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.

• Bolzano-Weierstrass theorem.

Basic concepts

• Hessian matrix

Numerical methods

• Runge-Kutta

Differential equations

• famous equations

Functional analysis

• Banach space

• spectral theory

• symmetric operator

• Hermitian matrix and unitary matrix.

• variational problem

• extrema

• distribution (functional analysis)

• Stone's theorem

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es