slope field
[/sloʊp fiːld/]
nounpl: slope fields
campo de direções
1. A graphical representation in mathematics showing the slope of a differential equation at various points in a plane, used to visualize solutions without solving the equation analytically
The slope field illustrates how the solution curves of the differential equation dy/dx = x + y behave throughout the coordinate plane.
O campo de direções ilustra como as curvas solução da equação diferencial dy/dx = x + y se comportam em todo o plano de coordenadas.
2. A collection of small line segments or arrows at grid points, each with a slope determined by a differential equation
By sketching a slope field, students can predict the general shape of solution curves without explicit calculation.
Ao esboçar um campo de direções, os alunos podem prever a forma geral das curvas solução sem cálculo explícito.
This is a technical mathematical term used primarily in calculus and differential equations courses in both Brazilian and American educational contexts. There is no significant cultural variation in usage; the term is consistent across mathematical communities in English and Portuguese-speaking countries.
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