The Mathematica Guidebooks

# Index of the GuideBooks

Symbols, A-C | D-E | F-H | I-J | K-M | N-P |Q-S | T-W | X-Z | Download index (1.5 MB .pdf)

## T

`Table` P.5.2.2, P.6.1.1

`Table` P.6.Ex.8

Table, "symbolic" ~ P.4.1.1

`TableAlignments` P.6.2

`TableDepth` P.6.2

`TableDirections` P.6.2

`TableForm` P.6.2

`TableHeadings` P.6.2

Tables

• aligning row and columns in ~ P.6.2
• creation of ~ P.5.2.2, P.6.1.1
• displaying ~ P.6.2
• formatting of ~ P.6.2
• generalized ~ P.6.Sol.8
• of data P.6.Sol.1

`TableSpacing` P.6.2

Tachyonic, subluminal signal propagation N.1.10.2

Tagaki function N.1.4

Tagging cells In

`TagSet` P.3.4

`TagSetDelayed` P.3.4

`Take` P.6.3.1

`Take` versus `Part` P.6.3.1

Takeuchi function P.3.5

`TakeuchiT` P.3.5

Taking

• limits by hand S.1.Sol.35, S.3.Sol.2
• parts of expressions P.2.3.2, P.6.3.1

Tall

• cells N.2.Sol.1
• graphics of ~ objects G.1.1.3, G.2.1.5
• notebooks N.2.Sol.1

`TallPicture` G.2.1.5

`Tan` P.2.2.3

Tan function

• definition of the ~ P.2.2.3
• inside arctan P.2.Ex.6
• nested ~ N.1.Ex.26
• products of ~ N.1.Ex.26

Tangent, vector G.1.1.1, G.2.3.2

`Tanh` P.2.2.3

Tannhäuser P.6.5.2

`TanPowerIntegrate` P.3.5

Tap, dripping ~ P.1.Sol.1

`TargetFunctions` S.1.4

Taylor series

• calculating ~ S.1.6.4
• coefficients P.1.Sol.1
• generalized ~ S.1.6.1, S.1.Ex.2
• high-order ~ S.3.Ex.1
• Lagrange remainder of ~ N.1.Ex.15
• of operators S.1.Sol.45
• q-~ S.1.6.4
• summation of ~ S.3.Sol.1
• summed finite ~ S.3.7
• through integration S.1.Ex.2
• two-point ~ S.1.Ex.1
• visualizing the convergence of ~ G.1.2.1, G.3.1

Teaching

• graphics in ~ G.1.0
• surprises P.1.Sol.1

Tearing paper P.1.Sol.1

Teeth, gear~ P.1.Sol.1, G.2.Sol.19

Template, of a package P.4.6.5

`Temporary` P.4.6.2

Temporary

• changing system values P.4.6.3, G.2.2.1
• disabling graphics display G.1.1.3, G.2.2.1, N.1.5, S.3.8
• disabling messages S.3.Sol.13
• values of symbols P.4.6.2
• variables P.4.6.2

Tensor, identity ~ P.6.1.2

`TensorRank` P.6.2

Tensors

• algorithmic simplification of ~ S.1.6.1, S.1.Sol.17
• creating ~ P.6.1.1, P.6.2
• curvature ~ S.1.6.1
• dimensions of ~ P.6.5.1
• dual field strength ~ P.6.5.1
• field strength ~ P.6.5.1
• formatting ~ P.6.2
• in compiled functions N.1.3
• Levi-Civita ~ P.6.1.2, P.6.Ex.9
• lists as ~ P.6.2
• metric ~ S.1.6.1
• multidimensional ~ P.6.2
• packed ~ N.1.1.5
• rank of ~ P.6.2
• simplification of expressions involving ~ S.1.Sol.17
• totally antisymmetric ~ P.6.1.2, P.6.Ex.9

Term order, in polynomials S.1.2.2

Terms

• in the multinomial theorem N.2.Ex.1
• of a polynomial S.1.2.1
• of a series S.1.6.4
• secular ~ S.1.Ex.36
• symbolic ~ of a series S.1.8

Tessellations

• box spline ~ S.1.Ex.34
• in 3D G.2.3.1
• Islamic wicker ~ G.1.1.1
• of the hyperbolic plane G.1.5.8
• Rauzy ~ G.1.1.1
• with various tiles G.1.1.1, G.1.5.4

