Ateneo - UPO

Linear algebra and numerical methods for solving some basic mathematical problems. Ordinary differential equations.

+ M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 1 con elementi di geometria e algebra lineare, Ed. Zanichelli, 2008. + M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 2, Ed. Zanichelli, 2009. + A. Quarteroni , F. Saleri. Introduzione al Calcolo Scientifico. Esercizi e problemi risolti con MATLAB. Springer - Collana Unitext. 2002.

Knowledge of the main elements of linear algebra and numerical methods for solving basic mathematical problems useful for addressing practical applications in chemical sciences. Ability to apply this knowledge to solve problems in chemistry. Communication skills: acquire and know how to use appropriate technical language in relation to the topics covered in the course. Autonomy of judgement: developing the critical sense and independence in the analysis of problems, stimulating the ability to formulate autonomous and well-motivated judgements; encourage active participation and classroom discussions to develop a deeper understanding of the topics covered.

Course contents: Calculus I.

Theoretical lessons with practical exercises, stimulating discussion among students.

The control of ongoing learning will be carried out by carrying out exercises in the classroom with the active participation of students. Students with physical disabilities, Learning Disabilities or Special Education Needs can request specific services and tools via the __Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage: https://www.uniupo.it/en/services/servicesstudents-physical-or-learning-disabilities. Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam consists of a written test and an oral exam. The written test involves solving exercises related to the material covered during the lessons and lasts for half an hour. The oral exam consists of a discussion of the written test and the content outlined in the course syllabus. During the written test, it is not allowed to consult textbooks or personal paper notes. At the end of the written test, the teacher announces the results on the DIR platform. Students are admitted to the oral exam only if they have passed the written test. The oral exam takes place in the days immediately following the written test: the date and room for the oral exam will be communicated to students via their institutional email address. The results of the exam reflect the level of understanding of the theoretical concepts and the ability to apply them to solve new problems. A passing grade requires the ability to correctly adopt the chosen methodology, while excellence requires the ability to contextualize the concepts.

Linear algebra: vectors in the plane and in space, finite dimensional vector spaces, matrices and linear transformations, determinants, linear systems, calculus of eigenvalues, eigenvectors and diagonalization of matrices. Numerical methods for solving basic mathematical problems: nonlinear equations (bisection method and Newton's method), algebraic linear systems (LU factorization and Gaussian elimination method, QR factorization and Householder method), polynomial interpolation and approximation of functions using the discrete least squares method, interpolatory quadrature formulas (trapezoid method and Simpson's method), power method for the numerical calculation of eigenvalues ​​and eigenvectors. Ordinary differential equations: first-order equations with separable variables, first-order linear equations, second-order linear equations with constant coefficients.

1) Knowledge and understanding - ability to identify a solution methodology and develop it correctly. 2) Ability to apply knowledge and understanding - ability to use learned tools. 3) Autonomy of judgment - ability to critically analyze the results. 4) Ability to continue studying independently - to be able to read, understand and comment on technical material from books or other sources.