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  2. Partial derivative - Wikipedia

    en.wikipedia.org/wiki/Partial_derivative

    If all the partial derivatives of a function are known (for example, with the gradient), then the antiderivatives can be matched via the above process to reconstruct the original function up to a constant. Unlike in the single-variable case, however, not every set of functions can be the set of all (first) partial derivatives of a single function.

  3. Partial differential equation - Wikipedia

    en.wikipedia.org/wiki/Partial_differential_equation

    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.

  4. Integration by parts - Wikipedia

    en.wikipedia.org/wiki/Integration_by_parts

    In calculus, and more generally in mathematical analysis, integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an ...

  5. Matrix calculus - Wikipedia

    en.wikipedia.org/wiki/Matrix_calculus

    In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices.It collects the various partial derivatives of a single function with respect to many variables, and/or of a multivariate function with respect to a single variable, into vectors and matrices that can be treated as single entities.

  6. Method of characteristics - Wikipedia

    en.wikipedia.org/wiki/Method_of_characteristics

    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.

  7. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    An ordinary differential equation is a differential equation that relates functions of one variable to their derivatives with respect to that variable. A partial differential equation is a differential equation that relates functions of more than one variable to their partial derivatives. Differential equations arise naturally in the physical ...

  8. Second partial derivative test - Wikipedia

    en.wikipedia.org/wiki/Second_partial_derivative_test

    Thus, the second partial derivative test indicates that f(x, y) has saddle points at (0, −1) and (1, −1) and has a local maximum at (,) since = <. At the remaining critical point (0, 0) the second derivative test is insufficient, and one must use higher order tests or other tools to determine the behavior of the function at this point.

  9. List of nonlinear partial differential equations - Wikipedia

    en.wikipedia.org/wiki/List_of_nonlinear_partial...

    Name Dim Equation Applications Landau–Lifshitz model: 1+n = + Magnetic field in solids Lin–Tsien equation: 1+2 + = Liouville equation: any + = Liouville–Bratu–Gelfand equation