This repository contains every material of the Applied Mathematics course followed at SISSA (joint course with UniTS), teached by Prof. Rozza, Dr. Girfoglio, Dr. Siena, during the academic year 2023/24.
The syllabus and other infos can be found here where you'll also find the links to Rozza's lectures and Python codes.
Four Modules of 12h each (1.5 CFU for each module), for a total of 48h, 6 CFU
- Well posedness, condition numbers
- Polynomial based approximations
- Power basis interpolation,
- Lagrange interpolation
- Weierstrass approximation theorem)
- Interpolatory Quadrature rules
- Orthogonal polynomials and Gauss Quadrature Formulas
- L2 projection
- Review of elementary PDEs
- Introduction to Finite Difference Methods
- Introduction to Finite Element Methods
- Least square methods
- Solution methods for Linear Systems
- direct solvers
- iterative solvers
- Eigenvalues/Eigenvectors
- Solution methods for non-Linear systems
- Review of ODEs
- Data assimilation in biomechanics, statistics, medicine, - electric signals
- Model order reduction of matrices
- Linear models for hydraulics, networks, logistics
- State equations (real gases), applied mechanics systems, - grow population models, financial problems
- Applications of ODEs
- example in electric phenomena, signals and dynamics of - populations (Lotke-Volterra)
- Models for prey-predator, population dynamics, automatic - controls
- Applications of PDEs, the poisson problem
- Elastic rope
- Bar under traction
- Heat conductivity
- Maxwell equation
- Introduction to Python, Numpy, Scipy
- Working with numpy arrays, matrices and nd-arrays
- Exercises on Condition numbers, interpolation, quadratures
- Using numpy for polynomial approximation
- Using numpy for numerical integration
- Using numpy/scipy for ODEs
- Solving non-linear systems of equations
- Using numpy/scipy for simple PDEs