Test

• Fermat ~ S.1.Ex.20
• pattern ~ P.5.2.2

Testing

• for being a machine real number N.1.1.1
• for being a matrix P.5.1.2
• for being a number P.5.1.1
• for being a numerical quantity P.5.1.1
• for being a polynomial P.5.1.2
• for being a vector P.5.1.2, P.5.1.2
• for being an atomic expression P.5.1.2
• for being an even integer P.5.1.1
• for being an exact number P.5.1.1
• for being an inexact number P.5.1.1
• for being an integer P.5.1.1
• for being an odd integer P.5.1.1
• for being contained in an interval N.1.1.2
• for being explicitly true P.5.1.1
• for being identical P.5.1.2
• for being inside a polygon G.1.6
• for being mathematically identical P.5.1.2
• for being ordered P.5.1.2
• for being packed N.1.1.5
• for being prime P.5.1.1
• for containing an expression P.5.1.2
• for having a value P.5.1.2
• functions P.5.1.1
• `Integrate` S.1.Sol.16
• Mathematica G.1.Sol.16, S.1.Sol.16
• `Sort` P.6.Ex.15
• special function evaluations S.3.Ex.9
• the absence of expressions P.5.1.2

Tetrahedral group P.6.Sol.8

Tetrahedron

• eigenfunctions in a ~ G.3.Ex.3
• hyperbolic ~ G.2.3.10
• maximal ~ volume S.1.Ex.46
• morphing ~ G.2.1.5
• recursively subdivided ~ G.2.3.1
• volume of a ~ S.1.Ex.1

Tetraview Riemann surface animation G.2.Ex.21

`Text` G.1.1.1, G.2.1.1

Text

• analyzing ~ P.6.6, N.1.1.5
• fourierized in 2D N.1.5
• fourierized in 3D N.1.5
• Hershey ~ G.1.1.3, G.2.1.2
• in 2D graphics G.1.1.1, G.1.1.1
• in 3D graphics G.2.1.2, G.2.1.2
• in plots G.1.2.1
• printing ~ P.4.1.1
• printing ~ in cells P.4.1.1
• rotated ~ G.1.1.1
• styles in graphics G.1.1.1

Texts

• long-range correlations in ~ N.1.1.5
• subsequences in ~ P.1.Sol.1

`TextStyle` G.1.1.3

Texture

• Fourier-based ~ N.1.Ex.32
• on a double torus G.3.Ex.20
• on knots G.2.3.2, G.3.Ex.17
• on surfaces G.2.Ex.11

Theorem

• Abel-Ruffini S.1.5
• addition ~s for trigonometric functions S.1.4
• addition ~s for elliptic functions S.3.Ex.3, S.3.Ex.4
• arcsine ~ for divisors N.2.Ex.1
• Bertrand's ~ N.1.10.1
• binomial ~ P.5.Ex.8, N.2.3
• Bloch ~ S.3.11, S.3.11
• Cauchy ~ P.1.2.1, N.1.7, N.1.Sol.29
• Cayley-Hamilton ~ P.6.5.3
• central limit ~ N.1.Ex.25, N.2.Sol.6
• classical multinomial ~ N.2.3
• differential binomial ~ S.1.3
• Fibonacci-Binomial ~ N.2.4
• four-color ~ Pr
• fundamental ~ of algebra P.1.2.1
• fundamental ~ of calculus S.1.6.2
• fundamental ~ of number theory N.2.1
• Gauss-Bonnet G.3.Ex.15
• Gauss-Lucas ~ S.3.Ex.18
• generalized multinomial ~ N.2.Ex.14
• geometric ~ proving P.1.2.3, S.1.2.2, S.1.Ex.1
• Hellmann-Feynman ~ N.1.Sol.5
• Hölder's ~ S.1.5
• Khinchin-Levy ~ N.1.1.3
• Kirchhoff's ~ N.1.4
• Kochen-Specker ~ G.2.Sol.17
• Lagrange-Bürmann ~ S.1.Ex.17, S.1.Sol.24, S.3.Sol.22
• Lochs' ~ N.1.1.3
• Newton-Leibniz ~ S.1.6.2, S.1.Ex.33
• Picard's P.2.2.3
• proving in Mathematica S.1.2.3
• proving with quantifier elimination S.1.2.3
• Pythagoraen ~ G.1.1.1
• q-Binomial ~ P.5.Sol.8
• Ramanujan's master ~ S.1.8
• residue ~ P.1.2.1
• Richardson ~ S.1.2.1
• Riesz-Fischer ~ S.1.8
• Schwarz ~ S.1.6.1
• Smith's Sturmian word ~ N.2.Ex.5
• Sturm's ~ S.3.Sol.18
• three gap ~ N.2.1
• Unsöld S.2.6
• Wilson's ~ N.2.3

