The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described. The course is introductory to scientific computation. The basic numerical methods for the solution of classical problems are presented and described.
Basic linear algebra and computer programming.
The course in Numerical Methods in Engineering aims to provide valuable tools for the resolutions of engineering problems through the techniques of Numerical Analysis. Many of the results presented, such as the technique of Numerical Quadrature, or polynomial interpolation Solutions Series, allow to simplify the solution of complex problems that arise in science and technology.
• Basic concepts of floating-point arithmetic. Conditioning of a problem. Numerical stability of an algorithm.
• Linear systems: direct methods (Gaussian eliminitations, LU-decomposition, Choleski) and iterative methods (Jacobi, Gauss-Seidel, SOR).
• Approximation of functions and data: polynomial and piecewise polynomial interpolation, splines, discrete least squares.
• Non-linear equations and systems: Newton’s method and its discrete variants, fixed-point iteration.
• Numerical integration: Newton-Cotes formulas, Gaussian quadrature rules, composite rules.
• Initial value problems for ordinary differential equations: one-step methods (Runge-Kutta methods) and multistep (Adams) methods. Stiff problems.
More specifically, it will be necessary to acquire a deep knowledge of the following exam
issues, whose contents are treated in the videolessons and in the exam texts as well:
1) The MATLAB programming language: an introduction.
Video lessons: 1, 2, 3, 4
Books: R. Hamming, Numerical Methods for Scientists and Engineers, Dover, 1962; William
J. Palm III, MATLAB & Simulink Based Books, McGraw-Hill, 2008.
2) The MATLAB programming language: applications.
Video lessons: 5, 6, 7, 8, 9, 10, 11
Books: William J. Palm III, MATLAB & Simulink Based Books, McGraw-Hill, 2008.
3) Polynomial interpolation.
Video lessons: 12, 13, 14, 15, 16
Books: G.M. Phillips & P.J. Taylor, Theory and Applications of Numerical Analysis, Ac. Press
4) Numerical methods for ODE by using MATLAB.
Video lessons: 17, 18, 19, 20, 21, 22, 23, 24, 25
Books: William J. Palm III, MATLAB & Simulink Based Books, McGraw-Hill, 2008; G.M.
Phillips & P.J. Taylor, Theory and Applications of Numerical Analysis, Ac. Press 1973.
The activities, which envisage the tutor’s support, include:
- Participation in thematic chats sessions on the conceptual area upon which the module is
based according to a calendar fixed in the Agenda;
- Participation in the module related discussions and contacts with tutor through audio and
video-chats, telephone, e-mails or face to face;
- Qualitative assessments of the learning progress made by the tutor during the module
delivery period by sending sheets including questions specifically prepared for the students’
class (fac-simile of the exam test) sent during the testing chat session to each student.