 Associated Legendre functions
 Associated Legendre functions – orthogonality
 Chain rule for derivatives
 Chain rule – examples
 Curl & Stokes’s theorem
 Curvilinear coordinates
 Derivatives
 Derivatives of trigonometric functions
 Dirac delta function
 Dirac delta function in three dimensions
 Discrete Fourier transforms
 Divergence & Gauss’s theorem
 Functionals and functional derivatives
 Functional derivatives: more examples
 Gaussian integral
 Gradient
 Hermite differential equation – generating functions
 Hermite polynomials
 Integrals
 Laguerre polynomials – normalization
 Legendre equation – Legendre polynomials
 Legendre polynomials – geometric derivation
 Legendre polynomials – orthogonality
 Legendre polynomials – recurrence relations & ODE
 Limits
 Product rule and integration by parts
 Product rule: generalized with Leibniz’s formula
 Selfadjoint differential equations
 Taylor series

Index

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