MATHEMATICS, PHYSICS & CHEMISTRY WITH WOLFRAM LANGUAGE

The Wolfram language is the programming language of Mathematica, used increasingly by scientists due to its ease of learning and user-friendliness. This book focuses on applications of the Wolfram language to applied mathematics, physics and chemistry. Topics discussed are broad and comprehensive, from differential equations and special functions to fractals and chess, from electromagnetism and optics to relativity and black holes. There is also extensive coverage of quantum theory and quantum chemistry, and the book is peppered with more than 200 color graphics to aid visualization of these concepts. The program codes are provided online as Mathematica notebooks, allowing readers to modify them and manipulate the graphics in real time. This book should be a valuable resource for researchers, educators and students in science and computing who can profit from a more interactive form of instruction.

Contents:

• Preface
• About the Author
• Introduction to the Wolfram Language:
  • Basic Operations in Mathematica
  • Manipulate
  • Lists
  • Functions and Plots
  • Other Types of Plots
  • 2D Graphics
  • 3D Graphics
  • Wolfram Alpha
  • Random Numbers
  • Binomial Distributions
  • Matrices
  • Demonstrations
• Mathematics: Some Applications of the Wolfram Language to Applied Mathematics:
  • Complex Variables
  • The Gamma Function
  • The Error Function
  • Exponential Integral
  • The Dirac Deltafunction
  • Spherical Trigonometry
  • First-Order Differential Equations
  • Second-Order Differential Equations
  • Partial Differential Equations
  • Bessel Functions
  • Spherical Bessel Functions
  • Legendre Polynomials
  • Spherical Harmonics
  • Special Functions using Leibniz's Product Rule
  • Confluent Hypergeometric Functions
  • Special Functions
  • Expansions of Functions
  • Asymptotic Expansions
  • Closest Packing of Spheres
  • Fractals
  • Group Theory
  • Prime Numbers
  • The Riemann Zeta Function
  • Topology
  • Los Alamos Chess
• Physics: Electromagnetism:
  • Electrical Circuits
  • AC Circuits
  • AC Circuits (Continued)
  • Electric and Magnetic Fields
  • Maxwell's Equations
  • Electromagnetic Radiation
  • Optics
  • Dielectrics
• Physics: Quantum Theory I, Principles:
  • Fundamental Principles
  • The Harmonic Oscillator
  • The Hydrogen Atom
• Physics: Quantum Theory II, Applications:
  • Exact Solutions of the Schrödinger Equation
  • Approximate Solutions of the Schrödinger Equation
  • Nuclear and Particle Physics
  • Quantum Computers
• Physics: Further Topics:
  • Relativity
  • Astronomy and Astrophysics
  • Mechanics
  • Fluid Mechanics
  • Semiconductors
  • Superconductivity
  • Solitons
• Theoretical Chemistry:
  • The Periodic Table
  • Atomic Structure
  • Atomic Orbitals
  • The Helium Atom
  • Complex Atoms
  • Molecules 1
  • Molecules 2
  • Molecules 3
  • Molecules 4
• Instructions for Accessing Online Supplementary Material
• Index

Readership: Researchers, faculty, instructors, graduate and undergraduate students in mathematics, physics, chemistry and computing, and especially scientific fields and courses related to quantum theory. Those interested in active learning and use of technology in science education.

Dr S M Blinder is Professor Emeritus of Chemistry and Physics at the University of Michigan, USA. He obtained a PhD in chemical physics from Harvard University under the direction of W E Moffitt and J H Van Vleck (Nobel Laureate in Physics, 1977). He has nearly 200 research publications and 8 books in several areas of theoretical chemistry and mathematical physics. He was the first to derive the exact Coulomb (hydrogen atom) propagator in Feynman's path-integral formulation of quantum mechanics. He has taught a multitude of courses in chemistry, physics, mathematics and philosophy, mostly on the subject of quantum theory. In earlier incarnations, he was a Junior Master in chess and an accomplished cellist. He is currently a telecommuting senior scientist with Wolfram Research, and lives with his wife in Ann Arbor.

'This book will be of great help for instructors teaching math, physics and chemistry classes. While the topics covered can be found in other textbooks, the uniqueness of this book lies in translating them into interactive Mathematica code. This makes it possible for students and instructors to interact with the problem dynamically in a manner that is not possible when using more traditional graphical aids. This compute-to-learn approach can be thought of as a form of active learning. In the process, it also provides an intuitive learn-by-example way of teaching the reader how to use coding in order to solve and provide graphic interpretation for a wide range of mathematical and scientific problems. The fact that the code is provided and explained as an integral part of the text is very helpful and would make it possible for the reader to experiment with altering the code and optimizing it to the reader's needs. I thoroughly enjoyed reading it.' - Eitan GevaProfessor, University of Michigan, USA

'The Wolfram Language is a unique knowledge-based symbolic language that grew out of, and now powers, the Mathematica system. It's a computational language with applications across a vast range of fields and covering all forms of technical computing. A language long 'spoken' by respected scientific practitioner, academician, author and Wolfram Senior Scientist S M Blinder. Based on his hundreds of published submissions to the Wolfram Demonstrations Project, and expertise applied as the technical reviewer for thousands more, I can't imagine a more satisfyingly practical and informative collection of math, physics, and chemistry content gathered in one volume, and no better guide than Professor Blinder as your computational concierge.' - Andre KuzniarekWolfram Research, USA