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157 relations: Abstract differential equation, Acta Eruditorum, Albert Einstein, Algebraic equation, American Journal of Physics, American Mathematical Society, Annalen der Physik, Antiderivative, Applied mathematics, Bernoulli differential equation, Biology, Black–Scholes model, Calculus, Cauchy–Riemann equations, Chaos theory, Chemical reaction, Chemistry, Classical electromagnetism, Classical mechanics, Closed-form expression, Complex analysis, Complex differential equation, Computer simulation, Convection–diffusion equation, Curvature, Daniel Bernoulli, Delay differential equation, Dependent and independent variables, Derivative, Differential-algebraic system of equations, Diffusion, Diffusion equation, Dynamical system, Economics, Einstein field equations, Einstein tensor, Elasticity (physics), Electric charge, Electric current, Electric field, Electrical network, Electrostatics, Energy, Engineering, Equation, Equations of motion, Eric W. Weisstein, Euler–Lagrange equation, Exact differential equation, Fluid dynamics, ..., Function (mathematics), Function of a real variable, Functional differential equation, Fundamental interaction, General relativity, Gottfried Wilhelm Leibniz, Gravitation (book), Gravity, Hamiltonian mechanics, Harmonic function, Harmonic oscillator, Heat, Heat equation, Heat transfer, Hodgkin–Huxley model, Holonomic function, Initial condition, Integral equation, International Union of Pure and Applied Chemistry, Isaac Newton, IUPAC books, Jacob Bernoulli, James Clerk Maxwell, Jean le Rond d'Alembert, Joseph Fourier, Joseph-Louis Lagrange, Lagrangian mechanics, Lamar University, Laplace's equation, Leonhard Euler, Linear differential equation, Linear equation, Linearization, Logistic function, Lorentz force, Lorenz system, Lotka–Volterra equations, Magnetic field, Malthusian growth model, Mass balance, Massachusetts Institute of Technology, Mathematical model, Mathematics, MathWorld, Matter, Maxima (software), Maxwell's equations, Mechanics, Method of Fluxions, Molecular dynamics, Momentum, Multidimensional system, Multivariable calculus, Musical instrument, Navier–Stokes equations, Navier–Stokes existence and smoothness, Newton's law of cooling, Newton's laws of motion, Nonlinear system, Nuclear physics, Numerical analysis, Numerical methods for ordinary differential equations, Optics, Ordinary differential equation, Partial derivative, Partial differential equation, PDF, Peano existence theorem, Pendulum, Physics, Picard–Lindelöf theorem, Poisson's equation, Poisson–Boltzmann equation, Population dynamics, Providence, Rhode Island, Pure mathematics, Quantum mechanics, Radioactive decay, Rate equation, Reaction rate, Recurrence relation, Replicator equation, Schrödinger equation, Second derivative, Sethi model, Shallow water equations, Solow–Swan model, Sound, Spacetime, Special functions, Springer Science+Business Media, Stochastic differential equation, Stochastic partial differential equation, Stochastic process, Stress–energy tensor, Symmetry, Tautochrone curve, Tensor, Thermodynamics, Thin-film equation, Universal differential equation, University of Illinois at Urbana–Champaign, Variable (mathematics), W. H. Freeman and Company, Wave equation, Wave function, Wiener process. Expand index (107 more) »
Abstract differential equation
In mathematics, an abstract differential equation is a differential equation in which the unknown function and its derivatives take values in some generic abstract space (a Hilbert space, a Banach space, etc.). Equations of this kind arise e.g. in the study of partial differential equations: if to one of the variables is given a privilegiate position (e.g. time, in heat or wave equations) and all the others are put together, an ordinary "differential" equation with respect to the variable which was put in evidence is obtained.
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Acta Eruditorum
Acta Eruditorum (Latin for "reports/acts of the scholars") was the first scientific journal of the German lands, published from 1682 to 1782.
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Albert Einstein
Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).
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Algebraic equation
In mathematics, an algebraic equation or polynomial equation is an equation of the form where P and Q are polynomials with coefficients in some field, often the field of the rational numbers.
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American Journal of Physics
The American Journal of Physics is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics.
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American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
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Annalen der Physik
Annalen der Physik (English: Annals of Physics) is one of the oldest scientific journals on physics and has been published since 1799.
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Antiderivative
In calculus, an antiderivative, primitive function, primitive integral or indefinite integral of a function is a differentiable function whose derivative is equal to the original function.
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Applied mathematics
Applied mathematics is the application of mathematical methods by different fields such as science, engineering, business, computer science, and industry.
