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Mathematical theorem using Laplace transform
In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches
Initial_value_theorem
Type of calculus problem
calculus, an initial value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown
Initial_value_problem
Existence and uniqueness of solutions to initial value problems
equations, the Picard–Lindelöf theorem gives a set of sufficient (but not necessary) conditions under which an initial value problem has a unique solution
Picard–Lindelöf_theorem
Relation between frequency- and time-domain behavior at large time
In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain
Final_value_theorem
Theorem in probability theory
theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value
Optional_stopping_theorem
Existence and uniqueness theorem for certain partial differential equations
Cauchy initial value problems. A special case was proven by Augustin Cauchy (1842), and the full result by Sofya Kovalevskaya (1874). This theorem is about
Cauchy–Kovalevskaya_theorem
Final value theorem (mathematical analysis) Initial value theorem (integral transform) Mellin inversion theorem (complex analysis) Stahl's theorem (matrix
List_of_theorems
Theorem regarding the existence of a solution to a differential equation
guarantees the existence of solutions to certain initial value problems. Peano first published the theorem in 1886 with an incorrect proof. In 1890 he published
Peano_existence_theorem
About simultaneous modular congruences
In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then
Chinese_remainder_theorem
Theorem in economics
which they value something more once they actually have possession of it. Thus, the Coase theorem would not always work in practice because initial allocations
Coase_theorem
Topics referred to by the same term
virtualization Intermediate value theorem, a theorem in mathematical analysis Initial value theorem, a mathematical theorem using Laplace transform Integrated
IVT
Integral transform useful in probability theory, physics, and engineering
transform: Initial value theorem f ( 0 + ) = lim s → ∞ s F ( s ) . {\displaystyle f(0^{+})=\lim _{s\to \infty }{sF(s)}.} Final value theorem f ( ∞ )
Laplace_transform
Mathematical rule for inverting probabilities
Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes (/beɪz/), gives a mathematical rule for inverting conditional probabilities
Bayes'_theorem
Statement on solutions to ordinary differential equations
solution to the initial value problem. Mathematics portal Picard–Lindelöf theorem Cauchy–Kowalevski theorem Coddington & Levinson (1955), Theorem 1.2 of Chapter
Carathéodory's existence theorem
Carathéodory's_existence_theorem
Matrix decomposition
{T}}\mathbf {M} \mathbf {x} \end{aligned}}\right..} By the extreme value theorem, this continuous function attains a maximum at some u {\displaystyle
Singular_value_decomposition
Limitative results in mathematical logic
Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Thermodynamic theorem
thermodynamics, albeit under the assumption of low-entropy initial conditions. The H-theorem is a natural consequence of the kinetic equation derived by
H-theorem
Partial results found before the complete proof
descent. Fermat's Last Theorem states that no three positive integers (a, b, c) can satisfy the equation an + bn = cn for any integer value of n greater than
Proof of Fermat's Last Theorem for specific exponents
Proof_of_Fermat's_Last_Theorem_for_specific_exponents
Theorem in statistical mathematics
The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently
Fluctuation_theorem
Zeta-like functions approximate arbitrary holomorphic functions
beginning of this article, there exist values of t that satisfy inequality (1). An effective universality theorem places an upper bound on the smallest
Zeta_function_universality
Theorem in mathematics
the multiplicative inverse of the derivative of f. The theorem applies verbatim to complex-valued functions of a complex variable. It generalizes to functions
Inverse_function_theorem
17th-century conjecture proved by Andrew Wiles in 1994
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that there are no positive integers a
Fermat's_Last_Theorem
Index of articles associated with the same name
Cauchy–Kowalevski theorem is the main local existence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems
Uniqueness_theorem
Relation between sides of a right triangle
In mathematics, the Pythagorean theorem or Pythagoras's theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle
Pythagorean_theorem
Parameter in differential equations and dynamical systems
In mathematics and particularly in dynamical systems, an initial condition is the initial value (often at time t = 0 {\displaystyle t=0} ) of a differential
Initial_condition
Theorem in numerical analysis
for a well-posed linear initial value problem, the method is convergent if and only if it is stable. The importance of the theorem is that while the convergence
Lax_equivalence_theorem
Used in the summation of divergent series
In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named
Abelian and Tauberian theorems
Abelian_and_Tauberian_theorems
Complete, full information, perfectly competitive markets are Pareto efficient
