Analysis

• Laplace transform, Fourier transform, Mellin transform
• functional dependence
• entire function
• Riemann zeta function
• Padé aproximant
• integration and derivation
• Lipschitz continuous function and uniformly continuous function
• Weierstrass theorem.
• Bessel functions.
• Jacobi elliptic function.
• Bolzano-Weierstrass theorem.
  Basic concepts
• Hessian matrix
• integration on Rn

Numerical methods

• Runge-Kutta

Differential equations

• famous equations
• Green's function method

Functional analysis

• Banach space
• spectral theory
• symmetric operator
• Hermitian matrix and unitary matrix.
• variational problem
• extrema
• distribution (functional analysis)
• Stone's theorem