Ateneo - UPO

The course provides notions on error analysis, finite precision number system and arithmetic, numerical approximation of the solution of nonlinear equations, efficient methods for the solution of systems of linear equation. The course also approaches the main issues related to function approximation and numerical integration.

Teacher's notes available on the DIR platform.

The student who successfully completes the course will be able to demonstrate a solid knowledge of the basic topics of numerical calculus. In particular, he/she will be able to evaluate a numerical scheme from both the point of views of the accuracy of the approximation it provides and the computational cost of its implementation.

The knowledge of the main notions provided during a basic course of Mathematics is required. In more details:
Functions and sequences, Limits, Differential calculus, Taylor expansion, Integral calculus in one variable, Initial value problems for ordinary differential equations;
Vector spaces, Linear systems, Matrix algebra, Eigenvalues.

Teaching will take place through lectures on the blackboard and exercises in the computer lab. In addition to the theoretical lessons, the teacher will carry out exercises in the computer lab with the active involvement of the students to deepen the topics covered during the theoretical lessons. The concepts covered by the course will be discussed collegially in the classroom and applied directly during laboratory exercises to stimulate students' critical sense and autonomy of judgment.

Attendance: Advised

Oral exam on the topics covered during the theoretical and practical lessons (computer lab). During the oral exam, the student must be able to demonstrate his/her knowledge of the main course contents using the appropriate terminology. He/She must also demonstrate ability of putting into practice, with critical awareness, some of the activities carried out in laboratory during the course.

The course provides notions on error analysis, finite precision number system and arithmetic, numerical approximation of the solution of nonlinear equations, efficient methods for the solution of systems of linear and non linear equations. The course also approaches the main issues related to function approximation and numerical integration. Finally, the use of the Matlab software from the command window and by using M-files is presented.

At the end of the course the student must have acquired the basic techniques for the development of numerical methods and the study of their main properties. The student must be able to identify the most appropriate methods for solving some specific numerical problems also in relation to the required accuracy and the available computing resources. He/she must therefore be able to pass from the development and analysis of the methods to their implementation, their use and the related correctness and accuracy tests. The student, on the basis of the analysis of the methods studied, must be able to provide an evaluation of the pros and cons of each method in order to make informed choices in solving problems. The student must also be able to evaluate the quality of the results provided by the numerical tests carried out by means of the codes presented by the teacher in the classroom or made by the student himself. The student will have to acquire the ability to describe, for each problem studied, the nature of the problem itself, the difficulties in solving it on the computer and the ways in which these difficulties are faced. He/she will also have to acquire the ability to effectively present the results of his/her numerical experiences. On the basis of the problems, the methods studied and their analysis, the student will have to acquire the ability to independently develop solution strategies to be applied to new problems.