Aerospace engineering

1. Problem conditioning and algorithm stability 2. Iterative methods for nonlinear equations and nonlinear systems: bisection method, iterative methods, Newton's method, secant method; convergence and stopping criteria 3. Numerical linear algebra: direct methods to solve linear systems; iterative methods, Jacobi and Gauss-Seidel methods; convergence criteria 4. Polynomial approximation of data: linear least squares; interpolation with algebraic polynomials, Lagrange polynomials, divided and finite difference Newton polynomials, convergence criteria 5. Numerical integration: elementary and generalized trapezoidal and Simpson’s rules; convergence criteria for generalized formulas 6. Numerical methods to solve ODE: Euler and Runge-Kutta methods for initial value problems, implicit methods convergence criteria 7. Finite difference methods for boundary value problems: linear and non linear ODEs 8. Introduction to programming and numerical computing 9. Matlab: primitive data types, variables, expressions and assignment, array and matrices, conditional statements and boolean expressions, loop statements (for and while), function and script 10. Matlab codes for presented numerical methods

Basic notions of calculus, geometry and linear algebra

Calcolo Numerico, L. Gori, Ed. Kappa, 2006 Esercizi di Calcolo Numerico, L. Gori-M.L. Lo Cascio, F. Pitolli, Ed. Kappa, 2007 Course Slides (download from e-learning platform)

The course includes both lectures and lab exercises. During the lectures, the teacher will outline and discuss the main features of the numerical methods listed in the program. During lab exercises, firstly the teacher will give an introduction to programming in Matlab, then the teacher will show how to code algorithms. During the course the teacher will also provide guided exercises on numerical methods and programming and will assign homeworks to students.

Attendance is recommended

The written test consists of 5 exercises; two of them require Matlab implementation. The written test lasts 3 hours. The score assigned to each exercise is in the range [0, 30]. The final score is the weighted mean of the individual scores; the weights are (2/9, 2/9, 1/9, 2/9, 2/9). The oral examination requires to pass the written test with a score greater than or equal to 16/30. The oral examination consists of a discussion concerning the written test and some questions oriented to assess the ability in analyzing a problem, selecting the most suitable numerical method for its solution and discussing the results. The score to the oral test is assigned according to the following criteria: minimal knowledge (rated between 18 and 20); average knowledge (21-23); ability to apply the knowledge in a sufficient manner (24-25); good ability to apply knowledge with sufficient communication skills and critical judgements (26-27); ability to apply knowledge in an excellent manner with good communication skills and critical judgements (28-30 cum laude). The final score is the arithmetic mean of the scores assigned to written and oral tests.

The course includes both lectures and lab exercises. During the lectures, the teacher will outline and discuss the main features of the numerical methods listed in the program. During lab exercises, firstly the teacher will give an introduction to programming in Matlab, then the teacher will show how to code algorithms. During the course the teacher will also provide guided exercises on numerical methods and programming and will assign homeworks to students.