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2. System of linear equations - Wikipedia

   en.wikipedia.org/wiki/System_of_linear_equations

   In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same variables. [1][2] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...

3. Separation of variables - Wikipedia

   en.wikipedia.org/wiki/Separation_of_variables

   t. e. In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation.

4. Equation solving - Wikipedia

   en.wikipedia.org/wiki/Equation_solving

   Equation solving. In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns.

5. Green's function for the three-variable Laplace equation

   en.wikipedia.org/wiki/Green's_function_for_the...

   The free-space Green's function for the Laplace operator in three variables is given in terms of the reciprocal distance between two points and is known as the "Newton kernel" or "Newtonian potential". That is to say, the solution of the equation is where are the standard Cartesian coordinates in a three-dimensional space, and is the Dirac ...

6. Linear equation - Wikipedia

   en.wikipedia.org/wiki/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 section. If b = 0, the line is a vertical line (that is a line parallel to ...

7. Cubic equation - Wikipedia

   en.wikipedia.org/wiki/Cubic_equation

   Here the function is and therefore the three real roots are 2, -1 and -4. In algebra, a cubic equation in one variable is an equation of the form in which a is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients a, b, c, and d of the cubic ...