Complements of mathematics and calculus

A.Y. 2017/2018
6
Max ECTS
60
Overall hours
SSD
MAT/01 MAT/02 MAT/03 MAT/04 MAT/05 MAT/06 MAT/07 MAT/08 MAT/09
Language
Italian
Learning objectives
The course aims at:
1) completing the Students' knowledge in Mathematics, by studying some of the problems frequently encountered in Applied Sciences;
2) providing the basic tools regarding the numerical simulation of mathematical problems of applicative interest;
3) providing the basic tools for an appropriate usage of Scientific Computing software.
Expected learning outcomes
Conoscenza dei fondamenti matematici dell'algebra lineare, della statistica descrittiva e del calcolo numerico. Utilizzo di Excel e MATLAB a livello elementare.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
Goals
Basic knowledge of Numerical Computing, regarding both the theory and the implementation (in MATLAB language). The course will also complete some mathematical topics introduced in the math course of the first semester.

Course content:
Floating-Point representation of real numbers. Vectors, products, matrices, linear algebra, determinants, matrix inverse. Linear systems. Direct methods, Gaussian elimination, pivoting, LU factorization. Aigenvalues and eigenvectors of a matrix. Iterative methods, Jacobi and Gauss-Seidel, convergence criteria, stopping tests. Polynomial approximation of functions and data. Polynomial interpolation, Lagrange polynomials, interpolation error. Spline functions. Least square methods, linear regression. Nonlinear equations. Bisection and Newton methods, theoretical results, stopping tests. Numerical integration. Open and close Newton-Cotes formulae, midpoint, trapezoidal and Simpson rules. Error analysis and composite formulae. Ordinaru differential equations. Existence and uniqueness results. One-step methods, explicit and implicit Euler, Crank-Nicolson, Heun. Consistency and local truncation error, order of convergence. Global error evaluation and adaptivity. Absolute stability. Runge-Kutta methods. Multistep methods. Systems of ordinary differential equations, kinetic reactions.

Suggested prerequisites:
The concepts introduced in the math corse of the first semester will be necessary.

Reference material:
- A., Quarteroni, F. Saleri, P. Gervasio, Calcolo scientifico. Springer, 2012.
- G. Naldi, L. Pareschi: MATLAB Concetti e progetti. Milano, Apogeo 2002.
- G . Naldi, L. Pareschi, G. Russo, Introduzione al calcolo scientifico. Metodi e applicazioni con Matlab, McGraw-Hill Education.

Prerequisites:
The math course of the first semester.

Assesment methods:
Written exam.
The written exams consists if the solution of both theoretical and Matlab problems.

Attendance policy:
Strongly recommended

Mode of teaching:
Frontal lectures + Malab Lab

Course webpage: http://www.mat.unimi.it/users/beirao/Chimici_2015.htm
MAT/01 - MATHEMATICAL LOGIC - University credits: 0
MAT/02 - ALGEBRA - University credits: 0
MAT/03 - GEOMETRY - University credits: 0
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS - University credits: 0
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 0
MAT/06 - PROBABILITY AND STATISTICS - University credits: 0
MAT/07 - MATHEMATICAL PHYSICS - University credits: 0
MAT/08 - NUMERICAL ANALYSIS - University credits: 0
MAT/09 - OPERATIONS RESEARCH - University credits: 0
Practicals: 24 hours
Lessons: 36 hours
Shifts:
Professor: Zampieri Elena
Turno A
Professor: Bressan Nicoletta
Turno B
Professor: Fierro Francesca