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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
  
Laplacian(function, [varlist], [mode])
function
This is defined by the mode parameter as cartesian coordinates (mode=0), cylindrical coordinates (mode=1) or spherical coordinates (mode=2).

[varlist]
This parameter is optional and when not defined uses the following values.
mode=0 : [x, y, z]
mode=1 : [r, Φ, z]
mode=2 : [r, θ, Φ]

When other variables are used these have to be declared in the varlist as [ var1 , var2 , var3 , ...].

[mode]
The default value is 0.

Returns the Laplacian of the function.

This is normally denoted as Laplacian(F) = ∇2F

Examples  





Cartesian coordinates

Cylindrical coordinates

Spherical coordinates

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



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