Riccati Equations (Mathematica Tutorial)

A Riccati equation is a first-order equation of the form This equation was used by Count Riccati of Venice (1676–1754) to help in solving second-order ordinary differential ...

Exact Equations (Mathematica Tutorial)

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Sqrt (Built-in Mathematica Symbol)

Sqrt[z] or Sqrt[z] gives the square root of z.

RotationMatrix (Built-in Mathematica Symbol)

RotationMatrix[\[Theta]] gives the 2D rotation matrix that rotates 2D vectors counterclockwise by \[Theta] radians.RotationMatrix[\[Theta], w] gives the 3D rotation matrix ...

PowerExpand (Built-in Mathematica Symbol)

PowerExpand[expr] expands all powers of products and powers. PowerExpand[expr, {x_1, x_2, ...}] expands only with respect to the variables x_i.

Not (Built-in Mathematica Symbol)

! expr is the logical NOT function. It gives False if expr is True, and True if it is False.

IntegerQ (Built-in Mathematica Symbol)

IntegerQ[expr] gives True if expr is an integer, and False otherwise.

Sech (Built-in Mathematica Symbol)

Sech[z] gives the hyperbolic secant of z.

ByteCount (Built-in Mathematica Symbol)

ByteCount[expr] gives the number of bytes used internally by Mathematica to store expr.

FromCoefficientRules (Built-in Mathematica Symbol)

FromCoefficientRules[list, {x_1, x_2, ...}] constructs a polynomial from a list of rules for exponent vectors and coefficients.