CORE COURSES

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