else nothing). The second theorem states that any Pareto optimum can be supported as a competitive equilibrium for some initial set of endowments. The implication
Fundamental theorems of welfare economics
Fundamental_theorems_of_welfare_economics
Theorem in topology
Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f
Brouwer_fixed-point_theorem
Mathematical theorem
the existence of solutions of certain initial values problems with continuous right hand side, H. Kneser's theorem deals with the topology of the set of
Kneser's theorem (differential equations)
Kneser's_theorem_(differential_equations)
differential equations the Chaplygin Theorem states about the existence and uniqueness of the solution to an initial value problem for the first order explicit
Chaplygin's Theorem and Method for Solving ODE
Chaplygin's_Theorem_and_Method_for_Solving_ODE
Statement on the gravitational attraction of spherical bodies
shell theorem gives gravitational simplifications that can be applied to objects inside or outside a spherically symmetric body. This theorem has particular
Shell_theorem
Linear transform from the time domain to the frequency domain
_{C}X_{1}(v)X_{2}^{*}({\tfrac {1}{v^{*}}})v^{-1}\mathrm {d} v} Initial value theorem : If x [ n ] {\displaystyle x[n]} is causal, then x [ 0 ] = lim
Z-transform
Austrian economic theory of the purchasing power of money
theory of value. Mises first presented the argument in his 1912 book The Theory of Money and Credit and later restated it in Human Action. The theorem addresses
Regression_theorem
Type of problem involving ODEs or PDEs
thus the term "initial" value). A boundary value is a data value that corresponds to a minimum or maximum input, internal, or output value specified for
Boundary_value_problem
On distances between points on a circle
In mathematics, the three-gap theorem, three-distance theorem, or Steinhaus conjecture states that if one places n {\displaystyle n} points on a circle
Three-gap_theorem
Theorem in quantum mechanics
The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position
Ehrenfest_theorem
Theorem in electrical circuit analysis
organization. Thévenin's theorem and its dual, Norton's theorem, are widely used to make circuit analysis simpler and to study a circuit's initial-condition and
Thévenin's_theorem
Decision rule used for minimizing the possible loss for a worst-case scenario
values are very important in the theory of repeated games. One of the central theorems in this theory, the folk theorem, relies on the minimax values
Minimax
In differential calculus, the domain-straightening theorem states that, given a vector field X {\displaystyle X} on a manifold, there exist local coordinates
Straightening theorem for vector fields
Straightening_theorem_for_vector_fields
Property of a partially ordered set
such as the intermediate value theorem, the Bolzano–Weierstrass theorem, the extreme value theorem, and the Heine–Borel theorem. It is usually taken as
Least-upper-bound_property
Root-finding algorithm
mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class
Fixed-point_iteration
Expressing a measure as an integral of another
In mathematics, the Radon–Nikodym theorem, named after Johann Radon and Otto M. Nikodym, is a result in measure theory that expresses the relationship
Radon–Nikodym_theorem
1995 publication in mathematics
Together with Ribet's theorem, it provides a proof for Fermat's Last Theorem. Both Fermat's Last Theorem and the modularity theorem were believed to be
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
On converting relations to functions of several real variables
In multivariable calculus, the implicit function theorem is a theorem that provides sufficient conditions under which a planar curve specified by F ( x
Implicit_function_theorem
Key result in Hamiltonian mechanics and statistical mechanics
In physics, Liouville's theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics
Liouville's theorem (Hamiltonian)
Liouville's_theorem_(Hamiltonian)
Mathematical theorem
probability and mathematical statistics, Ignatov's theorem is a basic result on the distribution of record values of a stochastic process. Let X1, X2, ... be
Ignatov's_theorem
Theorem in classical statistical mechanics
mechanics, the equipartition theorem relates the temperature of a system to its average energies. The equipartition theorem is also known as the law of
Equipartition_theorem
Theory of speed in physics
The theorem is a special case of the more general kinematics equations for uniform acceleration. Science in the Middle Ages Scholasticism Mean value theorem
Mean_speed_theorem
Combinatorial game theory theorem
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap
Sprague–Grundy_theorem
Theorem in quantum information science
In physics, the no-cloning theorem states that it is impossible to create an independent and identical copy of an arbitrary unknown quantum state, a statement
No-cloning_theorem
Key results in general relativity on gravitational singularities
The Penrose–Hawking singularity theorems (after Roger Penrose and Stephen Hawking) are a set of results in general relativity that attempt to answer the
Penrose–Hawking singularity theorems
Penrose–Hawking_singularity_theorems
Concept in quantum mechanics
