# Mathematics Resources

## Videos Explaining Math Relevant to Physics

### Compiled by the WFU Physics Faculty

**Cross products**– used in the definition of angular momentum, torque, force on a charged particle moving in a magnetic field, Biot-Savart law for finding magnetic fields due to current line elements, etc.

Several Khan Academy videos; first one – https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/linear-algebra-cross-product-introduction**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/multivariable-calculus/integrating-multivariable-functions/line-integrals-vectors/v/line-integrals-and-vector-fields.

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/linear-algebra/alternate-bases/eigen-everything/v/linear-algebra-introduction-to-eigenvalues-and-eigenvectors**Fourier Series**– useful in mechanics to describe the forced harmonic oscillator, in E&M to describe time-varying fields, and in Quantum Mechanics to describe the wavefunctions for the particle in a box.

See Khan Academy – https://www.khanacademy.org/science/electrical-engineering/ee-signals/ee-fourier-series/v/ee-fourier-series-intro**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=RJJKq7Uc-9I**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