Updated 2009-06-05 19:39
List rules for lenses and mirrors. When are focal length and radii negative? When are image positions and heights negative? When are images virtual? When are they real? What are the magnification equations? What equations let you predict positions of images?
List relativity rules for speeds near light speed. How do mass, length, and time change? How do electric and magnetic fields change?
List equations for magnetic fields due to moving charges, currents, solenoids. List Ampere's Law, Biot-Savart Law. Induced voltages due to change in magnetic flux. Energy of a magnetic moment in a magnetic field. Forces between two currents. Forces on currents and charges due to magnetic fields.
List Laplacians, Gradients, Divergences, and Curls in 2-D and 3-D.
2-D would be cartesian x,y or polar r,θ coordinates.
3-D would be cartesian x,y,z or cylindrical r,θ,z or spherical r,θ,φ coordinates.
List spherical harmonics.
Add charts of common Fourier Transforms and Laplace Transforms and their generating functions.
Add charts about Euler Angles, rotation operators, and quaternions.
List functions for atomic orbitals (1s, 2s, 2p, 3s, 3p, 4s, 3d, 3p, etc.) in spherical r,θ,φ coordinates.
List solutions for Laplace's Equation for the inside and outside of spheres, cylinders, and boxes. This kind of thing used to be common on Physics Ph.D. Qualifier Exams.
Many of the above can be found in books like:
"Mathematical Methods for Physics" by H. W. Wyld
Math concepts used in Physics Labs:
How to handle significant digits under addition, subtraction, multiplication, division, exponents, sin's, cos's, log's, etc. List the rules, then show many examples. Match the expressison on the left with the right number of sig digits on the right.
How to add, multiply, divide numbers in scientific notation. List the rules, then show many examples. Match the expression on the left with the correct answer on the right.
What are the rules for rounding numbers? List the rules, then list many examples.
How to estimate errors properly. %error vs. %deviation. relative vs. absolute error. standard deviation vs. average deviation. How to combine error ranges like X±ΔX and Y±ΔY under addition, subtraction, multiplication, division, or when they are raised to higher powers.
See Math Ideas for more.
Moments of Inertia
|solid disk||(1/2) m r2|
|hollow cylinder about its length||m r2|
|solid cylinder about its length||(1/2) m r2|
|football about its long axis|
|football about one of its two equivalent short axes|
|rod about center of its length|
|rod about its length||(1/2) m r2|
|rod about one end|
|parallel axis theorem|
# of electrons in each orbital
|orbital||# of electrons|