Mathematics Resources

Videos Explaining Math Relevant to Physics

Compiled by the Physics Faculty

1. 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
2. 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.
3. 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
4. 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
5. 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
6. 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
7. The Del operator, gradient, divergence, and curl - used to determine force from potential and in the differential formulation of Maxwell's equations.
• Del operator and gradient
• Divergence and the divergence theorem
• Curl and Stokes' Theorem