Theory, Galois ~ S.1.5

Theta functions

• addition theorems for ~ S.3.Ex.12
• graphs of ~ G.1.2.1
• in PDE solutions S.3.Ex.12
• Ramanujan ~ S.3.0

`Thickness` G.1.1.2, G.2.1.2

Thickness

• of lines in 2D graphics G.1.1.2
• of lines in 3D graphics G.2.1.2
• of surfaces G.2.Sol.20
• of thickened curves N.1.Ex.32

Thomas precession S.1.Ex.29

Thomas-Fermi equation N.1.10.1, S.1.Ex.17

Thompson's lamp N.1.Ex.26

`Thread` P.6.4.3

Threading, over arguments P.6.4.3

Three gap theorem N.2.1

Three-body problem N.1.10.1, S.1.Ex.24

`Through` P.3.8

Throw angle, optimal ~ S.1.Ex.10

`Ticks` G.1.1.3, G.2.1.3

Ticks

• customized ~ G.1.Sol.19
• in 2D graphics G.1.1.3
• in 3D graphics G.2.1.3

Tie knots P.1.Sol.1

Tiling

• Kepler ~ P.1.2.2, G.2.3.1
• lozenge ~ G.2.1.5
• octagonal G.2.3.7

Tilings

• Ammann-Beenker ~ G.1.5.5
• aperiodic ~ G.1.5.4, G.1.5.5, G.1.Ex.22, G.2.3.1
• fractal ~ G.1.5.5
• of an L G.1.5.4
• Penrose ~ G.1.5.5
• polyomino ~ G.1.5.4
• quaquaversal ~ G.2.3.1
• spiral ~ N.1.8
• triangle-based ~ G.1.5.4, G.3.Sol.3
• warped ~ G.1.Ex.8

Time

• -dependent differential equations N.1.10.2, N.1.Ex.35, N.1.Ex.36, S.3.3, S.3.5
• current ~ P.4.3.1
• evolution G.2.2.2, S.1.Ex.45
• maximal ~ for a computation P.4.2.2
• maximum ~ for simplifications S.1.1
• used for an evaluation P.3.5
• uses in a session P.4.2.2

`TimeConstrained` P.4.2.2, S.1.1

`Times` P.2.2.2

`TimeUsed` P.4.2.2

`Timing` P.3.5

Timings

• for larger calculations G.2.4
• ideal steak cooking ~ P.1.Sol.1
• of 3D rendering G.2.1.5
• of array constructions P.6.1.1
• of compiled functions N.1.3
• of computations P.3.5, G.2.2.2
• of continued fraction expansions N.1.1.3
• of differentiations S.1.6.1
• of elementary function evaluations N.1.2
• of exact summations S.1.6.6
• of Fourier transforms N.1.5
• of function applications P.3.4
• of functional list manipulations P.6.3.3
• of Gröbnerizations S.1.2.2
• of high-order series expansions S.1.6.4
• of integer arithmetic P.1.2.1
• of large calculations S.1.9.3
• of larger numerical calculations S.3.5
• of linear algebra operations P.6.5.1
• of list creations P.6.4.1
• of machine versus high-precision calculations P.4.3.1, N.1.Ex.23
• of numerical differential equation solving N.1.10.1
• of numerical equation solving N.1.8
• of numerical Fourier transforms N.1.5
• of numerical integrations N.1.7
• of numerical minimization N.1.9
• of numerical root finding N.1.8
• of orthogonal polynomial evaluations S.2.Sol.11
• of packed array arithmetic N.1.1.5
• of polynomial expansions S.1.2.1
• of quantifier elimination S.1.2.3
• of simplifications S.1.1, S.3.1
• of summation P.6.1.1
• of symbolic versus numeric calculations P.6.5.1, G.1.1.1, N.1.4
• of unioning P.6.4.1
• of variable localizations P.4.6.3
• of various list operations P.6.Sol.2
• reproducibility of ~ In

Tippe top P.1.Sol.1

Titchmarsh function S.3.0

Toast, falling buttered ~ P.1.Sol.1

`ToColor` G.1.1.2

`ToExpression` P.4.1.2

`Together` S.1.3

`ToHeldExpression` P.4.1.2

Tolkowsky cut G.2.1.5

Top ten functions used P.6.6

`ToRadicals` S.1.5

Tori

• animation of interlocked ~ P.1.2.4
• chain of ~ G.3.3
• glued on a sphere G.3.Sol.9
• glued together G.3.3
• interlocked ~ G.2.Ex.2, G.3.Ex.15
• made from pieces G.2.Ex.2

