Index - Mathematics

• 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