About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 82. Chapters: Partial differential equation, Partial derivative, Curvature, Lagrange multiplier, Scalar field, Laplace operator, Multiple integral, Frenet-Serret formulas, Ridge detection, Contour line, Isoperimetric inequality, Invariant factorization of LPDOs, Implicit function theorem, Directional derivative, Matrix calculus, Jacobian matrix and determinant, Total derivative, Implicit and explicit functions, Exact differential, Surface integral, Hessian matrix, Differential operator, Material derivative, Inverse function theorem, Multipole moment, Tortuosity, Symmetry of second derivatives, Change of variables, Critical point, Parametric equation, Inexact differential, Second partial derivative test, Level set, Saddle point, Sard's theorem, Contact, Triple product rule, Equipotential, Vector Laplacian, Laplace invariant, Upper convected time derivative, Volume integral, Saddle surface, Comparametric equation, Monkey saddle, List of multivariable calculus topics, Shift theorem, Critical value, Equipotential surface. Excerpt: In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several independent variables and their partial derivatives with respect to those variables. Partial differential equations are used to formulate, and thus aid the solution of, problems involving functions of several variables; such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity. Seemingly distinct physical phenomena may have identical mathematical formulations, and thus be governed by the same underlying dynamic. They find their generalization in stochastic partial differential equations. Just as ordinary differential equations often model dynamical systems, partial differential equations often model mult...