Toroidal coordinates S.3.Ex.14

Torus

• chain G.3.3
• cubed ~ G.2.2.1
• double ~ G.3.3
• enclosed by a double ~ S.1.Ex.13
• four ~ G.3.3
• graphics G.2.1.5
• hypocycloidal ~ G.2.3.5
• implicitization of a ~ G.3.Ex.7, S.1.9.3
• implicitly described ~ G.3.3, G.3.Ex.7, S.1.9.3
• interlocked ~ G.3.Ex.15
• made from hexagons G.2.Ex.2
• made from interwoven bands G.2.Ex.2
• mapped onto a ~ G.2.Ex.11
• parametrized ~ P.1.2.2, G.2.Sol.2
• pieces glued together G.2.Ex.2
• six ~ G.3.3
• sketched ~ G.2.Ex.6
• smoothed ~ G.2.Ex.2
• squeezed ~ S.1.2.3
• textured ~ G.2.Ex.2
• twisted ~ G.2.Sol.2
• warped ~ G.2.Ex.2
• with a rough surface G.2.Ex.2, G.2.Sol.2
• with changing polygonal cross section N.1.2
• with wireframe surafce G.2.Sol.2

`ToString` P.4.1.2

Total least-squares N.1.2

Totient function N.2.2

Tower, Eiffel ~ P.1.2.2

Toy, walking ~ P.1.Sol.1

`Tr` P.6.5.1

`Trace` P.4.5

Trace

• comparisons of ~ implementations P.6.5.1
• of matrices P.6.5.1
• of product of Dirac matrices P.6.Ex.9

`Trace` versus `On` P.4.5

Tracing evaluations P.4.5

`TraditionalForm` P.2.1, P.2.1

Traffic jam modeling P.1.Sol.1

Trail systems P.1.Sol.1

Train, relativistic ~ P.1.Sol.1

Trajectories

• chaotic ~ P.1.2.1, N.1.Sol.10
• downhill ~ N.1.Sol.11
• in a oscillating potential N.1.Ex.11
• in a wave N.1.10.1
• in an egg crate potential N.1.Ex.10
• of quantum particles P.1.Sol.1, N.1.10.1
• of thrown stones S.1.Ex.10
• of vortices P.1.2.3, N.1.10.1, N.1.Ex.28, S.3.Ex.3
• potential with orthogonal ~ P.1.Sol.1
• pseudoperiodic ~ P.1.2.1

Transcendental

• solution of a ~ equation S.3.10
• solving ~ equations S.1.5
• solving ~ equations using polynomials N.1.8

Transfer matrix method N.1.Sol.5

Transform

• Fourier~ N.1.5, S.1.8
• Laplace~ S.1.8

Transformation

• Aitken ~ N.1.Ex.6
• Darboux ~ S.2.Ex.9
• general Lorentz ~ S.1.Ex.29
• Kramers-Kronig ~ S.1.6.2
• Liouville ~ S.1.Ex.11, S.3.Ex.17
• Lorentz ~ P.1.Sol.1, P.6.5.1, S.1.Ex.29, S.1.Ex.29
• pretzel ~ G.2.Sol.2
• Tschirnhaus ~ S.3.13

`TransformationFunctions` S.1.1

Transformations

• evaluation as applying ~ P.4.7
• Foldy-Wouthuysen ~ P.1.Sol.1
• modular ~ G.1.1.1, S.1.Ex.18
• sequence ~ N.1.Ex.6
• used by `Simplify` S.1.1

Transition, animation, of a radial-azimuthal ~ G.3.Ex.12

Transitions

• between lattices G.2.3.1
• between Platonic solids G.2.1.5
• dimension ~ G.1.1.1

`TranslateShape` G.2.1.1

Transmission

• through a square well G.3.1
• through layers S.2.Ex.3
• trefoil ~ G.2.Ex.19

`Transpose` P.6.4.1

Transposing matrices P.6.4.1

Transpositions, all possible ~ P.6.4.1

`Trapezoidal` N.1.7

Tree

• binary search ~ G.3.Sol.13
• genealogical ~ P.1.Sol.1
• phylogenetic ~ P.1.Sol.1
• Sierpinski ~ G.2.Ex.22
• simplifications using ~s S.1.Sol.17

Tree form

• of big expressions P.2.3.2
• of expressions P.2.1

`TreeForm` P.2.1

`TreeOfPythagoras` G.1.1.1

Trees

• modeling ~ with L systems G.1.5.9
• pseudorandom ~ P.6.Ex.8
• rooted ~ S.1.Sol.17

