounded on an interval
- Interval order
- von Neumann stability analysis
- Feigenbaum–Cvitanović functional equation
- Milnor–Thurston kneading theory
- Convergence of the Neumann series for Volterra kernels
- Bendixson–Dulac theorem
- Carathéodory's existence theorem
- Center manifold theorem
- Limit set
- Quasi-arithmetic mean
- Spectral decomposition theorem
- Frobenius method
- Method of lines
- Comparison theorem
- Invariant set
- Reduction of an initial value problem to a Volterra equation
- Alternating-direction implicit method
- Period three implies chaos
- Bihari–LaSalle inequality
- Kolmogorov–Nagumo characterization of quasi-arithmetic means
- Crisis
- Linear multistep method
- Stiff equation
- Melnikov method
- Euler's elastica
- Path homotopy
- Homoclinic orbit
- Euler–Maruyama method
- Interval arithmetic
- Liénard equation
- Lax equivalence theorem
- Affine arithmetic
- Anosov flow
- Heteroclinic orbit
- Midpoint convex function
- Feigenbaum constants
- Center manifold
- Intermittency
- Reduction of a first-kind Volterra equation to the second kind
- Floquet theory
- Bogdanov–Takens bifurcation
- Absolutely monotonic function
- Bifurcation diagram
- Path lifting property
- Abel equation of the first kind
- Runge–Kutta methods
- Poincaré map
- Differentiable dependence on parameters
- Routh–Hurwitz stability criterion
- Structural stability
- Crank–Nicolson method
- Homoclinic bifurcation
- Rössler attractor
- Bernstein–Doetsch theorem
- Hyperbolic set
- Symplectic integrator
- Operator monotone function
- Löwner's theorem
- Kneser's theorem on solution sets
- Separation of variables
- Bifurcation theory
- Duhamel's principle
- Annihilator method
- Logistic map
- Mild solution
- Heun's method
- Phase space
- Axiom A
- Duffing equation
- Saddle-node bifurcation
- Magnus expansion
- Pitchfork bifurcation
- Exponential stability
- Smale's fourteenth problem
- Jakobson's theorem
- d'Alembert's equation
- Van der Pol oscillator
- Stable manifold theorem
- Unique solvability of Volterra equations of the second kind
- Lorenz system
- Anosov diffeomorphism
- Jensen inequality as a functional inequality
- Stability conjecture
- Singer's theorem
- Sharkovskii's theorem
- Sierpiński's theorem on measurable midpoint convex functions
- Hill differential equation
- Normal form
Further reading
- Web https://en.wikipedia.org/wiki/Interval_(mathematics), lead section
About this page
| Tag | 0Q1D85B8G6 |
|---|---|
| URI | m2://0Q1D85B8G6 |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26A03 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
The writing levels say how complete the text of a page is. They do not measure its truth.
What links here
Used by
- Solution of an ordinary differential equation
- Grönwall's inequality
- Linear differential equation of order n
- Separable equation
- Linear first-order equation
- O-minimal theory
- Darboux's theorem on additive functions bounded on an interval
- Interval order
- Quasi-arithmetic mean
- Period three implies chaos
- Kolmogorov–Nagumo characterization of quasi-arithmetic means
- Path homotopy
- Interval arithmetic
- Affine arithmetic
- Midpoint convex function
- Absolutely monotonic function
- Path lifting property
- Bernstein–Doetsch theorem
- Operator monotone function
- Löwner's theorem
- Jensen inequality as a functional inequality
- Sharkovskii's theorem
- Sierpiński's theorem on measurable midpoint convex functions