Essential Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs.

The first section, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. Its aim is to provide the reader with Mathematica proficiency quickly and efficiently.

The second section covers a broad range of applications in physics, engineering and applied mathematics, including Egyptian Fractions, Happy Numbers, Mersenne Numbers, Multibases, Quantum Harmonic Oscillator, Quantum Square Potential, Van der Pol Oscillator, Electrostatics, Motion of a Charged Particle inan Electromagnetic Field, Duffing Oscillator, Negative and Complex Bases, Tautochrone Curves, Kepler’s Laws, Foucault’s Pendulum, Iterated Function Systems, Public-Key Encryption, and Julia and Mandelbrot Sets.

The first part - examples, not long explanations. The second part-attractive applications.

From the reviews:

"Mathematica is a software package that makes mathematics easier for scientists and engineers. … The range of examples is amazing … . The book is well written … . Summing Up: Highly recommended. Upper-division undergraduates through professionals." (P. Cull, CHOICE, Vol. v4 (3), November, 2007)

"The book ensures a thorough training in Mathematica, which is one of the most popular software packages … . The structure of the volume was designed to cover the objectives of different groups of readers, with various levels of knowledge, from beginners needing assistance for the basic exploitation of the package, to experienced users focusing on specific types of problems. … reflects a considerable teaching experience which also recommends it as a valuable companion for educators interested in preparing or upgrading lecture notes and seminars." (Octavian Pastravanu, Zentralblatt MATH, Vol. 1134 (12), 2008)