Issues in teaching physics

• Concepts
• Connections
• Problem solving

Advantages of using Maple (the Maple operator)

• less time on math allowing us
• more time to cover concepts, connections, problem solving
• more interesting "real" problems
• visualization of "physics"
• no need to "do algebra" associated with vector calculus

Resources:

• Books:
  While there are numerous books on teaching electromagnetism to undergraduates, there appear to be none which attempt to heavily apply computers to the topic. In addition, there appears to be no books on using Maple / Mathematica / Matlab in electromagnetism. Some books which might be used with an electromagnetics course using Maple:
• Introduction to Electrodynamics, David J. Griffiths, Prentice Hall. (1989)
  This book attempts to reduce the number of topics, presents derivations of the most important relationships. Numerous exercises lead to numerical/symbolic calculations.
• Multivariable Calculus with Maple, C.K. Cheung, John Harer, John Wiley & Sons (1993)
• Electricity and Magnetism Simulations: CUPS. Robert Ehrlich, Jaroslaw Tuszynski, Lyle Roelofs, Ronald Stoner, John Wiley & Sons (1995)
  Includes numerous software applications which can be used either as is or may be used as models for Maple worksheets. Example simulations which lead to simple Maple worksheets include Fields which display the scalar and vector fields for a given function, EMWaves and others.
• Waves and Optics Simulations: CUPS. Wolfgang Christian (Editor), et al, John Wiley (1995). See notes above.
• Web sites:
• Rose-Hulman Electromagnetic theory
• Rose-Hulman Introductory Electromagnetics
• A future site will be at Claremont.
• Worksheets
• Rose-Hulman Electromagnetic theory
• Rose-Hulman Introductory Electromagnetics

Topics and examples which lead themselves to Maple worksheets

Many of the topics covered in electromagnetism involve vector calculus. This means that are numerous problems which require the students to work in multiple dimensions. Maple is good at storing columns of data and representing those columns as simple variables. In addition many of the calculation involve calculation gradients, such as using the electric potential to calculate the field or integrations, such as using the charge distribution to calculate a field or potential. Specific examples of using Maple:

• E field to potential, potential to charge density, charge density to field
• Laplace equation: boundary value problems (directly or after separation of variables)
• Visualizing electric fields, electric potentials (field and contour plots)
• current density to magnetic field to vector potential
• effects of multipole expansion
• atomic polarization on electric fields
• effects of dielectrics on E fields
• drawing of magnetic fields (dipoles)
• quick calculations of energy, work for different E, B fields
• quick calculations of free charge, density current, etc.
• visualization of waves (animation, interference, refection, attenuation)
• examples with complex EM waves, TEM
• visualization of EM fields of oscillators, antenna
• all 4-vector problems are solve by vector representation

Beyond intermediate electromagnetism

One of the major advantages of using Maple is the ability to extend beyond the standard undergraduate upper-division course. Such examples of problems include: (under construction.)

Major Areas in Electromagnetism:

1. Electrostatic fields
1. a. in vacuum
2. b. in dielectric materials
2. Magnetic fields
1. in vacuum
2. in magnetic materials
3. Maxwell's Equations
4. Electromagnetic waves
1. propagation of plane waves
2. reflection/refraction of waves
3. guided waves
5. Radiation
6. Relativity

• Electrostatics
• - charge
• - forces / Coulomb_s law
• - electric fields - electric potential
• - dipoles / multipole expansion
• - energy of E fields / Work
• - polarization
• - electric displacement
• - free, bound charge
• Magnetostatics
• - forces (wires, on charges)
• - magnetic field
• - vector potential
• - current density
• - magnetic dipole moment
• - Faraday induction
• - magnetization
• - magnetic field intensity (auxiliary field)
• - susceptibility
• - energy of magnetic fields
• Maxwell_s equation
• - lorentz conditions
• - current density
• Electromagnetic waves
• - wave equation (and solutions)
• - poynting vector
• - reflection/ refraction
• Radiation
• Relativity