Triangle

• -hexagon transition G.2.1.5
• area P.1.2.3, S.1.2.3
• average area of a ~ in a square S.1.9.1
• based tilings G.1.5.4
• eigenmodes of a ~ G.3.Ex.3, G.3.Sol.13
• Heilbronn ~ problem S.1.9.1
• map N.1.Ex.9
• of largest area S.1.Ex.46
• puzzle S.1.Ex.42
• q-Pascal ~ P.5.Sol.8
• right isosceles ~ G.1.5.2
• tilings G.1.Ex.22

Triangles

• contour plots in ~ G.3.1
• filled densely with a curve G.1.5.2
• formed by cubic roots S.1.Ex.22
• formed from five points S.1.Ex.1
• forming polyhedra P.6.0
• generating new theorems about ~ S.1.2.3
• hyperbolic G.1.5.8
• in 3D contour plots G.3.Ex.19
• inequalities for ~ S.1.2.3
• mapping graphics into ~ G.3.Sol.16
• modified Sierpinski ~ G.1.5.1
• nested ~ from PDEs N.1.10.2
• numeration in ~ S.1.Sol.7
• oscillations of ~ G.3.Ex.3
• points and lines in ~ P.1.3
• proving theorems about ~ S.1.2.3
• Pythagoraen ~ G.1.1.1
• shortest path in ~ S.1.Ex.40
• Sierpinski ~ G.1.5.1, N.1.8
• subdivision of ~ G.1.5.4, G.1.Sol.3, G.2.Sol.22
• triangulations of ~ G.3.Sol.3
• with touching vertices P.1.2.2
• with vertices on circles S.1.Ex.46

`TriangularIntegration` S.1.Sol.7

Triangulation

• of a pentagon G.2.3.10
• of polygons G.3.Sol.20
• of surfaces P.1.3, G.2.3.4, G.2.Sol.6, G.3.3
• smooth refinement of a ~ G.2.Ex.6

Tridiagonal, matrix N.1.Ex.5

`Trig` S.1.1

`TrigExpand` P.3.1.1

`TrigFactor` P.3.1.1

Trigonometric functions

• algebraization of ~ S.1.2.2, S.1.9.3
• all ~ P.2.2.3
• autosimplification of ~ P.2.2.4
• converting ~ to exponential functions S.1.4
• converting from ~ S.1.4
• expanding ~ P.3.1.1
• expressed in radicals S.1.Ex.18
• expressed through logarithms and square roots P.2.2.5
• factoring ~ P.3.1.1
• generalized ~ N.1.Ex.2
• in real radicals S.1.Ex.18
• iterated ~ P.2.2.3, G.1.2.1
• nested ~ N.1.3
• periodicity of ~ P.2.2.4
• rewriting ~ P.3.1.1
• special values of ~ P.2.2.4

Trigonometric interpolation N.1.5

`TrigReduce` S.1.4

`TrigToExp` S.1.4

Trinoid, Jorge-Meeks ~ N.1.Ex.19

Trinomial

• coefficient N.2.Ex.17
• theorem G.2.Ex.5

Triple torus

• interlocked ~ G.3.Ex.15
• made from pieces G.2.Ex.2
• sketched ~ G.2.Sol.6

Triptych fractals G.1.Sol.10

Trott's constant P.1.2.3

Truchet pictures

• 3D ~ G.2.3.1
• colored ~ G.1.Ex.21
• hexagonal ~ G.1.5.6
• on a double torus G.3.Ex.20
• square ~ G.1.5.6, N.1.3

`Truchet3D` G.2.3.1

`True` P.5.1.1

True

• functions returning ~ or False P.5.1.1
• the truth value ~ P.5.1.1

`TrueQ` P.5.1.1

Truncation

• for display P.2.3.1
• of a series S.1.6.4
• of approximative numbers N.1.1.1

Truth values P.5.1.1

Tryptich fractal G.1.Ex.10

Tschirnhaus transformation S.3.13

`TubeFunctionalShort` G.2.3.2

Tubes

• along curves G.2.1.3, G.2.3.2, N.1.11.1
• along nondifferentiable curves P.1.2.4
• along random walks G.2.3.2
• constructed from points P.6.Ex.5
• graphic of broken ~ G.2.Sol.1
• intersecting ~ G.3.3
• intertwined ~ G.2.Sol.1
• interwoven ~ G.2.3.1
• inverted ~ array G.2.1.2
• random-closed ~ G.2.3.2