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Bernoulli differential equation
In mathematics, an ordinary differential equation of the form: is called a Bernoulli differential equation where n is any real number and n \ne 0 and n \ne 1.
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Biology
Biology is the natural science that studies life and living organisms, including their physical structure, chemical composition, function, development and evolution.
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Black–Scholes model
The Black–Scholes or Black–Scholes–Merton model is a mathematical model for the dynamics of a financial market containing derivative investment instruments.
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Calculus
Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.
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Cauchy–Riemann equations
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which, together with certain continuity and differentiability criteria, form a necessary and sufficient condition for a complex function to be complex differentiable, that is, holomorphic.
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Chaos theory
Chaos theory is a branch of mathematics focusing on the behavior of dynamical systems that are highly sensitive to initial conditions.
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Chemical reaction
A chemical reaction is a process that leads to the transformation of one set of chemical substances to another.
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Chemistry
Chemistry is the scientific discipline involved with compounds composed of atoms, i.e. elements, and molecules, i.e. combinations of atoms: their composition, structure, properties, behavior and the changes they undergo during a reaction with other compounds.
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Classical electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model.
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Classical mechanics
Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars and galaxies.
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Closed-form expression
In mathematics, a closed-form expression is a mathematical expression that can be evaluated in a finite number of operations.
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Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers.
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Complex differential equation
A complex differential equation is a differential equation whose solutions are functions of a complex variable.
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Computer simulation
Computer simulation is the reproduction of the behavior of a system using a computer to simulate the outcomes of a mathematical model associated with said system.
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Convection–diffusion equation
The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection.
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Curvature
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.
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Daniel Bernoulli
Daniel Bernoulli FRS (8 February 1700 – 17 March 1782) was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family.
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Delay differential equation
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.
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Dependent and independent variables
In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.
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Derivative
The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).
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Differential-algebraic system of equations
In mathematics, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system.
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Diffusion
Diffusion is the net movement of molecules or atoms from a region of high concentration (or high chemical potential) to a region of low concentration (or low chemical potential) as a result of random motion of the molecules or atoms.
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Diffusion equation
The diffusion equation is a partial differential equation.
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Dynamical system
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in a geometrical space.
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Economics
Economics is the social science that studies the production, distribution, and consumption of goods and services.
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Einstein field equations
The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.
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Einstein tensor
In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold.
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Elasticity (physics)
In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed.
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Electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
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Electric current
An electric current is a flow of electric charge.
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Electric field
An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.
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Electrical network
An electrical network is an interconnection of electrical components (e.g. batteries, resistors, inductors, capacitors, switches) or a model of such an interconnection, consisting of electrical elements (e.g. voltage sources, current sources, resistances, inductances, capacitances).
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Electrostatics
Electrostatics is a branch of physics that studies electric charges at rest.
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Energy
In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.
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Engineering
Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.
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Equation
In mathematics, an equation is a statement of an equality containing one or more variables.
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Equations of motion
In physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time.
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Eric W. Weisstein
Eric Wolfgang Weisstein (born March 18, 1969) is an encyclopedist who created and maintains MathWorld and Eric Weisstein's World of Science (ScienceWorld).
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Euler–Lagrange equation
In the calculus of variations, the Euler–Lagrange equation, Euler's equation, or Lagrange's equation (although the latter name is ambiguous—see disambiguation page), is a second-order partial differential equation whose solutions are the functions for which a given functional is stationary.
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Exact differential equation
In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in physics and engineering.
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Fluid dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Function of a real variable
In mathematical analysis, and applications in geometry, applied mathematics, engineering, and natural sciences, a function of a real variable is a function whose domain is the real numbers, or a subset of that contains an interval of positive length.
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Functional differential equation
A functional differential equation (FDE) is a differential equation with deviating argument.
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Fundamental interaction
In physics, the fundamental interactions, also known as fundamental forces, are the interactions that do not appear to be reducible to more basic interactions.
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General relativity
General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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Gravitation (book)
Gravitation is a physics book on Einstein's theory of gravity, written by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler and originally published by W. H. Freeman and Company in 1973.
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Gravity
Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.
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Hamiltonian mechanics
Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.
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Harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f: U → R where U is an open subset of Rn that satisfies Laplace's equation, i.e. everywhere on U. This is usually written as or.
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Harmonic oscillator
In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: where k is a positive constant.
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Heat
In thermodynamics, heat is energy transferred from one system to another as a result of thermal interactions.
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Heat equation
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time.
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Heat transfer
Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems.
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Hodgkin–Huxley model
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated.
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Holonomic function
In mathematics, and more specifically in analysis, a holonomic function is a smooth function in several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory.
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Initial condition
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted t.
