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MATHEMATICA FOR PHYSICS
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WHAT: A new book for doing Physics with Mathematica
TITLE: MATHEMATICA FOR PHYSICS
AUTHORS: Robert L. Zimmerman (U. of Oregon)
Fredrick I. Olness (Southern Methodist University)
with a foreword by Stephen Wolfram
LENGTH: 436 pages
ISBN 0-201-53796-6
For ordering information, call 1-800-822-6339
Addison-Wesley Publishing Company
MathSource Number: 0206-862
Communication with the authors:
Fredrick I. Olness: olness@mail.physics.smu.edu
Robert L. Zimmerman: bob@zim.uoregon.edu
TOPICS: General Physics
Classical Mechanics
Electrostatics
Quantum Mechanics
Oscillation Systems (Linear and Non-Linear)
Special Relativity
General Relativity
Cosmology
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GENERAL AUDIENCE
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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.
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About: MATHEMATICA FOR PHYSICS
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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.
Highlights include:
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.
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Table of contents
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Chpt 1: Getting Started
Chpt 2: General Physics
Chpt 3: Oscillating Systems
Chpt 4: Lagrangians and Hamiltonians
Chpt 5: Electrostatics
Chpt 6: Quantum Mechanics
Chpt 7: Relativity and Cosmology
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BEST FEATURES OF THE BOOK
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With Mathematica, the entire approach to problem solving can be
drastically changed. We give some brief examples.
DOUBLE PENDULUM: This is a topic that is generally treated as an
"advanced" topic. With Mathematica, the solution is relatively
straightforward. Once the solutions is 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 wavefunctions, and consider the disastrous
consequences of choosing a non-integral value for the principal
quantum number.
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BIO STATEMENT
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Robert Zimmerman is a Professor of Physics and research
associate in the Institute of Theoretical Science at the
University of Oregon. He has written papers on Mathematical
Physics, Elementary Particles, Astrophysics, Cosmology, and
General Relativity. He has taught graduate courses in
Mathematical Physics, Theoretical Mechanics, Electrodynamics,
Quantum Mechanics, General Relativity and Cosmology. He received
his Ph.D. from the University of Washington.
Fredrick Olness is an Assistant Professor of Physics at Southern
Methodist University in Dallas Texas. His research is in
Theoretical High Energy Physics and he studies the Quantum
Chromodynamic (QCD) theory of the strong interaction. He
received his Ph.D. from the University of Wisconsin, received an
SSC Fellowship in 1993, and is a member of the CTEQ
collaboration--a novel collaboration of theorists and
experimentalists.