Turing, A. P.4.0

Turning points S.1.Sol.21, S.3.5

TV show, favored ~ G.1.3.1

Two-point Taylor expansion S.1.Ex.1

`TwoOrThreeOrFourOrFiveOrSeven` N.2.Sol.9

`TwoPointTaylorSeries` S.1.Sol.1

Type declarations

• for simplifications S.1.1, S.3.1
• in `Compile` N.1.3

Typeface

• in traditional form P.2.2.1
• used in the GuideBooks In

Types

• explicitly declared ~ S.1.1
• implicitly assumed ~ S.1.2.3
• of fonts and letters P.1.1.2

Typesetting In, P.1.2.3, P.2.1

## U

Ultimate

• laptop P.1.Sol.1
• shortened code G.2.3.10

Umbral calculus N.2.Ex.13, S.1.Ex.2

`UnaliasedFourier` N.1.5

`UnaliasedInverseFourier` N.1.5

Uncertainty relations N.1.5, S.1.Ex.21

Unchangeable, variables P.3.3

Underdetermined linear systems P.6.5.1, N.2.Sol.2, S.1.Sol.13, S.3.Sol.25

Underflow, catching machine ~ N.1.1.1

`Unequal` P.5.1.2

`Unevaluated` P.3.3, P.3.Ex.5, P.4.Ex.2

`Unevaluated`

• in action P.6.4.2, N.1.Sol.21
• limits S.1.Ex.32
• passing arguments ~ P.3.3
• patterns P.5.2.1
• surviving ~ P.4.Sol.2

Uniform

• ~ly distributed random numbers G.1.5.6
• asymptotics S.3.5

Uniformity conjecture S.1.Sol.16

`Union` P.6.3.1, P.6.4.1

`Unique` P.4.6.2

Unique symbol names P.4.6.2

Units

• choice of physical ~ In
• used in the GuideBooks In

`UnitStep` S.1.8

Universal, differential equation S.1.5

Universality, reason of Mathematica's ~ P.2.0

Unlocking chains P.1.Sol.1

`Unprotect` P.3.3

`UnsameQ` P.5.1.2

`Unset` P.3.1.2

Unsöld theorem S.2.6

`UnsortedUnion` S.1.Sol.17

`UpSet` P.3.4

`UpSetDelayed` P.3.4

`UpValues` P.3.4

`Utilities`Annotation` P.4.6.6

Utility packages P.4.6.6

## V

Validated, numerical calculations N.1.1.2

`ValueQ` P.5.1.2

Values

• binomial ~ N.2.Ex.5
• inside `Block` P.4.Ex.9
• internal form of ~ P.3.4
• of expressions P.3.4
• of symbols P.3.4

van Der Corput sequence N.1.7

van der Waal's gas N.1.Ex.12

`VanDerCorputSequence` N.1.7

Vandermonde matrix P.1.2.3

`VandermondMatrix` P.1.2.3

Vardi, I. N.2.Ex.7

`Variables` S.1.2.1

Variables

• assignments to ~ P.3.4
• assumptions about ~ S.1.1, S.1.6.2
• auxiliary ~ P.1.1.2
• change of ~ in differential equations S.1.Ex.11, S.1.Ex.14
• change of ~ in integrals S.1.6.1, S.1.Sol.9
• change of ~ in multidimensional integrals S.1.Sol.35
• change of ~ in ODEs N.1.11.2, S.3.5
• clearing ~ P.3.1.2
• clearing many ~ P.3.1.2
• collision of ~ names P.4.6.5
• context of ~ P.4.6.4
• created inside `Block` P.4.6.2, P.6.Ex.23
• created inside `Module` P.4.6.2, P.6.Ex.23
• creating new ~ P.4.6.2
• dummy ~ P.3.6
• dummy integration ~ P.5.1.2
• elimination of ~ S.1.2.2, S.1.5
• from all packages P.4.6.6
• genericity assumptions about ~ P.4.1.1, S.1.1
• in different contexts P.4.Ex.7
• in differentiation S.1.Sol.32
• in integration S.1.Sol.32
• in packages P.4.6.4
• in polynomials S.1.2.1
• in pure functions P.3.6
• in summation S.1.Sol.32
• inside scoping constructs P.4.6.2
• introducing common ~ S.1.7.1
• localization of ~ P.4.6.3, P.6.Ex.23
• method of separation of ~ S.3.5
• number of ~ in contexts P.4.6.4
• of all contexts P.4.6.6
• protected ~ P.3.3
• removed ~ P.3.1.2
• removing many ~ P.3.1.2
• scoping of ~ in assignments P.4.6.3
• scoping of ~ in integrals S.1.Ex.3, S.1.Sol.17
• scoping of ~ in iterators P.4.6.1
• scoping of ~ in numerical integration N.1.7
• scoping of ~ in subprograms P.4.6.2
• shadowed ~ P.4.6.5
• strange ~ P.4.1.1
• symbolic calculations without ~ P.1.Sol.1
• temporary ~ P.4.6.2
• to avoid P.4.6.3
• unchangeable ~ P.3.3
• unique ~ P.4.6.2

