Wake Forest Physics…
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Mathematics Resources
Videos Explaining Math Relevant to Physics
Compiled by the Physics Faculty
 Cross products  used in the definition of angular momentum, torque, force on a charged particle moving in a magnetic field, BiotSavart law for finding magnetic fields due to current line elements, etc.
Several Khan Academy videos; first one  https://www.khanacademy.org/math/linearalgebra/vectorsandspaces/dotcrossproducts/v/linearalgebracrossproductintroduction
 Line integrals  used in the concept of work, potential energy, electric potential.
See Khan Academy, where the first video is at this link https://www.khanacademy.org/math/multivariablecalculus/integratingmultivariablefunctions/lineintegralsvectors/v/lineintegralsandvectorfields. There are a substantial number of subsequent videos that gradually increase the level of complexity for handling line integrals.
 Eigenvalues and eigenvectors  used in moment of inertia tensor or matrix, normal modes of vibration, measureable values of operators corresponding to physical quantities in quantum mechanics, etc.
See Khan Academy  https://www.khanacademy.org/math/linearalgebra/alternatebases/eigeneverything/v/linearalgebraintroductiontoeigenvaluesandeigenvectors
 Fourier Series  useful in mechanics to describe the forced harmonic oscillator, in E&M to describe timevarying fields, and in Quantum Mechanics to describe the wavefunctions for the particle in a box.
See Khan Academy  https://www.khanacademy.org/science/electricalengineering/eesignals/eefourierseries/v/eefourierseriesintro
 Series solutions to differential equations  useful in E&M and in solving the Schrodinger Eqn for the hydrogen atom, etc.
YouTube video  https://www.youtube.com/watch?v=RJJKq7Uc9I
 Fourier Transforms  useful in forced harmonic oscillator, E&M for describing Electric field pulses, Optical fields, Heisenberg uncertainty principle, resolution of a microscope, etc.
YouTube video  https://www.youtube.com/watch?v=vQLH7qTeJRM
 The Del operator, gradient, divergence, and curl  used to determine force from potential and in the differential formulation of Maxwell's equations.