The adiabatic theorem is a concept in quantum mechanics. Its original form, due to Max Born and Vladimir Fock (1928), was stated as follows: A physical
Adiabatic_theorem
Reformulation of general relativity
The initial value formulation of general relativity is a reformulation of Albert Einstein's theory of general relativity that describes a universe evolving
Initial value formulation (general relativity)
Initial_value_formulation_(general_relativity)
Measure of algorithmic complexity
theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's Kolmogorov complexity can return a value essentially
Kolmogorov_complexity
2.71828...; base of natural logarithms
Mathematics. Dover. pp. 44–48. A standard calculus exercise using the mean value theorem; see for example Apostol (1967) Calculus, § 6.17.41. Sloane, N. J. A
E_(mathematical_constant)
Initial estimate or framework to the solution of a mathematical problem
equation(s), the theorem(s), or the value(s) describing a mathematical or physical problem or solution. It typically provides an initial estimate or framework
Ansatz
A rigid body with 3 distinct axes of inertia is unstable rotating about the middle axis
The tennis racket theorem, or intermediate axis theorem, is a kinetic phenomenon of classical mechanics which describes the movement of a rigid body with
Tennis_racket_theorem
Property of differential equations describing physical phenomena
results on this topic. For example, the Cauchy–Kowalevski theorem for Cauchy initial value problems essentially states that if the terms in a partial
Well-posed_problem
differential equation is a solution that is singular or one for which the initial value problem (also called the Cauchy problem by some authors) fails to have
Singular_solution
Theorem in linear algebra
controlled by the eigenvalue of A with the largest absolute value (modulus). The Perron–Frobenius theorem describes the properties of the leading eigenvalue and
Perron–Frobenius_theorem
Equations of degree 5 or higher cannot be solved by radicals
In mathematics, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) states that there is no solution in radicals to general polynomial
Abel–Ruffini_theorem
Class of ordinary differential equations
continuous function we have u ( c ) = 0 {\textstyle u(c)=0} . By The Mean Value Theorem we have that for all h > 0 {\textstyle h>0} there exists some θ ∈ [
Sturm–Liouville_theory
Theorem in classical mechanics
In classical mechanics, Newton's theorem of revolving orbits identifies the type of central force needed to multiply the angular speed of a particle by
Newton's theorem of revolving orbits
Newton's_theorem_of_revolving_orbits
Upper bound on a graph's Shannon capacity
28. Lovász (1979), Theorem 3. Lovász (1979), Theorem 4. Lovász (1979), Theorem 5. Riddle (2003). Lovász (1979), Lemma 2 and Theorem 7. Lovász (1979), Corollary
Lovász_number
Construction on any polygon that yields a regular polygon with the same number of sides
yields a regular polygon having the same number of sides as the initial polygon. The theorem was first published by Karel Petr (1868–1950) of Prague in 1905
Petr–Douglas–Neumann_theorem
Generalized function whose value is zero everywhere except at zero
Sokhotski–Plemelj theorem, important in quantum mechanics, relates the delta function to the distribution p.v. 1/x, the Cauchy principal value of the function
Dirac_delta_function
Coarsest topology making certain functions continuous
completely regular if and only if it has the initial topology with respect to its family of (bounded) real-valued continuous functions. Every topological space
Initial_topology
Problem in computer science
the standard form of Gödel's First Incompleteness Theorem is completely unconcerned with the truth value of a statement, but only concerns the issue of whether
Halting_problem
Theorem on genetic algorithms
Holland's schema theorem, also called the fundamental theorem of genetic algorithms, is an inequality that results from coarse-graining an equation for
Holland's_schema_theorem
Japanese mathematician (1905–1948)
conditions on initial value problems of ordinary differential equations for the solution to be unique. He also refined the second mean value theorem of integration
Hiroshi_Okamura
Theorem in complex analysis
Mergelyan's theorem also holds for open Riemann surfaces. Let A ( K ) {\displaystyle {\mathcal {A}}(K)} be set of all continuous and complex-valued functions
Mergelyan's_theorem
Maximized objective function of an optimization problem
conditions for the differentiability of the value function, which in turn allows an application of the envelope theorem, see Benveniste, L. M.; Scheinkman, J
Value_function
Strong form of uniform continuity
condition of the Picard–Lindelöf theorem which guarantees the existence and uniqueness of the solution to an initial value problem. A special type of Lipschitz
Lipschitz_continuity
Subfield of automated reasoning and mathematical logic
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving
Automated_theorem_proving
Bound on eigenvalues
In mathematics, the Gershgorin circle theorem (also called Gershgorin Disk Theorem) may be used to bound the spectrum of a square matrix. It was first
Gershgorin_circle_theorem
Branch of ordinary differential equations