`VariablesTester` P.4.6.5

Variational

• calculations S.1.Ex.8, S.1.Ex.8
• calculus S.1.8

Vase, graphic of a ~ G.2.Sol.1

Vector

• algebra P.6.4.3
• analysis S.1.Sol.29, S.3.Sol.14
• as a list P.5.1.2
• binormal ~ G.2.3.2
• fields N.1.Sol.10
• four ~ P.6.5.1
• normal ~ G.2.3.2
• packed ~ N.1.1.5
• potential ~ S.3.Sol.2
• solving ~ equations S.1.Ex.29
• tangent ~ G.2.3.2
• testing for being a ~ P.5.1.2

`VectorQ` P.5.1.2, P.5.1.2

Vectors, unioning ~ P.6.Ex.12

`VectorUnion` P.6.Ex.12

`Verbatim` P.5.2.1

Verbatim patterns P.5.2.1

Verde-Star identity S.3.2

`VerifyConvergence` N.1.6

Verifying

• integrals S.1.6.2
• solutions of equations S.1.5
• solutions of ODEs S.1.7.1
• special function values S.3.Ex.9

`VerifySolutions` S.1.5

Version-related data P.4.3.1

Vibrating membrane

• arbitrarily-shaped ~ S.3.5
• circular ~ S.3.5
• ellipse-shaped ~ S.3.11
• square-shaped ~ G.3.Ex.3, N.2.Sol.18
• triangular-shaped ~ G.3.Ex.3

Vieta

• polynomial P.1.2.3
• relations S.1.2.2, S.1.5, S.2.Ex.5

View angle G.1.6, G.2.1.5

`ViewCenter` G.2.1.3

Viewing directions, in 3D graphics G.2.1.5

`ViewPoint` G.2.1.3

Viewpoint, in 3D graphics G.2.1.3, G.2.1.5, G.2.3.6, G.2.Ex.15

`ViewPointInAbsoluteCoordinates` G.2.Sol.15

`ViewVertical` G.2.1.3

Virtual matrix P.6.Ex.23

Visible, form of expressions In, P.2.1

Visualizations

• in Mathematica In, G.1.0, G.2, G.3, N.1.11
• in mathematics G.1.0
• of conformal maps G.1.1.1
• of divergent series S.3.Sol.1
• of hydrogen orbitals S.2.Ex.6
• of inequalities P.1.2.3, S.1.Ex.25
• of inverse functions G.2.Sol.21, S.3.Sol.3
• of radiation isosurfaces G.2.2.1
• of vector fields N.1.Sol.10

Visualizations of saddle points G.3.Ex.2

Voderberg

• H. G.1.1.4
• nonagon G.1.1.4
• polygons N.1.8
• spiral N.1.8

Volumes

• of special triangles S.1.Ex.22
• of spheres S.3.Ex.1
• of superspheres S.3.1
• of tetrahedra S.1.Ex.1

Von Neumann neighborhood N.1.Sol.32

Voronoi

• cell G.2.4
• diagram G.1.Ex.15
• regions G.2.4

Vortex

• lattices S.3.Ex.3
• motion P.1.2.3, N.1.10.1, N.1.Ex.28
• points S.1.Sol.5

Vortices, graphics of ~ G.3.1

Voting, d'Hondt ~ P.6.Ex.11

## W

Wagner, R. P.6.5.2

Walk

• Gröbner ~ S.1.2.2
• random ~ P.1.Sol.1, G.1.5.6, G.2.Ex.9, S.3.5

Walking toy P.1.Sol.1

Wallis product S.3.Ex.1

`Walsh` G.1.Sol.12

Walsh function G.1.Ex.12

Wannier functions S.3.11

`WannierW` S.3.11

Waring formula S.2.Ex.5

`WaringFormula` S.2.Sol.5

Warnings

• about using experimental functions P.4.6.6
• about using internal functions N.2.3
• in Mathematica P.4.1.1
• versus errors P.4.1.1

Warped

• tilings G.1.Ex.8
• torus G.2.Ex.2

`WarpedBeamedPlatonicSolid` G.2.3.10

Water

• dripping ~ P.1.Sol.1
• dripping ~ drops P.1.Sol.1
• falling from fountains P.1.Sol.1
• light rays in a ~ drop G.1.Ex.7
• waves P.1.Sol.1

