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Vector Calculus
Angle, Cross, Curl, Divergence, Dot, Duf, Gradient, Hessian, Jacobian, Laplacian, Norm, SurfaceNormal

Algebra
Apart, Coefficient, Degree, Denominator, Divisors, DivisorSigma, Eval, Expand, Factor, GCD, LCM, PolyDivide, PolyFit, PolyGCD, PolyLCM, PowerExpand, Quotient, Remainder, Sequence, SimplifyPoly, Solve, SolveSystem, Together

Basic
Abs, Arg, Conj, Exp, Hyperbolic Functions, Im, Ln, Log, Re, Trigonometric Functions

Calculus
D, Diff, DSolve, fDiff, FourierCos, FourierSeries, FourierSin, iDiff, iLaplace, Integrate, Laplace, Limit, NIntegrate, pDiff, Product, Series, Sum

CAS
Append, Call, Caps, Char, Choose, Clear, Command, Date, Delete, Extract, Function, Insert, IsList, IsMatrix, IsNumber, IsPoly, Left, Length, List, Matrix, Part, Replace, Reshape, Reverse, Right, Size, Sort, String, Value, Variables

Data
Constant, Finance, HRStoHMS, LoadList, LoadMatrix, Table

Elementary
Binomial, Ceil, Eulerian, Factorial, Floor, fPart, iPart, Mod, Multinomial, nCr, nPr, nRoot, Pochhammer, Round, Sign, Sqrt

Graphing
clip, FullRectSineWave, HalfRectSineWave, SawToothWave, SquareWave, StaircaseWave, TriangleWave

Manual
Code Files, Commands, Creating Scripts, Entering Expressions, Graphing Equations, Include Folder, Lists, Matrices, Strings, Symbols, Time Graphing

Matrix
Cholesky, coFactor, Det, Eigenvalues, Eigenvectors, Identity, Inverse, LUDecomposition, QR, RowReduce, SVD, Transpose

Number
AlternatingSeries, Catalan, cFrac, Convergents, IsPrime, LegendreP, nFactors, nPrimes, Pi_Digits, Random

Plot
BodePlot, ContourPlot, CylindricalPlot3D, FractalPlot, ImagePlot, ImplicitPlot, JuliaPlot, ListPlot, ListPlot3D, MultiPlot, MultiPlot3D, ParametricPlot, ParametricPlot3D, Plot, Plot3D, PolarPlot, SphericalPlot3D, VectorPlot, VectorPlot3D

Scripting
Animate, CheckBox, Draw, DrawColor, DrawWindow, Else If, Error, If, Include, Loop, Message, Scroll, Trace, While

Special
AiryAi, AiryBi, BesselI, BesselJ, BesselK, BesselY, Beta, Chi, Ci, Dawson, DiGamma, DiLog, Dirichlet_Eta, Dirichlet_Lambda, Ei, Erf, Erfc, FresnelCos, FresnelSin, Gamma, Gudermannian, HankelH1, HankelH2, Harmonic, Hypergeom_2F1, invGudermannian, KelvinBei, KelvinBer, KelvinKei, KelvinKer, LambertW, Li, LnGamma, PolyGamma, PolyLog, Psi, RK4, RK45, Shi, Si, Zeta

Special Polynomials
Bernoulli, ChebyshevT, ChebyshevU, Euler, Fibonacci, GegenbauerC, HermiteH, LaguerreL, LegendreQ, Lucas

Statistical
BinomialCDF, BinomialPDF, ChiSquareCDF, ChiSquarePDF, Fcdf, Fpdf, GeoCDF, GeoPDF, InverseNormal, Max, Mean, Min, NormalCDF, NormalPDF, PoissonCDF, PoissonPDF, StandardDeviation, StudentTCDF, StudentTPDF, Variance

Trigonometric
DEGtoDMS, ExpConvert, TrigCollect, TrigConvert, TrigExpand, TrigReduce
  
Jacobian(function, [varlist], [point])
[varlist]
This parameter is optional and default value is [x,y,z].

[point]
This parameter is optional and if omitted the Jacobian matrix is returned. When point is given the matrix is evaluated at that point. If point is given and the number of equations = number of variables then the Jacobian determinant is returned

Returns either the Jacobian matrix or the Jacobian determinant of a function list function(varlist) evaluated at point.

Examples  




References
http://mathworld.wolfram.com/Jacobian.html
http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant



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