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Integral equation
In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
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International Union of Pure and Applied Chemistry
The International Union of Pure and Applied Chemistry (IUPAC) is an international federation of National Adhering Organizations that represents chemists in individual countries.
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Isaac Newton
Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, astronomer, theologian, author and physicist (described in his own day as a "natural philosopher") who is widely recognised as one of the most influential scientists of all time, and a key figure in the scientific revolution.
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IUPAC books
The International Union of Pure and Applied Chemistry publishes many books, which contain its complete list of definitions.
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Jacob Bernoulli
Jacob Bernoulli (also known as James or Jacques; – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
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James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish scientist in the field of mathematical physics.
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Jean le Rond d'Alembert
Jean-Baptiste le Rond d'Alembert (16 November 1717 – 29 October 1783) was a French mathematician, mechanician, physicist, philosopher, and music theorist.
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Joseph Fourier
Jean-Baptiste Joseph Fourier (21 March 1768 – 16 May 1830) was a French mathematician and physicist born in Auxerre and best known for initiating the investigation of Fourier series and their applications to problems of heat transfer and vibrations.
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Joseph-Louis Lagrange
Joseph-Louis Lagrange (or;; born Giuseppe Lodovico Lagrangia, Encyclopædia Britannica or Giuseppe Ludovico De la Grange Tournier, Turin, 25 January 1736 – Paris, 10 April 1813; also reported as Giuseppe Luigi Lagrange or Lagrangia) was an Italian Enlightenment Era mathematician and astronomer.
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Lagrangian mechanics
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788.
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Lamar University
Lamar University, often referred to as Lamar or LU, is a public coeducational doctoral/research university in Beaumont, Texas.
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Laplace's equation
In mathematics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace who first studied its properties.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Linear differential equation
In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where,..., and are arbitrary differentiable functions that do not need to be linear, and are the successive derivatives of an unknown function of the variable.
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Linear equation
In mathematics, a linear equation is an equation that may be put in the form where x_1, \ldots, x_n are the variables or unknowns, and c, a_1, \ldots, a_n are coefficients, which are often real numbers, but may be parameters, or even any expression that does not contain the unknowns.
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Linearization
In mathematics, linearization is finding the linear approximation to a function at a given point.
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Logistic function
A logistic function or logistic curve is a common "S" shape (sigmoid curve), with equation: where.
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Lorentz force
In physics (particularly in electromagnetism) the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields.
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Lorenz system
The Lorenz system is a system of ordinary differential equations first studied by Edward Lorenz.
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Lotka–Volterra equations
The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
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Magnetic field
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials.
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Malthusian growth model
A Malthusian growth model, sometimes called a simple exponential growth model, is essentially exponential growth based on a constant rate.
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Mass balance
A mass balance, also called a material balance, is an application of conservation of mass to the analysis of physical systems.
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Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private research university located in Cambridge, Massachusetts, United States.
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Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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MathWorld
MathWorld is an online mathematics reference work, created and largely written by Eric W. Weisstein.
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Matter
In the classical physics observed in everyday life, matter is any substance that has mass and takes up space by having volume.
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Maxima (software)
Maxima is a computer algebra system (CAS) based on a 1982 version of Macsyma.
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Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
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Mechanics
Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.
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Method of Fluxions
Method of Fluxions is a book by Isaac Newton.
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Molecular dynamics
Molecular dynamics (MD) is a computer simulation method for studying the physical movements of atoms and molecules.
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Momentum
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object.
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Multidimensional system
In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one dependent variable exists (like time), but there are several independent variables.
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Multivariable calculus
Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables, rather than just one.
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Musical instrument
A musical instrument is an instrument created or adapted to make musical sounds.
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Navier–Stokes equations
In physics, the Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous fluid substances.
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Navier–Stokes existence and smoothness
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, one of the pillars of fluid mechanics (such as with turbulence).
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Newton's law of cooling
Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings provided the temperature difference is small and the nature of radiating surface remains same. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant.
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Newton's laws of motion
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics.
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Nonlinear system
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.
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Nuclear physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions.
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Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).
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Numerical methods for ordinary differential equations
Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
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Optics
Optics is the branch of physics which involves the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it.
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Ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.
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Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).
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Partial differential equation
In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.
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The Portable Document Format (PDF) is a file format developed in the 1990s to present documents, including text formatting and images, in a manner independent of application software, hardware, and operating systems.
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Peano existence theorem
In mathematics, specifically in the study of ordinary differential equations, the Peano existence theorem, Peano theorem or Cauchy–Peano theorem, named after Giuseppe Peano and Augustin-Louis Cauchy, is a fundamental theorem which guarantees the existence of solutions to certain initial value problems.
