Mathematica is computer algebra software that can perform symbolic computation as well as numerical computation, graphics, programming, and more. This guide provides a quick introduction on how to use Mathematica, covering releases 7, 8, and 9. Readers will find the basic information that almost every user of the software should know. Each chapter defines relevant commands, addresses their syntax, and incorporates basic examples. Five appendices are also included that explain how to work in the Mathematica worksheet environment, use certain input features, create customized Mathematica packages, learn more about Calculus, and work with scientific units and constants.
Getting Started with Mathematica, second edition 2005, 231pp. ISBN 0471478156, Dewey 510.285536 There is a 2009 third edition (224 + xiv pages, ISBN 978-0-470-45687-3, https://www2.bc.edu/gerard-keough/pub...). The authors' online documentation that was on their Boston College webpage as of Dec 2019, is gone as of June 2020.
Quick intro to many of Mathematica's abilities.
Much but not all of the syntax the book presents also works in the free online Wolfram Alpha, https://www.wolframalpha.com/