Separation of Variables
A method of solving partial differential equations in a function 
and variables 
, 
, ... by makinga substitution of the form
breaking the resulting equation into a set of independent ordinary differential equations, solving these for
,
, ..., and then plugging them back into the original equation. This technique works because if the product of functions of independent variables is a constant, each function must separatelybe a constant. Success requires choice of an appropriate coordinate system and may not be attainable at all depending on theequation. Separation of variables was first used by L'Hospital 
in 1750. It is especially useful in solvingequations arising in mathematical physics, such as Laplace's Equation, the Helmholtz Differential Equation, andthe Schrödinger equation. 
References
Arfken, G. ``Separation of Variables'' and ``Separation of Variables--Ordinary Differential Equations.'' §2.6 and §8.3 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 111-117 and 448-451, 1985. Morse, P. M. and Feshbach, H. ``Separable Coordinates'' and ``Table of Separable Coordinates in Three Dimensions.'' §5.1 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 464-523 and 655-666, 1953.
- Milnor's Conjecture
- Milnor's Theorem
- Minimal Cover
- Minimal Discriminant
- Minimal Matrix
- Minimal Residue
- Minimal Set
- Minimal Surface
- Minimax Approximation
- Minimax Polynomial
- Minimax Theorem
- Minimum
- Minkowski-Bouligand Dimension
- Minkowski Convex Body Theorem
- Minkowski Geometry
- Minkowski-Hlawka Theorem
- Minkowski Integral Inequality
- Minkowski Measure
- Minkowski Metric
- Minkowski Sausage
- Minkowski Space
- Minkowski Sum
- Minkowski Sum Inequality
- Minor
- Minor Axis