# Mathematical Methods


• Education
The Personal Fonemate & Other Cautionary Tales, a discussion of appropriate and inapproriate uses of computers in teaching.
• Education 2
The Physical Pendulum in an Advanced Undergraduate Course in Mechanics, a paper that appeared in the journal Computers in Physics 8, 416-419 (1995). It discusses studies of the pendulum and computer algorithms to solve the equations of the pendulum.
• Error Propagation
Propagation of errors of precision using Mathematica and the Experimental Data Analyst package. This brief discussion is suitable for students at all levels who need to do a fair amount of error propagation calculations.
• Fitting Techniques
A brief introduction to fitting data to models. The emphasis is on least-squares techniques. The level is somewhat beyond what we expect from a typical first year student.
• Heat Equation
Solving partial differential equations (PDEs) by computer, particularly the heat equation. The emphasis is on the explicit, implicit, and Crank-Nicholson algorithms. Other types of PDE's are discussed, including the Schrödinger equation. Used by upper-year physics majors and specialists.
• Learning About UNIX-GNU / Linux
The link to the left provides access to five Modules on the UNIX-GNU/Linux computing environment. Each Module has been used as class notes for a 2 hour discussion on this computing environment.
• Maple Libraries
A tutorial on library creation and maintenance for the Maple programming language.
• Monte Carlo Simulation
Discusses the computer generation of events obeying some statistical model using Monte Carlo simulation. Brief reviews of Special Relativity and High Energy physics are also provided, and a small discussion of the generation of pseudo-random numbers is included. Used by upper year physics majors and specialists.
• The Multipole Expansion
A multipole expansion is a mathematical series representing a function that depends on angles—usually the two angles on a sphere. These series are useful because they can often be truncated, meaning that only the first few terms need to be retained for a good approximation to the original function. Multipole expansions are very frequently used in the study of electromagnetic and gravitational fields, where the fields at distant points are given in terms of sources in a small region.
• Visualisation and Transformation of Data
A brief discussion of techniques for exploration of data with visualization and transformation. Not terribly technical, but does examine techniques often considered to be advanced.

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