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 ...

Symbolic Parameters and Inexact ... (Mathematica Tutorial)

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

Minimization and Maximization (Mathematica Tutorial)

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Introduction to Step Control (Mathematica Tutorial)

Even with "Newton methods" where the local model is based on the actual Hessian, unless you are close to a root or minimum, the model step may not bring you any closer to the ...

The Secant Method (Mathematica Tutorial)

When derivatives cannot be computed symbolically, "Newton's" method will be used, but with a finite difference approximation to the Jacobian. This can have costs in terms of ...

Symbolic Evaluation (Mathematica Tutorial)

The functions FindMinimum, FindMaximum, and FindRoot have the HoldAll attribute and so have special semantics for evaluation of their arguments. First, the variables are ...

Statistical Plots Package (Statistical Plots Package Tutorial)

A wide variety of plots and charts are used to gain an overview of data from a statistical perspective. Some summarize statistical computations on the data, while others ...

PseudoDiameter (Graph Utilities Package Symbol)

PseudoDiameter[g] give the pseudo-diameter of the undirected graph g, and the two vertices that achieve this diameter.

Table (Mathematica Import/Export Format)

Generic tabular data. Stores numerical and textual information, formatted as a table. Supports user-defined field and record separators, field delimiters, currency tokens, ...

ArrayFlatten (Built-in Mathematica Symbol)

ArrayFlatten[{{m_11, m_12, ...}, {m_21, m_22, ...}, ...}] creates a single flattened matrix from a matrix of matrices m i j. ArrayFlatten[a, r] flattens out r pairs of levels ...