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Fig. 1: Isoclines (blue), slope field (black), and some solution curves (red) of y' = xy. The solution curves are y = C e x 2 / 2 {\displaystyle y=Ce^{x^{2}/2}} . Given a family of curves , assumed to be differentiable , an isocline for that family is formed by the set of points at which some member of the family attains a given slope .
the slope field is an array of slope marks in the phase space (in any number of dimensions depending on the number of relevant variables; for example, two in the case of a first-order linear ODE, as seen to the right). Each slope mark is centered at a point (,,, …,) and is parallel to the vector
Desmos was founded by Eli Luberoff, a math and physics double major from Yale University, [3] and was launched as a startup at TechCrunch's Disrupt New York conference in 2011. [4] As of September 2012 [update] , it had received around 1 million US dollars of funding from Kapor Capital , Learn Capital, Kindler Capital, Elm Street Ventures and ...
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94, 96, 99SB, 03, GS, ii, Automatic FF generator [1] No No No No UFF-Dreiding-like field For proteins, DNA, ligands AMBER: Yes Yes Via chamber tool since v11 Yes No No No Ascalaph Designer: UA 94, 99SB, 03 No No No No No Avogadro: No No No Yes 94, 94s No Yes Balloon: No No No No 94 No No MMFF94-like BOSS: Yes No No No No No No CHARMM: Yes* Yes ...
Slope field; Metadata. This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
Keeping in mind that the slope is at most , the problem now presents itself as to whether the next point should be at (+,) or (+, +). Perhaps intuitively, the point should be chosen based upon which is closer to the line at +. If it is closer to the former then include the former point on the line, if the latter then the latter.
Slope illustrated for y = (3/2)x − 1.Click on to enlarge Slope of a line in coordinates system, from f(x) = −12x + 2 to f(x) = 12x + 2. The slope of a line in the plane containing the x and y axes is generally represented by the letter m, [5] and is defined as the change in the y coordinate divided by the corresponding change in the x coordinate, between two distinct points on the line.