Numerical Computing
2025-fall, Università della Svizzera italiana, Faculty of Informatics, 2025
This course provides a comprehensive introduction to numerical methods and their implementation in computational environments, focusing on both theory and practical applications. Students will learn to solve mathematical problems using numerical techniques and apply these methods to real-world scenarios in science and engineering.
Key topics include:
- Numerical solutions to equations
- Interpolation and approximation
- Numerical integration and differentiation
- Numerical linear algebra
- Error analysis and stability
- Applications in science and engineering
Schedule
| Week | Date | Topic | Materials | Code/Assets |
|---|---|---|---|---|
| 1 | 2025-09-22 | Introduction to Numerical Computing | Notes · Slides | Code |
| 2 | 2025-09-29 | Computer Arithmetic and Error Analysis | Notes · Slides | Code |
| 3 | 2025-10-06 | Root-Finding Methods | Notes · Slides | Code |
| 4 | 2025-10-13 | Linear Algebra Foundations | Notes · Slides | Code |
| 5 | 2025-10-20 | Direct Methods for Linear Systems | Notes · Slides | Code |
| 6 | 2025-10-27 | Least Squares and QR Decomposition | Notes · Slides | Code |
| 7 | 2025-11-03 | Iterative Methods for Linear Systems | Notes · Slides | Code |
| 8 | 2025-11-10 | Eigenvalue Problems | Notes · Slides | Code |
| 9 | 2025-11-17 | Interpolation and Approximation | Notes · Slides | Code |
| 10 | 2025-11-24 | Numerical Integration (Quadrature) | Notes · Slides | Code |
| 11 | 2025-12-01 | Nonlinear Least Squares and Gauss-Newton | Notes · Slides | Code |
| 12 | 2025-12-08 | Constrained Optimization | Notes · Slides | Code |
Slight adjustments may occur; official meterial will be ultimatelly uploaded to icorsi.
Course Outline
- Mathematical foundations; error sources and propagation; well‑posedness vs ill‑posedness.
- Floating‑point arithmetic (IEEE 754), machine epsilon, roundoff, cancellation; numerical stability.
- Nonlinear equations and root finding: bisection, Newton, secant; convergence theory and basins.
- Interpolation and approximation: Lagrange, Newton forms, splines; Runge phenomenon and remedies.
- Numerical differentiation and quadrature: error analysis, composite rules, Romberg, Gauss.
- Numerical linear algebra: conditioning, Gaussian elimination, LU/QR; least squares and SVD.
- Eigenvalue problems: power method, QR iteration; applications.
- Optimization: gradient methods, line search, constraints, Gauss‑Newton and Levenberg‑Marquardt.
For up-to-date information on schedule and lecture room, visit the official USI course page.