defines the state of the stability of solutions. The main theorem of Floquet theory, Floquet's theorem, due to Gaston Floquet (1883), gives a canonical form
Floquet_theory
second theorem of DFT states that the energy functional for the Hamiltonian [i.e., the energy content of the Hamiltonian] reaches its minimum value (i.e
Rayleigh theorem for eigenvalues
Rayleigh_theorem_for_eigenvalues
Fundamental result in the branch of mathematics known as character theory
Brauer's theorem on induced characters, often known as Brauer's induction theorem, and named after Richard Brauer, is a basic result in the branch of mathematics
Brauer's theorem on induced characters
Brauer's_theorem_on_induced_characters
Algorithm for finding zeros of functions
zeroes) of a real-valued function. The most basic version starts with a real-valued function f, its derivative f′, and an initial guess x0 for a root
Newton's_method
Theorem on extension of bounded linear functionals
In functional analysis, the Hahn–Banach theorem is a central result that allows the extension of bounded linear functionals defined on a vector subspace
Hahn–Banach_theorem
Concept in probability theory and gambling
This is a corollary of a general theorem by Christiaan Huygens, which is also known as gambler's ruin. That theorem shows how to compute the probability
Gambler's_ruin
Approach to finding numerical solutions of ordinary differential equations
procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary
Euler_method
Statistical theorem
then evaluate that conditional expected value to get an estimator that is in various senses optimal. The theorem is named after C.R. Rao and David Blackwell
Rao–Blackwell_theorem
Solution of some Diophantine equation
the integers is a notoriously hard open problem. The MRDP theorem (so named for the initials of the four principal contributors to its solution) states
Diophantine_set
Concept in statistics
uniformly distributed random phase. Where applicable, the central limit theorem dictates that at any point, the sum of these individual plane-wave contributions
Gaussian_random_field
Theorem in mathematical logic
compactness theorem states that a set of first-order sentences has a model if and only if every finite subset of it has a model. This theorem is an important
Compactness_theorem
Problem of constructing equal-area shapes
area; this principle can be seen as a form of the modern intermediate value theorem. The more general goal of carrying out all geometric constructions using
Squaring_the_circle
Hypothetical self-improving program
theorem into proof, thus trivializing proof verification. Appends the n-th axiom as a theorem to the current theorem sequence. Below is the initial axiom
Gödel_machine
Theorem in statistics and econometrics
the theorem is sometimes called the regression anatomy theorem. An initial version of the theorem was introduced by Udny Yule in 1907, though it was not
Frisch–Waugh–Lovell_theorem
Stochastic process modeling random walk with friction
equation with initial condition P ( x , t 0 ) = δ ( x − x 0 ) {\displaystyle P(x,t_{0})=\delta (x-x_{0})} . Conditioned on a particular value of x 0 {\displaystyle
Ornstein–Uhlenbeck_process
Providing boundary conditions for Maxwell's equations uniquely fixes a solution
satisfy the following requirements: At t = 0 {\displaystyle t=0} , the initial values of all fields (E, H, B and D) everywhere (in the entire volume considered)
Electromagnetism uniqueness theorem
Electromagnetism_uniqueness_theorem
functional theory, the Runge–Gross theorem (RG theorem) shows that for a many-body system evolving from a given initial wavefunction, there exists a one-to-one
Runge–Gross_theorem
Statistical measures of whether a finding is likely to be true
PPV and NPV can be derived using Bayes' theorem. Although sometimes used synonymously, a positive predictive value generally refers to what is established
Positive and negative predictive values
Positive_and_negative_predictive_values
Physics theorem for symmetries of action
physics, Noether's second theorem relates symmetries of an action functional with a system of differential equations. The theorem is named after its discoverer
Noether's_second_theorem
Equation in statistical mechanics
experiments with biomolecules to numerical simulations. The Crooks fluctuation theorem, proved two years later, leads immediately to the Jarzynski equality. Many
Jarzynski_equality
Theorem in relativistic quantum mechanics
positive-operator valued measures that are compatible with the restrictions imposed by the Hegerfeldt theorem. Specifically, Hegerfeldt's theorem refers to a
Hegerfeldt's_theorem
Methods of calculating definite integrals
be reduced to an initial value problem for an ordinary differential equation by applying the first part of the fundamental theorem of calculus. By differentiating
Numerical_integration
Power series with rational exponents
all possible initial terms of Puiseux series that are solutions of P ( y ) = 0. {\displaystyle P(y)=0.} The proof of Newton–Puiseux theorem will consist
Puiseux_series
Mathematical result in differential geometry
In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential
Atiyah–Singer_index_theorem
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM
INITIAL VALUE-THEOREM