*Mathematica* is a powerful symbolic
manipulator which provides very useful tools for solving problems and exploring
the results. Its symbolic and graphical tools allow the student to focus more
upon physics than upon algebra. A collection of notebooks has been prepared
for several important topics and you are encouraged to use these notebooks as
templates for the solution of other problems.

To view the notebooks without running *Mathematica* itself, you
should obtain a copy of *MathReader*.
We also offer a course entitled *Essential
Mathematica for Students of Science*.

Most of these notebooks were originally written in 1996, but have been
extensively revised in subsequent years; please check the dates to make sure that your
copies are current. The present versions were prepared using *Mathematica 4.0,*
but most should still run under *Mathematica 3.0* with little or no
change. Some notebooks may be temporarily unavailable, depending upon the
choice of homework problems. For some notebooks postscript output is provided
for students without access to *Mathematica*.

*Last updated: Mar. 14, 2002*

**ReviewThermodynamics**nb pdf- Provides a brief review of thermodynamics and some of the techniques for
derivation of thermodynamic relationships.
*Revised Feb. 15, 2002*. **StatisticalPostulate**nb pdf- The basic postulates of statistical mechanics are used to derive and
explain the laws of thermodynamics. Our approach relies upon the
information-theory concept of disorder and identifies the disorder within a
statistical ensemble with thermodynamic entropy.
*Revised Feb. 19, 2002*. **Ensembles**nb pdf- Two methods for construction of canonical probability distributions are
presented. The first is based upon thermal interaction between a sample
and a much larger reservoir of heat. The second maximizes entropy
subject to constraints upon mean values of energy and perhaps other variables.
*Revised Mar. 14, 2002*. **Semiclassical**nb pdf- The properties of ensembles composed of points in classical phase space are
studied. Two important theorems, equipartition and virial, are
developed. Correspondence with quantum mechanics is used to establish a
fundamental cell size in phase space that permits computation of finite
entropy for semiclassical ensembles. Applications are made to ideal
gases and diatomic molecules.
*Revised Apr. 15, 2002*. **Fluids**nb pdf- The effects of intermolecular interactions upon the mechanical and thermal
equations of state are studied for classical fluids. The temperature
dependence of the second virial coefficient, which governs these effects for
dilute systems, is derived for realistic potentials and explained using a
model from which one can also derive the van der Waals equation. Next we
discuss the measurement of the pair correlation function in denser systems
using X-ray or neutron scattering. Finally, the relationship between
correlations and density fluctuations is developed.
*Revised Apr. 15, 2002*. **IdealQuantumGases**nb pdf- The indistinguishability of identical particles has profound effects at low
temperatures and/or high densities where quantum mechanical wavepackets
overlap appreciably. The occupation representation is used to study the
statistical mechanics and thermodynamics of ideal quantum gases satisfying
Fermi-Dirac or Bose-Einstein statistics. This notebook concentrates upon
formal and conceptual developments, while the auxiliary notebook
*occupy.nb*,*fermi.nb*, and*bose.nb*provide technical support.*Revised Apr. 15, 2002*.

- stirling.nb
- Derives an asymptotic expansion of the gamma function and investigates the accuracy of Stirling approximations.
- binomial.nb
- Investigates some of the properties of the binomial, Poisson, and Gaussian
distributions.
*Revised Jan. 11, 2000*. - spin-half.nb
- Uses the microcanonical ensemble to investigate the paramagnetism of
spin-1/2 systems. The physical interpretation of the phenomenon of negative
spin temperature is discussed in some detail.
*Revised Jan. 11, 2000*. - hotherm.nb
- Uses the microcanonical ensemble to investigate the thermodynamics of
independent oscillators. The Einstein model of lattice vibrations is presented.
*Revised Jan. 11, 2000*. - ising1d.nb
- The combinatorial method is used to solve the Ising model for a
one-dimensional chain of spin-1/2 atoms in an external magnetic field with
nearest neighbor spin-spin interactions.
*Revised Jan. 11, 2000*. - Weiss.nb
- Uses a mean-field model to study spontaneous magnetization for ferromagnetic
systems, with particular attention to behavior near the critical point.

*Revised Jan. 3, 2001*. - thermo2.nb
- Uses the canonical ensemble to investigate the thermodynamics of binary
systems. The Schottky effect is discussed as a manifestation of the
quantization of the excitation-energy spectrum.
*Revised Jan. 11, 2000*. - paramag.nb
- Investigates the thermodynamics of paramagnetism for arbitrary spin using
the canonical ensemble. The classical limit is developed also.
*Revised Mar. 9, 2000*. - debye.nb
- Compares the Debye and Einstein models of lattice vibrations of a crystal.
The Grueneisen model of expansivity is also developed.
*Revised Mar. 9, 2000*. - planck.nb
- Compares the Planck model of black-radiation with earlier classical
models. Also discusses Hawking radiation from black holes.
*Revised Jan. 11, 2000*. - rotvib.nb
- Studies rotational and vibrational contributions to the heat capacity of
ideal gases composed of diatomic molecules.
*Revised Jan. 11, 2000* - virial.nb
- The second virial coefficient for classical gases is evaluated for
realistic intermolecular potentials.
*Revised Jan. 11, 2000* - vdwaals.nb
- Properties of the van der Waals gas, including the Maxwell construction,
are developed.
*Revised Jan. 11, 2000* - occupy.nb
- Investigates the statistics of occupation numbers for the Fermi-Dirac,
Bose-Einstein, and Maxwell-Boltzmann distributions. The dependencies on both
temperature and chemical potential are evaluated.
*Revised Jan. 11, 2000* - fermi.nb
- Investigates the thermodynamics of ideal nonrelativistic Fermi-Dirac
gases.
*Revised Jan. 11, 2000* - bose.nb
- Investigates the thermodynamics of ideal nonrelativistic Bose-Einstein
gases.
*Revised Jan. 11, 2000*