Index of the GuideBooks

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

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

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

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