INSEAD Library

Includes bibliographical references and index

CD available inside back cover

Digitized

The Mathematica Guide Book For Symbolics Contents 0. Introduction and Orientation xix CHAPTER 1 Symbolic Computations 1.0 Remarks 1 1.1 Introduction 1 1.2 Operations on Polynomials 13 1.2.0 1.2.1 1.2.2 1.2.3 Remarks 13 Structural Manipulations on Polynomials 13 Polynomials in Equations 25 Polynomials in Inequalities 50 1.3 Operations on Rational Functions 78 1.4 Operations on Trigonometric Expressions 88 1.5 Solution of Equations 94 1.6 Classical Analysis 129 1.6.1 1.6.2 1.6.3 1.6.4 1.6.5 1.6.6 Differentiation 129 Integration 156 Limits 184 Series Expansions 189 Residues 220 Sums 221 1.7 Differential and Difference Equations 233 1.7.0 1.7.1 1.7.2 1.7.3 Remarks 233 Ordinary Differential Equations 234 Partial Differential Equations 257 Difference Equations 260 1.8 Integral Transforms and Generalized Functions 266 1.9 Additional Symbolics Functions 294 1.10 Three Applications 298 1.10.0 Remarks 298 1.10.1 Area of a Random Triangle in a Square 298 1.10.3 Implicitization of a Trefoil Knot 321 Exercises 330 Solutions 371 References 749 CHAPTER Classical Orthogonal Polynomials 2.0 Remarks 803 2.1 General Properties of Orthogonal Polynomials 803 2.2 Hermite Polynomials 806 2.3 Jacobi Polynomials 816 2.4 Gegenbauer Polynomials 823 2.5 Laguerre Polynomials 832 2.6 Legendre Polynomials 842 2.7 Chebyshev Polynomials of the First Kind 849 2.8 Chebyshev Polynomials of the Second Kind 853 2.9 Relationships Among the Orthogonal Polynomials 860 2.10 Ground-State of the Quartic Oscillator 868 Exercises 885 Solutions 897 References 961 2 CHAPTER 3 Classical Special Functions 3.0 Remarks 979 3.1 Introduction 989 3.2 Gamma, Beta, and Polygamma Functions 1001 3.3 Error Functions and Fresnel Integrals 1008 3.4 Exponential Integral and Related Functions 1016 3.5 Bessel and Airy Functions 1019 3.6 Legendre Functions 1044 3.7 Hypergeometric Functions 1049 3.8 Elliptic Integrals 1062 3.9 Elliptic Functions 1071 3.10 Product Log Function 1081 3.11 Mathieu Functions 1086 3.12 Additional Special Functions 1109 3.13 Solution of Quintic Polynomials 1110 Exercises 1125 Solutions 1155 References 1393 Index 1431