Wave, motion in a ~ N.1.10.1

Wave equation

• 1D ~ N.1.10.2
• 2D ~ N.1.Ex.36
• 3D ~ N.1.Ex.36
• d'Alembert solution of the ~ S.1.6.2
• modeling ~ using Huygens' principle P.1.Sol.1
• nD ~ N.1.Ex.36
• separability of ~ P.1.Sol.1

Wave packet

• formed by superposition S.2.Ex.9
• in a sextic potential S.2.Ex.11
• in a triple well S.3.Ex.8
• in the Calogera potential S.2.Ex.11
• nonspreading ~ S.3.5
• scattered ~ N.1.10.2

Waveguide, crossing ~ N.1.4

Waves

• Bragg-reflected ~ S.3.Ex.13
• Poincaré ~ S.3.Ex.13
• scattering of ~ S.3.Ex.13, S.3.Ex.13
• spherical standing ~ S.1.Ex.29
• spiral ~ S.3.Ex.13
• superposed G.3.1

Weak measurement identity S.1.Ex.41

Web

• connections P.1.Sol.1
• reading data from the ~ N.1.1.5
• resources for problems P.1.Sol.1
• spider ~ G.1.3.1
• stochastic ~ N.1.Ex.9

Web map N.1.Ex.9

Weber-Schafheitlin integrals S.3.5

Website

• ~s about computer algebra A.1.1
• ~s about special functions S.3.0
• ~s related to Mathematica A.1.3
• about orthogonal polynomials S.2.9
• favored ~ In
• of the GuideBooks Pr
• on mathematical constants P.2.2.4
• with Mathematica graphics G.1.0

Wedge, mirror charges in a ~ N.2.Ex.4

Weekday

• dates N.2.Ex.7
• of teaching surprises P.1.Sol.1

Weierstrass

• analytic continuation method S.1.6.6
• function P.1.2.2, G.1.2.2, N.1.1.1
• root finding method N.1.Ex.15
• zeta function S.3.Ex.3
• sigma function S.3.Ex.3
• p function S.3.Ex.3
• p function iterations N.1.1.1

`WeierstrassMinimalSurface` S.1.6.2

`WeierstrassP` N.1.1.1

`WeierstrassSigma` S.3.Ex.3

`WeierstrassZeta` S.3.Ex.3

Weight

• finite difference ~s P.5.Ex.7
• Freud's ~ function S.2.Sol.4
• function of first kind Chebyshev polynomials S.2.7
• function of Gegenbauer polynomials S.2.4
• function of Hermite polynomials S.2.2
• function of Jacobi polynomials S.2.3
• function of Laguerre polynomials S.2.5
• function of Legendre polynomials S.2.6
• function of second kind Chebyshev polynomials S.2.8
• functions for classical orthogonal polynomials S.2.1, S.2.Ex.4, S.2.Sol.2
• matrix S.1.2.2

Weights

• discontinuous ~ S.2.Sol.4
• in linear functionals S.1.6.4
• Newton-Cotes ~ N.1.2
• quadrature ~ N.1.8

Weyl

• sums G.1.3.1
• system N.1.Ex.5

`WhatsGoingOnWithContexts`` P.4.6.5

`Which` P.5.1.4

`While` P.5.1.4

While loop P.5.1.4

Whip, cracking ~ P.1.Sol.1

Whispering gallery modes S.3.Sol.13

Wigner function G.2.2.2, S.3.0

Wild cards in strings P.4.1.1

Wilson's theorem N.2.3

Wine bottle labels, bubbles in ~ P.1.Sol.1

Wire, charged ~ P.1.Sol.1, G.3.Sol.12

Witch house, graphic of a ~ G.2.2.1

`With` P.4.6.2

Withoff, D. G.1.Ex.17

WKB approximation S.1.Ex.21, S.3.5

`WKBCorrection` S.1.Sol.21

Woodpecker, modeling a ~ toy P.1.Sol.1

Words

• different P.6.6
• most frequent ~ P.6.6, N.1.1.5

`WorkingPrecision` N.1.7, S.1.5

World plot G.3.2

Worn stones, graphics of ~ G.2.Sol.1

`WriteRecursive` P.6.3.3

Wronski polynomials S.2.Ex.5

Wronskian P.6.5.1, S.3.13, S.3.Ex.14

`WronskiDet` P.6.Sol.18

`WronskiPolynomial` S.2.Sol.5

www.MathematicaGuideBooks.com Pr

functions.wolfram.com S.3.1

www.wolfram.com Pr

Wynn's epsilon algorithm N.1.Ex.6

`WynnDegree` N.1.6