Mathematica for Physics, 2nd Edition

By Robert L. Zimmerman

Fredrick I. Olness

Foreword by Stephen Wolfram

Publisher:  Addison Wesley Publishing

 

This book is intended for the advanced undergraduate and graduate physics students taking core courses in the physics curriculum. The students are shown how to use Mathematica to solve the standard problems in physics. Since we cover the canonical problems from the core courses, the students can practice with our solutions, and then modify these solutions to solve additional problems.  The students can focus on the physics, and leave the algebraic complications to Mathematica. This book takes the reader beyond the "textbook" solutions by challenging the students to cross check the results using the wide variety of Mathematica's analytical, numerical, and graphical tools.

      The downloads for the chapters are given below.  Version 4 have been tested for the Mathematica version 4 and Version 5 work for the Mathematica version 5

 

Chapters: (These notebooks can also be found at http://www.physics.smu.edu/~olness)

 

Chapter 1: Getting Started                             Version 4         Version 5

Chapter 2: General Physics                            Version 4         Version 5

Chapter 3: Oscillating Systems                       Version 4         Version 5

Chapter 4: Nonlinear Systems and Chaos      Version 4          Version 5

Chapter 5: Discrete Systems and Chaos         Version 4         Version 5

Chapter 6: Lagrangians and Hamiltonians      Version 4         Version 5

Chapter 7: Orbiting Bodies                              Version 4         Version 5

Chapter 8: Electrostatics                                 Version 4         Version 5

Chapter 9: Quantum Mechanics                      Version 4         Version 5

Chapter 10: Relativity and Cosmology            Version 4         Version 5

 

Press to Download User-Defined Procedures

 

Authors Address:

bob@zim.uoregon.edu                  

http://darkwing.uoregon.edu/~phys600/

olness@mail.physics.smu.edu    

http://www.physics.smu.edu/~olness

 

General Information and Ordering:

ISBN: 0-8053-8700-5

Mathematica Information Center: http://library.wolfram.com/infocenter/Books/3588

http://www.aw-bc.com/catalog/academic/product/0,4096,0805387005,00.html

http://www.amazon.com

 

Audience:

This book is intended for the advanced  undergraduate and graduate physics student taking core courses in the physics curriculum.  We expect this text to be a supplement to the standard course text. The student would use this book to get ideas on how to use Mathematica to solve the problems assigned by the instructor.

 

Since we cover the canonical problems from the core courses, the student can practice with our solutions, and then modify our solutions to solve the particular problems assigned. This should help the student move up the Mathematica learning curve quickly.

 

Highlights:

* Provides Mathematica solutions for the canonical problems in the physics curriculum.

* Covers essential problems in: Mechanics, Electrodynamics, Quantum Mechanics, Special and

* General Relativity, Cosmology, Elementary Circuits, Oscillating Systems.

* Uses the power of Mathematica to go beyond "textbook" solutions and bring the problems alive with animations, and other graphical tools.

* Emphasizes the graphical capability of Mathematica to develop the reader's intuition and visualization in problem solving.

* Introduces the reader to the aspects of Mathematica that are particularly useful for physics.

 

Overview

Mathematica for Physics chooses the canonical problems from the physics curriculum, and solves these problems using Mathematica. This book takes the reader beyond the "textbook" solutions by challenging the student to cross check the results using the wide variety of Mathematica’s analytical, numerical, and graphical tools. Throughout the book, the complexity of both the physics and Mathematica is systematically extended to broaden the tools the reader has at his or her disposal, and to broaden the range of problems that can be solved. As such, this text is an appropriate supplement for any of the core advanced undergraduate and graduate physics courses. This electronic supplement contains the initialization files for all chapters, and selected solutions and examples.

About: Mathematica for Physics:

Mathematica is a powerful mathematical software system for students, researchers, and anyone seeking an effective tool for mathematical analysis. Tools such as Mathematica have begun to revolutionize the way science is taught, and research performed. Now there is a book specifically for students and teachers of physics who wish to use Mathematica to visualize and display physics concepts and to generate numerical and graphical solutions to physics problems.

 

Mathematica for Physics chooses the canonical problems from the physics curriculum, and solves these problems using Mathematica. This book takes the reader beyond the "textbook" solutions by challenging the student to cross check the results using the wide variety of Mathematica's analytical, numerical, and graphical tools. Throughout the book, the complexity of both the physics and Mathematica is systematically extended to broaden the tools the reader has at his or her disposal, and to broaden the range of problems that can be solved.

 

As such, this text is an appropriate supplement for any of the core advanced undergraduate and graduate physics courses.

 

Example from the Book:

DOUBLE PENDULUM

This is a topic that is generally treated as an "advanced" topic. With Mathematica, the solution is relatively straightforward. Once the solutions are obtained, the textbooks try to describe (in words) the general properties of the system, and the normal modes. (In particular, the property that the energy is transferred back and forth between the two segments of the pendulum.) With the animation capability of Mathematica, we do not need to lead the student to these conclusions, but we can point them in the general direction, and let them discover these results on their own by varying the amplitudes of the separate normal modes.

 

E&M BOUNDARY VALUE PROBLEMS

For the beginning student, it is easy to become overwhelmed by boundary value problems. With the power of Mathematica, it is easy to show how straightforward these solutions are--especially with the help of the different coordinate systems built into Mathematica. When the student finishes the problem with pen and paper, they have only a set of formulas that may mean very little to the student. With Mathematica, we encourage the student to plot the final solution so that they can verify visually if the boundary conditions are satisfied. This techniques encourages the student to think about the solution, and not simply grind out the math.

 

HYDROGEN ATOM

In the standard solution of the hydrogen atom, the student is completely lost in the mathematics. Mathematica is able to recognize that the solution of the radial equation is a Laguerre polynomial, assemble the constants to form the principal quantum number, and plot the solutions. The student then has the energy and the curiosity to numerically investigate the behavior of the wave functions, and consider the disastrous consequences of choosing a non-integral value for the principal quantum number.

 

Additional Notes:

 

     What new subjects would you like to see in the third edition (bob@zim.uoregon.edu)?