Variational Methods (Variational Methods Package Tutorial)

The basic problem of the calculus of variations is to determine the function u(x) that extremizes a functional F=∫_SubscriptBox[x^StyleBox[min, FontSlant -> Italic], ...

Termination Conditions (Mathematica Tutorial)

Mathematically, sufficient conditions for a local minimum of a smooth function are quite straightforward: x^* is a local minimum if ∇f(x^*)=0 and the Hessian ∇^2f(x^*) is ...

IDA Method for NDSolve (Mathematica Tutorial)

The IDA package is part of the SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation Solvers) developed at the Center for Applied Scientific Computing of Lawrence ...

Newton's Method (Mathematica Tutorial)

One significant advantage Mathematica provides is that it can symbolically compute derivatives. This means that when you specify Method->"Newton" and the function is ...

Components and Data Structures (Mathematica Tutorial)

NDSolve is broken up into several basic steps. For advanced usage, it can sometimes be advantageous to access components to carry out each of these steps separately. NDSolve ...

Function (Built-in Mathematica Symbol)

Function[body] or body & is a pure function. The formal parameters are # (or #1), #2, etc. Function[x, body] is a pure function with a single formal parameter x. ...

Total (Built-in Mathematica Symbol)

Total[list] gives the total of the elements in list. Total[list, n] totals all elements down to level n. Total[list, {n}] totals elements at level n. Total[list, {n_1, n_2}] ...

New in 8.0: Mathematics & Algorithms (Mathematica Guide)

Mathematica 8 adds major new areas, including probability and statistics, graphs and networks, computational finance, control systems, wavelet analysis, and group theory. ...

Operator Input Forms (Mathematica Tutorial)

Characters that are not letters, letter-like forms, or structural elements are treated by Mathematica as operators. Mathematica has built-in rules for interpreting all ...

NDSolve (Built-in Mathematica Symbol)

NDSolve[eqns, y, {x, x_min, x_max}] finds a numerical solution to the ordinary differential equations eqns for the function y with the independent variable x in the range ...