Visual Mathematics, Illustrated by the TI-92 and the TI-89

Here is a selection of basic and advanced mathematics, unified by common themes and supported by graphical and formal calculations provided by the TI-92, the TI-92 Plus, and the TI-89 graphic calculators. The topics of mathematics covered are those of higher level university courses for students of mathematics, computer science, physics, engineering and other sciences. The subjects are treated in rigorous mathematical manner - almost all proofs are presented in detail - and are accompanied by screen-shot examples and short, complete calculator programs which illustrate the details. Topics covered are in the fields of classical analysis and linear algebra and in the overlap of the two. Chapters are devoted to discrete dynamical systems, differential equations, Fourier series, and approximation and interpolation theory, which serve as comprehensive and compact introductions to these fields. For example, the chapter on Fourier series gives a standard basic introduction with convergence issues, Cesaro summability, a Hilbert space perspective, discrete and Fast Fourier Transforms, and an introduction to wavelets. For each topic, there are illustrative programs which allow the reader to explore or to "Play" with the concepts introduced. While linearity concepts are used in the earlier chapters, the full toolkit of linear algebra is applied in the later coverage of orthogonal polynomials. Gauss quadrature, the decomposition or factorization of linear operators and matrices, and eigenvalue techniques. Some of the earlier material is then recast in a vector space setting. The book is really quite different from others which seek to integrate mathematics and technology. Unlike some "how-to" books which are based on Computer Algebra System JCAS) software, the mathematics is the primary emphasis here. The user of this book will have all the theorems and proofs necessary for learning new mathematics and will also be able to use the calculator technology to actively "see" and "touch" the mathematics at hand.