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ISBN 978-1-4704-6762-3. [9] Michael E. Taylor. Partial differential equations I. Basic theory. Second edition. Applied Mathematical Sciences, 115. Springer, New York, 2011. xxii+654 pp. ISBN 978-1-4419-7054-1 [10] Michael E. Taylor. Partial differential equations II. Qualitative studies of linear equations. Second edition. Applied Mathematical ...
In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives.. The function is often thought of as an "unknown" that solves the equation, similar to how x is thought of as an unknown number solving, e.g., an algebraic equation like x 2 − 3x + 2 = 0.
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can move with time.
In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.The key observation is that, given a Riemannian metric on M, every cohomology class has a canonical representative, a differential form that vanishes under the Laplacian operator of the metric.
In mathematics, the method of characteristics is a technique for solving partial differential equations.Typically, it applies to first-order equations, though in general characteristic curves can also be found for hyperbolic and parabolic partial differential equation.
Taylor, Michael E. (2011), Partial differential equations I. Basic theory, Applied Mathematical Sciences, vol. 115 (2nd ed.), Springer, ISBN 978-1-4419-7054-1. Zimmer, Robert J. (1990), Essential results of functional analysis , Chicago Lectures in Mathematics, University of Chicago Press, ISBN 0-226-98337-4 .
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