- Analytic continuation
- Anti-hermitian operators
- Associated Legendre functions
- Associated Legendre functions - orthogonality
- Branch points and cuts in the complex plane
- Contour integration
- Contour integration around a branch cut
- Coordinate transformations - the Jacobian determinant
- Curl and Stokes's theorem
- Diagonalization of matrices
- Dirac delta function
- Dirac delta function - Fourier transform
- Derivatives of the delta function
- Divergence & Gauss's Theorem
- Eigenvalues and eigenvectors
- Fourier transforms and Plancherel's theorem
- Functionals and functional derivatives
- Functions of hermitian operators
- Gaussian integrals
- Generalized product rule - Leibniz's formula
- Gram-Schmidt orthogonalization - a couple of examples
- Hermite differential equation - generating functions
- Hermite polynomials
- Hermitian operators
- Hermitian conjugate (adjoint) of an operator
- Hermitian operators - common eigenfunctions implies they commute
- Hermitian operators - equivalence of conditions
- Hermitian operators - a few theorems
- Inner products and Hilbert spaces
- Inverses of linear operators
- Jacobian determinants
- Lagrange multipliers
- Laguerre polynomials - normalization
- Legendre equation - Legendre polynomials
- Legendre polynomials - geometric origin
- Legendre polynomials - orthogonality
- Legendre polynomials - Rodrigues formula and orthogonality
- Linear functionals and adjoint operators
- Linear maps, linear operators and commutators
- Linear operators - change of basis, trace and determinant
- Logarithms - a few properties
- Matrix representation of linear operators
- Normal operators
- Null space, range, injectivity and surjectivity
- Orthonormal basis and orthogonal complement
- Projection operators
- Projection operators - formal treatment
- Self-adjoint differential equations
- Span, linear independence and basis
- Spectral theorem for normal operators
- Stirling's approximation for large factorials
- Subspaces and direct sums
- Taylor series
- Unitary operators
- Unitary operators - active and passive transformations of an operator
- Vector area
- Vector spaces