Solvers over Regions

The Wolfram Language deeply integrates regions into high-level solvers, including the ability to integrate or solve partial differential equations over regions, solve equations and inequalities with region constraints, or optimize over regions. The results can be either symbolic and exact or numeric and approximate.

ReferenceReference

Integrals

Integrate, NIntegrate integrate over a region

Probability  ▪  NProbability  ▪  Expectation  ▪  NExpectation

Partial Differential Equations »

NDSolve solve a partial differential equation over a region

NDSolveValue  ▪  DirichletCondition  ▪  NeumannValue  ▪  ...

Equations & Inequalities

Solve solve equations, inequalities, and region constraints

NSolve  ▪  Reduce  ▪  FindInstance  ▪  Resolve

Optimization »

Minimize optimize an objective over a region

NMinimize  ▪  FindMinimum  ▪  MinValue  ▪  ArgMin  ▪  ...

Visualization »

Plot3D plot a function over a region

ContourPlot  ▪  DensityPlot  ▪  ...

Geometric Solvers »

RegionNearest find the nearest point in a region

RegionMeasure  ▪  RegionCentroid  ▪  RegionDistance  ▪  ...