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Since resistors are linear components, it is particularly easy to determine the quiescent operating point of the non-linear device from a graph of its transfer function. The method is as follows: from linear network analysis the output transfer function (that is output voltage against output current) is calculated for the network of resistor(s ...
"A signal-flow graph is a diagram that represents a set of simultaneous algebraic equations. When applying the signal flow graph method to analysis of control systems, we must first transform linear differential equations into algebraic equations in [the Laplace transform variable] s.." — Katsuhiko Ogata: Modern Control Engineering, p. 104
Conversely, every line is the set of all solutions of a linear equation. The phrase "linear equation" takes its origin in this correspondence between lines and equations: a linear equation in two variables is an equation whose solutions form a line. If b ≠ 0, the line is the graph of the function of x that has been defined in the preceding ...
A linear congruential generator (LCG) is an algorithm that yields a sequence of pseudo-randomized numbers calculated with a discontinuous piecewise linear equation. The method represents one of the oldest and best-known pseudorandom number generator algorithms.
In mathematics, a generating function is a representation of an infinite sequence of numbers as the coefficients of a formal power series.Generating functions are often expressed in closed form (rather than as a series), by some expression involving operations on the formal series.
The best known plots of the Michaelis–Menten equation, including the double-reciprocal plot of / against /, [2] the Hanes plot of / against , [3] and the Eadie–Hofstee plot [4] [5] of against / are all plots in observation space, with each observation represented by a point, and the parameters determined from the slope and intercepts of the lines that result.
These equations, often complex and non-linear, can be linearized using linear algebra methods, allowing for simpler solutions and analyses. In the field of fluid dynamics, linear algebra finds its application in computational fluid dynamics (CFD), a branch that uses numerical analysis and data structures to solve and analyze problems involving ...
The Mandelbrot set, one of the most famous examples of mathematical visualization.. Mathematical phenomena can be understood and explored via visualization.Classically, this consisted of two-dimensional drawings or building three-dimensional models (particularly plaster models in the 19th and early 20th century).
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