New in 10.0: Symbolic & Numeric Computation
Geometric Computation »
Geometric computation framework for modeling and computing with geometric regions.
Plane Geometry »
SSSTriangle ▪ ArcLength ▪ Area ▪ ...
Solid Geometry »
Tetrahedron ▪ Volume ▪ RegionMember ▪ ...
Properties and Measures »
RegionNearest — find the nearest point in a region
RegionMeasure ▪ RegionCentroid ▪ RegionDistance ▪ ...
Solvers over Regions »
Integrate, NIntegrate — integrate over regions
NDSolve — solve partial differential equations over regions
Solve ▪ NSolve ▪ Minimize ▪ NMinimize ▪ ...
Special Regions »
Ball — a ball given by center and radius
Simplex ▪ Hexahedron ▪ InfiniteLine ▪ ...
Formula Regions
ImplicitRegion — a region given by combinations of inequalities and equalities
ParametricRegion — a region given by parametric functions
Mesh Regions »
MeshRegion — a region specified by a collection of mesh cells
BoundaryMeshRegion — a region boundary specified by a collection of mesh cells
HighlightMesh ▪ MeshCellStyle ▪ MeshCellLabel ▪ ...
Data Regions »
DelaunayMesh — a Delaunay triangulation mesh constructed from points
VoronoiMesh ▪ ConvexHullMesh ▪ ...
Region Converters »
DiscretizeGraphics, BoundaryDiscretizeGraphics — discretize 2D or 3D graphics
DiscretizeRegion, BoundaryDiscretizeRegion — discretize a region
Derived Regions »
RegionUnion — the union of regions
TransformedRegion — a region as the image of a transformation
RegionIntersection ▪ BooleanRegion ▪ RegionBoundary ▪ ...
Inactive Operators
Inactive — new inactive operator for working with formal operations
Inactivate — inactivate parts of expressions
Enhanced Calculus
DSolveValue, RSolveValue — new functions that can directly return functions of solutions
DSolve — now solves delay differential and hybrid differential equations
Sum — new algorithms for functional telescoping, multiple sums, and special functions
Product — new algorithms for functional telescoping
DifferenceDelta — new results for differences of special functions
DiscreteRatio — new results for ratios of special functions
Enhanced Algebraic Computation
NSolve — new homotopy-based algorithm for fast solution of polynomial systems
Reduce, Solve, FindInstance — new fast solving over the reals
Function Properties
FunctionPeriod — find the period of functions over the reals, integers, and complexes
FunctionDomain — find the domain of a function
FunctionRange — find the range of a function
Vector Analysis
ArcLength — length
ArcCurvature — curvature
FrenetSerretSystem — generalized curvatures and associated basis
Linear Algebra »
PositiveSemidefiniteMatrixQ — new and improved matrix predicates
NormalMatrixQ ▪ OrthogonalMatrixQ ▪ SquareMatrixQ ▪ ...
New Special Functions
LogisticSigmoid — the logistic function
CantorStaircase — the Cantor ternary function
MinkowskiQuestionMark ▪ ScorerHi ▪ ScorerGi ▪ FresnelF ▪ FresnelG ▪ RiemannXi ▪ DirichletBeta ▪ DirichletEta ▪ DirichletLambda ▪ Fibonorial ▪ AlternatingFactorial ▪ FareySequence
Nonlinear Control Systems »
AffineStateSpaceModel — affine model 
and 
FeedbackLinearize — linearization through nonlinear feedback and state transformation
AsymptoticOutputTracker — tracker with state feedback
NonlinearStateSpaceModel ▪ FullInformationOutputRegulator ▪ ...
Probability & Statistics
AutocorrelationTest — test for autocorrelation in data
Time Series Processes »
TimeSeriesModelFit — automatic fitting, diagnostics, and forecasting for time series
ARCHProcess, GARCHProcess — new classes of time series processes
ARProcess, ARMAProcess — full support for vector processes
MAProcess ▪ SARMAProcess ▪ FARIMAProcess
Markov Processes
HiddenMarkovProcess — hidden Markov process with discrete or continuous emissions
FindHiddenMarkovStates — hidden state decoding (Viterbi decoding etc.)
Parametric Processes »
TransformedProcess — transformations of random processes
WhiteNoiseProcess — new and improved capabilities for parametric processes
PoissonProcess ▪ WienerProcess ▪ GeometricBrownianMotionProcess ▪ ...