Ordinary differential equations | Functional analysis | Asymptotic analysis | Perturbation theory

Perturbation theory

In mathematics and applied mathematics, perturbation theory comprises methods for finding an approximate solution to a problem, by starting from the exact solution of a related, simpler problem. A critical feature of the technique is a middle step that breaks the problem into "solvable" and "perturbative" parts. In perturbation theory, the solution is expressed as a power series in a small parameter . The first term is the known solution to the solvable problem. Successive terms in the series at higher powers of usually become smaller. An approximate 'perturbation solution' is obtained by truncating the series, usually by keeping only the first two terms, the solution to the known problem and the 'first order' perturbation correction. Perturbation theory is used in a wide range of fields, and reaches its most sophisticated and advanced forms in quantum field theory. Perturbation theory (quantum mechanics) describes the use of this method in quantum mechanics. The field in general remains actively and heavily researched across multiple disciplines. (Wikipedia).

Video thumbnail

Applying the rules of exponents to simplify an expression with numbers

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

How Does the Rules of Exponents Allows to Multiply and Divide by Monomials

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

What is the product of powers of exponents

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Teaching the power of product rule without talking

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

What are the rules of exponents and the most common mistakes with the rules

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

What is an exponent - Teacher explains all

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Semi-Classics, Adiabatic Continuity and Resurgence in Quantum Theories (Lecture 1) by Mithat Unsal

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

Video thumbnail

Learn how to apply the quotient rule of exponents with numbers

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Introduction to Resurgence, Trans-series and Non-perturbative Physics II by Gerald Dunne

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography

Video thumbnail

33. Electronic Spectroscopy: Franck-Condon

MIT 5.61 Physical Chemistry, Fall 2017 Instructor: Professor Robert Field View the complete course: https://ocw.mit.edu/5-61F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg This lecture covers intermolecular interactions, electronic spectrosco

From playlist MIT 5.61 Physical Chemistry, Fall 2017

Video thumbnail

Semi-Classics, Adiabatic Continuity and Resuregence in Quantum Theories (Lecture 2) by Mithat Unsal

PROGRAM NONPERTURBATIVE AND NUMERICAL APPROACHES TO QUANTUM GRAVITY, STRING THEORY AND HOLOGRAPHY (HYBRID) ORGANIZERS: David Berenstein (University of California, Santa Barbara, USA), Simon Catterall (Syracuse University, USA), Masanori Hanada (University of Surrey, UK), Anosh Joseph (II

From playlist NUMSTRING 2022

Video thumbnail

What is the quotient of powers of exponents

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Gérald DUNNE - Resurgent Trans-series Analysis of Hopf Algebraic Renormalization

In the Kreimer-Connes Hopf algebraic approach to renormalization, for certain QFTs the Dyson-Schwinger equations can be reduced to nonlinear differential equations. I describe methods based on Ecalle's theory of resurgent trans-series to extract non-perturbative information from these Dyso

From playlist Algebraic Structures in Perturbative Quantum Field Theory: a conference in honour of Dirk Kreimer's 60th birthday

Video thumbnail

Quantum Geometry and Resurgent Perturbative/Non-perturbative Relations by Gerald Dunne

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography

Video thumbnail

Feynman Diagrams and Perturbation Theory: Calculating in Particle Physics

In this video, we talk about how physicists perform calculations in particle physics using perturbation theory and Feynman diagrams. We discuss what perturbation theory is, how it relates to Feynman diagrams, how to read Feynman diagrams and how one actually gets a mathematical result out

From playlist Standard Model

Video thumbnail

Gerald Dunne: Quantum geometry and resurgent perturbative/nonperturbative relations

Abstract: Certain quantum spectral problems have the remarkable property that the formal perturbative series for the energy spectrum can be used to generate all other terms in the entire trans-series, in a completely constructive manner. I explain a geometric all-orders WKB approach to the

From playlist Mathematical Physics

Video thumbnail

What is the Power to Product Rule of Exponents

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Video thumbnail

Resurgence and Transseries in String Theory by Ricardo Schiappa

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to

From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography

Video thumbnail

Why Does the Power Rule of Exponents Work

👉 Learn about the rules of exponents. An exponent is a number which a number is raised to, to produce a power. It is the number of times which a number will multiply itself in a power. There are several rules used in evaluating exponents. Some of the rules includes: the product rule, which

From playlist Simplify Using the Rules of Exponents

Related pages

Structural stability | Differential equation | Lyapunov stability | Average | Formal power series | Order of approximation | Dynamical system | Singular perturbation | Boundary layer | Normal mode | Applied mathematics | Deformation (mathematics) | Big O notation | Linear equation | Hydrogen atom | Hamiltonian (quantum mechanics) | Siméon Denis Poisson | Two-body problem | Fermi's golden rule | Three-body problem | Mathematics | Møller–Plesset perturbation theory | Chaos theory | Power series | Henri Poincaré | Energy | Wave equation | Perturbation theory (quantum mechanics) | Harmonic oscillator | Algebraic equation | Approximation theory | Method of dominant balance | Richard Feynman | Isaac Newton | Coupled cluster