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In multivariable calculus, an initial value problem [a] (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain. Modeling a system in physics or other sciences frequently amounts to
The National Eligibility cum Entrance Test (Postgraduate), abbreviated as NEET (PG) is an entrance examination in India conducted by the National Board of Examinations in Medical Sciences (NBEMS) for determining eligibility of candidates for admission to postgraduate medical programmes in government or private medical colleges, such as Doctor of Medicine (MD), Master of Surgery (MS), PG ...
Boundary value problems are similar to initial value problems.A boundary value problem has conditions specified at the extremes ("boundaries") of the independent variable in the equation whereas an initial value problem has all of the conditions specified at the same value of the independent variable (and that value is at the lower boundary of the domain, thus the term "initial" value).
Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
A standard proof relies on transforming the differential equation into an integral equation, then applying the Banach fixed-point theorem to prove the existence of a solution, and then applying Grönwall's lemma to prove the uniqueness of the solution.
A Riemann problem, named after Bernhard Riemann, is a specific initial value problem composed of a conservation equation together with piecewise constant initial data which has a single discontinuity in the domain of interest.
Lecture Notes in Physics (LNP) is a book series published by Springer Science+Business Media in the field of physics, including articles related to both research and teaching. It was established in 1969.
The following outline is provided as an overview of, and topical guide to, applied physics: Applied physics – physics intended for a particular technological or practical use. [ 1 ] It is usually considered as a bridge or a connection between "pure" physics and engineering .