Prerequisites. Essential elements of Linear Algebra, Calculus (infinitesimal, differential, and integral calculus, Taylor polynomials), and fundamental concepts in Computer Science (computer structure, basic knowledge of computer programming and computational complexity).
Teaching Methods. Classroom lectures
Verification of Learning. Grade is based on a final written exam. Exam texts include both theoretical questions and computational problems, with variable difficulty levels, aiming at evaluating students’ overall understanding and knowledge.
More Information. Learning resources available on the e-learning platform include problem sets, handouts, lecture slides, and are sufficient for self-study. Students are also given access to video-recorded lectures. However, class attendance is strongly encouraged.
Objectives
Students will learn to: – understand concepts, computational tools, and fundamental problems of Numerical Analysis; – foresee possibilities and limitations offered by principal techniques in Scientific Computing; – analyze and solve numerically simple computational problems in continuum mathematics; – estimate the reliability of numerical results and understand time and precision constraints set by computational resources.
Contents
Numerical Analysis deals with the study of algorithms, that is, constructive procedures, of continuum mathematics. This course introduces students to some basic topics and fundamental concepts in this broad discipline, by means of the study of main algorithms in numerical linear algebra, basic error analysis tools, and fundamental techniques in scientific computing. Detailed syllabus: – Error analysis and computer arithmetic – Matrix factorizations: LU, QR, SVD – Numerical solution of linear systems: direct and iterative methods – Numerical solution of nonlinear equations and systems
Texts
Teacher’s lecture notes.
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