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Pendulum
A pendulum is a weight suspended from a pivot so that it can swing freely.
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Physics
Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.
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Picard–Lindelöf theorem
In mathematics, in the study of differential equations, the Picard–Lindelöf theorem, Picard's existence theorem or Cauchy–Lipschitz theorem is an important theorem on existence and uniqueness of solutions to first-order equations with given initial conditions.
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Poisson's equation
In mathematics, Poisson's equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics.
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Poisson–Boltzmann equation
The Poisson–Boltzmann equation is a useful equation in many settings, whether it be to understand physiological interfaces, polymer science, electron interactions in a semiconductor, or more.
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Population dynamics
Population dynamics is the branch of life sciences that studies the size and age composition of populations as dynamical systems, and the biological and environmental processes driving them (such as birth and death rates, and by immigration and emigration).
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Providence, Rhode Island
Providence is the capital and most populous city of the U.S. state of Rhode Island and is one of the oldest cities in the United States.
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Pure mathematics
Broadly speaking, pure mathematics is mathematics that studies entirely abstract concepts.
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Quantum mechanics
Quantum mechanics (QM; also known as quantum physics, quantum theory, the wave mechanical model, or matrix mechanics), including quantum field theory, is a fundamental theory in physics which describes nature at the smallest scales of energy levels of atoms and subatomic particles.
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Radioactive decay
Radioactive decay (also known as nuclear decay or radioactivity) is the process by which an unstable atomic nucleus loses energy (in terms of mass in its rest frame) by emitting radiation, such as an alpha particle, beta particle with neutrino or only a neutrino in the case of electron capture, gamma ray, or electron in the case of internal conversion.
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Rate equation
The rate law or rate equation for a chemical reaction is an equation that links the reaction rate with the concentrations or pressures of the reactants and constant parameters (normally rate coefficients and partial reaction orders).
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Reaction rate
The reaction rate or rate of reaction is the speed at which reactants are converted into products.
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Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence or multidimensional array of values, once one or more initial terms are given: each further term of the sequence or array is defined as a function of the preceding terms.
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Replicator equation
In mathematics, the replicator equation is a deterministic monotone non-linear and non-innovative game dynamic used in evolutionary game theory.
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Schrödinger equation
In quantum mechanics, the Schrödinger equation is a mathematical equation that describes the changes over time of a physical system in which quantum effects, such as wave–particle duality, are significant.
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Second derivative
In calculus, the second derivative, or the second order derivative, of a function is the derivative of the derivative of.
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Sethi model
The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising.
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Shallow water equations
The shallow water equations are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid (sometimes, but not necessarily, a free surface).
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Solow–Swan model
The Solow–Swan model is an economic model of long-run economic growth set within the framework of neoclassical economics.
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Sound
In physics, sound is a vibration that typically propagates as an audible wave of pressure, through a transmission medium such as a gas, liquid or solid.
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Spacetime
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.
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Special functions
Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, functional analysis, physics, or other applications.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Stochastic differential equation
A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process.
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Stochastic partial differential equation
Stochastic partial differential equations (SPDEs) generalize partial differential equations via random force terms and coefficients, in the same way ordinary stochastic differential equations generalize ordinary differential equations.
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Stochastic process
--> In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a collection of random variables.
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Stress–energy tensor
The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.
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Symmetry
Symmetry (from Greek συμμετρία symmetria "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance.
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Tautochrone curve
A tautochrone or isochrone curve (from Greek prefixes tauto- meaning same or iso- equal, and chrono time) is the curve for which the time taken by an object sliding without friction in uniform gravity to its lowest point is independent of its starting point.
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Tensor
In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.
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Thermodynamics
Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.
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Thin-film equation
In physics and engineering, the thin-film equation is a partial differential equation that approximately predicts the time evolution of the x- and y-dependent local thickness h(x,y,t) of a liquid film (puddle, flat drop of liquid) that lies on a flat surface which coincides with the xy-plane.
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Universal differential equation
A universal differential equation (UDE) is a non-trivial differential algebraic equation with the property that its solutions can approximate any continuous function on any interval of the real line to any desired level of accuracy.
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University of Illinois at Urbana–Champaign
The University of Illinois Urbana–Champaign (also known as U of I, Illinois, or colloquially as the University of Illinois or UIUC) is a public research university in the U.S. state of Illinois and the flagship institution of the University of Illinois System.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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W. H. Freeman and Company
W.
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Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.
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Wave function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system.
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Wiener process
In mathematics, the Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener.
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References
[1] https://en.wikipedia.org/wiki/Differential_equation
