Further reading

Wolfram Mathematica® provides a collection of ready to use functions, and withits rules of programming it sets the stage like a chess board. Now it dependson you (and your imagination) how to combine these and make your move toattack the problem in hand. It always helps to look at different resources toget ideas of ways to combine the Mathematica functions.

There are excellent books written about Mathematica, for example IlanVardi [5], Stan Wagon [6], Shaw–Tigg [4] and Gaylord, Kamin, Wellin [2] toname a few. The reader is encouraged to have a look at them.

Wolfram demonstration projects http://demonstrations.wolfram.com/

contains many interesting examples of how to use Mathematica in differentdisciplines.

And finally, the Mathematica Help and its virtual book is a treasure, dig it!

R. Hazrat, Mathematica®: A Problem-Centered Approach,Springer Undergraduate Mathematics Series,DOI 10.1007/978-1-84996-251-3, © Springer-Verlag London Limited 2010

Bibliography

[1] R. Gaylord, Mathematica Programming Fundamentals, Lecture Notes,Available in MathSource 100

[2] R. Gaylord, S. Kamin, P. Wellin, An introduction to programming withMathematica, Cambridge University Press, 2005. 146, 184

[3] S. Rabinowitz, Index to Mathematical problems 1980–1984, Math pro Press.1992. viii

[4] W. Shaw, J. Tigg, Applied Mathematica, Addison-Wesley Publishing, 1994.184

[5] I. Vardi, Computational Recreations in Mathematica, Addison-Wesley Pub-lishing, 1991. 62, 92, 184

[6] S. Wagon, Mathematica in Action, Springer-Verlag, 1999. 146, 184

[7] E. Weisstein, MathWorld, http://mathworld.wolfram.com/. 53

R. Hazrat, Mathematica®: A Problem-Centered Approach,Springer Undergraduate Mathematics Series,DOI 10.1007/978-1-84996-251-3, © Springer-Verlag London Limited 2010

Index

Abs, 62Accumulate, 91Algebraic, 56Alt+., 9And, 55anonymous function, 23Apart, 10Append, 28, 59AppendTo, 59Apply, 48, 108Array, 129AxesStyle, 142

Background, 142BarChart, 31, 44Binomial, 8Block, 118Boolean expression, 54Boolean function, 35Booleans, 56

Cases, 102Clear, 13Cmd+., 9Coefficient, 71CoefficientList, 68Complement, 59Complexes, 56ContourPlot, 135ContourPlot3D, 153Count, 171

defining variables, 12

Degree, 12Delete, 28derivation, 163Det, 129DictionaryLookup, 43Divisible, 23Divisor, 39Divisors, 51Do, 72Dot, 129Drop, 26Dynamic, 16dynamic variable, 15D[], 163

Eigenvalues, 134Eigenvectors, 134EvenQ, 36Exist, 57Expand, 9

Factor, 9FactorInteger, 6Fibonacci, 21Fibonacci number, 21FillingStyle, 142FindInstance, 158FindRoot, 158First, 26FixedPointList, 87Flatten, 27, 83Fold, 90FoldList, 90, 146

R. Hazrat, Mathematica®: A Problem-Centered Approach,Springer Undergraduate Mathematics Series,DOI 10.1007/978-1-84996-251-3, © Springer-Verlag London Limited 2010

Index 187

For, 78ForAll, 57Frame, 142FrameLabel, 142FrameStyle, 142FromDigits, 37FullForm, 47FullSimplify, 4function, 19– multi def’s., 113– with condition, 112

Graphics, 147graphics, 135GraphicsColumn, 145GraphicsGrid, 145, 150GraphicsRow, 145GraphPlot, 94

Head, 48

If, 61if statement, 61Implies, 57Inner, 93inner product, 127Input, 77Insert, 28IntegerDigits, 37IntegerExponent, 111IntegerQ, 36Integers, 56Integrate, 163integration, 163Intersection, 58Inverse, 129

Join, 60

Last, 26Length, 35LengthWhile, 89Line, 147list, 25listable function, 32ListAnimate, 154ListPlot, 149loop, 72– Do-loop, 72– For-loop, 78– nested loop, 81– While-loop, 75

Manipulate, 17

Map, 33, 107MatchQ, 100matrix, 128MatrixForm, 129Maximize, 166MaxIterations, 97MaxRecursive, 145MemberQ, 78, 105Min, 52Minimize, 166Mod, 8Module, 118Most, 26

N, 3NestList, 84NestWhile, 86NestWhileList, 86Next, 84NIntegrate, 163NMaximize, 166NMinimize, 166Norm, 127Not, 55NProduct, 71NSolve, 158NSum, 69

OddQ, 36Or, 55Outer, 56, 93

palindromic, 43ParametrixPlot, 135ParametrixPlot3D, 153Partition, 177pattern matching, 100perfect number, 51Permutations, 98Piecewise, 63, 143Plot, 135Plot3D, 153PlotPoints, 145PlotStyle, 142PolarPlot, 135Prepend, 28Prime, 6prime number, 2PrimePi, 7Primes, 56Print, 30Product, 70pure function, 23

188 Index

Quiet, 97quit kernel, 9Quotient, 9, 87

RandomInteger, 34Range, 28Rationals, 56RealDigits, 146Reals, 56RecursionLimit, 123Reduce, 158RegionPlot, 135RegionPlot3D, 153ReplaceAll, 97ReplaceList, 107ReplaceRepeated, 97Rest, 26Reverse, 28, 37RotateLeft, 28RotateRight, 28rules, 96

Select, 34, 41Short, 45Show, 141Simplify, 4Slider, 16social number, 90Solve, 158solving equation, 158Sort, 28square free, 41StringDrop, 45

StringLength, 45StringReplace, 45StringReverse, 43, 44StringTake, 45sublime number, 53Sum, 65

Table, 28, 83Take, 26TakeWhile, 89Tally, 60Thread, 52three-dimensional graph, 153Thue-Morse seq., 98, 151Timing, 73Together, 10ToString, 45Transpose, 93TreeForm, 49TrigExpand, 11TrigFactor, 11two-dimensional graph, 135

Union, 40, 58

vector, 127

weird number, 53Which, 61which statement, 61While, 75With, 118