**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