Verification of the Solution (Mathematica Tutorial)

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

Differential Operators (Mathematica Guide)

Mathematica's approach to differential operators provides both an elegant and a convenient representation of mathematical structures, and an immediate framework for strong ...

Modulus (Built-in Mathematica Symbol)

Modulus -> n is an option that can be given in certain algebraic functions to specify that integers should be treated modulo n.

ModularLambda (Built-in Mathematica Symbol)

ModularLambda[\[Tau]] gives the modular lambda elliptic function \[Lambda](\[Tau]).

SymmetricReduction (Built-in Mathematica Symbol)

SymmetricReduction[f, {x_1, ..., x_n}] gives a pair of polynomials {p, q} in x_1, ..., x_n such that f == p + q, where p is the symmetric part and q is the ...

Introduction to Differential-Algebraic ... (Mathematica Tutorial)

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

Is the Problem Well-Posed? (Mathematica Tutorial)

DSolve returns a general solution for a problem if no initial or boundary conditions are specified. The general solution to this equation is returned. However, if initial or ...

Nonlinear PDEs (Mathematica Tutorial)

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

JacobiSN (Built-in Mathematica Symbol)

JacobiSN[u, m] gives the Jacobi elliptic function sn(u | m).

$Pre (Built-in Mathematica Symbol)

$Pre is a global variable whose value, if set, is applied to every input expression.