Preface

This section provides the general introduction to vector theory including inner and outer products. It also serves as a tutorial to operate with vectors using Mathematica. Although vectors have physical meaning in real life, they can be uniquely identified with an ordered tuple of real (or complex numbers). The latter is heavily used in computers to store data as arrays or lists.

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Introduction to Linear Algebra with Mathematica

Glossary

Preface

This section presents some properties of the most remarkable and useful in numerical computations Chebyshev polynomials of first kind \( T_n (x) \) and second kind \( U_n (x) .\) Both Chebyshev polynomials are eigenfunctions of the corresponding singular Sturm--Liouville problems. Other two Chebyshev polynomials of the third kind and the fourth kind are not so popular in applications.

Applications of Chebyshev polynomials

  1. Clenshaw, C.W., Norton, H.J.: The solution of nonlinear ordinary differential equations in chebyshev series. The Computer Journal, 1963, {\bf 6}, Issue 1, 88–92; https://doi.org/10.1093

 

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