Máster universitario en Modelización Computacional Atomística y Multiescala en Física, Química y Bioquímica

1) COMPUTATIONAL TOOLS

Linux operating system: basic commands, the VI editor, scripts and Bash Shell

Introduction to programming in high-level languages: Fortran 90. Libraries

Precision and errors in computation

Basic algorithmic structures

Basic concepts in code optimization, parallelization and vectorization

Use of software of general interest for scientific applications: Python, Maxima, Gnuplot/Origin/VMD.

2) INTRODUCTION TO SCIENTIFIC COMPUTATION

Data: Variables. Tables and lists. Functions. Matrices and vectors

Functions: discretization and precision. Zeros. Series, products and continued fractions.

Methods for approximating functions by means of lineal, polynomial and multilinear regressions. Interpolation and series approximations.

Elements of applied linear algebra: vector spaces and operators. Orthonormalization. Operations with matrices. Sets of linear equations. Matrix inversions. Eigenvectors and eigenvalues. Diagonalization. Linear transformations.

Numerical intergration and differentiation. Differentiation and integration of single-variable functions. Multivariate functions. Partial derivatives. Line, surface and volume integrals.

Ordinary differential equations. Formal aspects. Methods for their numerical solutions. Fourier methods. Nonlinear differential equations.

Partial derivative equations. Formal aspects: definitions and boundary conditions. Methods for their numerical solutions.

Optimization methods. Monte Carlo.

3) MULTISCALE MODELLING

Introduction to the scientific method and to the length and time scales present in Nature

Systems in equilibrium. The microscopic world: atomic-molecular structure. The macroscopic world: Equilibrium Thermodynamics. The mesoscopic world: Equilibrium Statistical Mechanics.

Examples of structure and macroscopic properties

Transport phenomena

Chemical reactivity

Complex systems

4) MOLECULAR MODELLING

Description of atomic and molecular systems at different scales

Mechanical and statistical basis of molecular modelling

Quantum models

Molecular Dynamics

The Monte Carlo method

Practical sessions of molecular modelling