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The characteristic equation of a third-order constant coefficients or Cauchy–Euler (equidimensional variable coefficients) linear differential equation or difference equation is a cubic equation. Intersection points of cubic Bézier curve and straight line can be computed using direct cubic equation representing Bézier curve.
Solving an equation symbolically means that expressions can be used for representing the solutions. For example, the equation x + y = 2x – 1 is solved for the unknown x by the expression x = y + 1, because substituting y + 1 for x in the equation results in (y + 1) + y = 2(y + 1) – 1, a true statement. It is also possible to take the ...
Bernoulli's equation; Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy of equations; Bessel's differential equation; Boltzmann equation; Borda–Carnot equation; Burgers' equation; Darcy–Weisbach equation; Dirac equation. Dirac equation in the algebra of physical space; Dirac–Kähler equation; Doppler equations; Drake equation (aka ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Such courses usually then go into simple algebra with solutions of simple linear equations and inequalities. Algebra I is the first course students take in algebra. Although some students take it as eighth graders, this class is most commonly taken in ninth or tenth grade, [44] after the students have taken Pre
In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as: