Complements of Mathematics and Calculus
A.Y. 2018/2019
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.
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.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
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
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
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
MAT/02 - ALGEBRA
MAT/03 - GEOMETRY
MAT/04 - MATHEMATICS EDUCATION AND HISTORY OF MATHEMATICS
MAT/05 - MATHEMATICAL ANALYSIS
MAT/06 - PROBABILITY AND STATISTICS
MAT/07 - MATHEMATICAL PHYSICS
MAT/08 - NUMERICAL ANALYSIS
MAT/09 - OPERATIONS RESEARCH
Practicals: 16 hours
Laboratories: 16 hours
Lessons: 32 hours
Laboratories: 16 hours
Lessons: 32 hours
Professors:
Bressan Nicoletta, Fierro Francesca, Zampieri Elena
Shifts:
Professor:
Zampieri Elena
Corso A
Professor:
Fierro FrancescaCorso B
Professor:
Bressan NicolettaProfessor(s)