Applying Functions to Lists (Mathematica Guide)

Many computations are conveniently specified in terms of applying functions in parallel to many elements in a list. Mathematica provides a suite of elegant functional ...

Matrix-Based Minimization (Mathematica Guide)

Optimization (Mathematica Guide)

Integrated into Mathematica is a full range of state-of-the-art local and global optimization techniques, both numeric and symbolic, including constrained nonlinear ...

Structural Operations on Expressions (Mathematica Guide)

Mathematica's unified symbolic architecture immediately allows it to perform structural transformations not only on objects like lists, but also on general symbolic ...

Numerical Operations on Functions (Mathematica Overview)

Arithmetic Numerical Mathematics in Mathematica The Uncertainties of Numerical Mathematics

CountRoots (Built-in Mathematica Symbol)

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.

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 ...

Data Transforms and Smoothing (Mathematica Guide)

Directly integrated into Mathematica's uniform architecture for handling lists of data is an array of highly optimized algorithms for transforming and smoothing datasets that ...

New in 6.0: Numerical Data Handling (Mathematica Guide)

Version 6.0 added a collection of carefully optimized functions to Mathematica's powerful arsenal of numerical handling capabilities.

Resolve (Built-in Mathematica Symbol)

Resolve[expr] attempts to resolve expr into a form that eliminates ForAll and Exists quantifiers. Resolve[expr, dom] works over the domain dom. Common choices of dom are ...