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44 relations: Characteristic equation (calculus), Contour line, Critical point (mathematics), Curve, David Hilbert, Derivative test, Differentiable function, Differential geometry of surfaces, Dimension, Dynamical system, Euclidean space, Function (mathematics), Gaussian curvature, Graph of a function, Hessian matrix, Hyperbolic equilibrium point, Hyperboloid, Hypersurface, Inflection point, Lagrange multiplier, Laplace's method, Mathematics, Max–min inequality, Maxima and minima, Method of steepest descent, Minimax theorem, Monkey saddle, Mountain pass, Nash equilibrium, Neighbourhood (mathematics), Orthogonal functions, Paraboloid, Periodic point, Point (geometry), Pringles, Saddle, Saddle (landform), Smoothness, Stable manifold, Stationary point, Surface (mathematics), Tangent space, Unit circle, Zero-sum game.
Characteristic equation (calculus)
In mathematics, the characteristic equation (or auxiliary equation) is an algebraic equation of degree n upon which depends the solution of a given n\,th-order differential equation or difference equation.
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Contour line
A contour line (also isocline, isopleth, isarithm, or equipotential curve) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.
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Critical point (mathematics)
In mathematics, a critical point or stationary point of a differentiable function of a real or complex variable is any value in its domain where its derivative is 0.
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Curve
In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but that need not be straight.
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David Hilbert
David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.
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Derivative test
In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point.
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Differentiable function
In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
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Differential geometry of surfaces
In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric.
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Dimension
In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it.
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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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Euclidean space
In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.
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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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Gaussian curvature
In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature 0 everywhere.
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Graph of a function
In mathematics, the graph of a function f is, formally, the set of all ordered pairs, and, in practice, the graphical representation of this set.
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Hessian matrix
In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.
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Hyperbolic equilibrium point
In the study of dynamical systems, a hyperbolic equilibrium point or hyperbolic fixed point is a fixed point that does not have any center manifolds.
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Hyperboloid
In geometry, a hyperboloid of revolution, sometimes called circular hyperboloid, is a surface that may be generated by rotating a hyperbola around one of its principal axes.
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Hypersurface
In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.
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Inflection point
In differential calculus, an inflection point, point of inflection, flex, or inflection (British English: inflexion) is a point on a continuously differentiable plane curve at which the curve crosses its tangent, that is, the curve changes from being concave (concave downward) to convex (concave upward), or vice versa.
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Lagrange multiplier
In mathematical optimization, the method of Lagrange multipliers (named after Joseph-Louis Lagrange) is a strategy for finding the local maxima and minima of a function subject to equality constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables).
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Laplace's method
In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form where ƒ(x) is some twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite.
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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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Max–min inequality
In mathematics, the max–min inequality is as follows: for any function f: Z × W → ℝ, \sup_ \inf_ f(z, w) \leq \inf_ \sup_ f(z, w).
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Maxima and minima
In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).
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Method of steepest descent
In mathematics, the method of steepest descent or stationary-phase method or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of steepest descent or stationary phase.
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Minimax theorem
A minimax theorem is a theorem providing conditions that guarantee that the max–min inequality is also an equality.
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Monkey saddle
In mathematics, the monkey saddle is the surface defined by the equation It belongs to the class of saddle surfaces and its name derives from the observation that a saddle for a monkey requires three depressions: two for the legs, and one for the tail.
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Mountain pass
A mountain pass is a navigable route through a mountain range or over a ridge.
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Nash equilibrium
In game theory, the Nash equilibrium, named after American mathematician John Forbes Nash Jr., is a solution concept of a non-cooperative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players, and no player has anything to gain by changing only their own strategy.
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Neighbourhood (mathematics)
In topology and related areas of mathematics, a neighbourhood (or neighborhood) is one of the basic concepts in a topological space.
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Orthogonal functions
In mathematics, orthogonal functions belong to a function space which is a vector space that has a bilinear form.
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Paraboloid
In geometry, a paraboloid is a quadric surface that has (exactly) one axis of symmetry and no center of symmetry.
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Periodic point
In mathematics, in the study of iterated functions and dynamical systems, a periodic point of a function is a point which the system returns to after a certain number of function iterations or a certain amount of time.
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Point (geometry)
In modern mathematics, a point refers usually to an element of some set called a space.
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Pringles
Pringles is an American brand of potato and wheat-based stackable snack chips owned by Kellogg's.
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Saddle
The saddle is a supportive structure for a rider or other load, fastened to an animal's back by a girth.
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Saddle (landform)
The saddle between two hills (or mountains) is the region surrounding the highest point of the lowest point on the line tracing the drainage divide (the col) connecting the peaks.
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Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of derivatives it has that are continuous.
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Stable manifold
In mathematics, and in particular the study of dynamical systems, the idea of stable and unstable sets or stable and unstable manifolds give a formal mathematical definition to the general notions embodied in the idea of an attractor or repellor.
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Stationary point
In mathematics, particularly in calculus, a stationary point or critical point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero.
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Surface (mathematics)
In mathematics, a surface is a generalization of a plane which needs not be flat, that is, the curvature is not necessarily zero.
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Tangent space
In mathematics, the tangent space of a manifold facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector that gives the displacement of the one point from the other.
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Unit circle
In mathematics, a unit circle is a circle with a radius of one.
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Zero-sum game
In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants.
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References
[1] https://en.wikipedia.org/wiki/Saddle_point
