66910 - Numerical Methods for Civil Engineering (Graduate Course)

Learning outcomes

Upon completion of the course, the student gains knowledge and computational tools of primary importance in the field of civil engineering, with particular focus on numerical methods for solving algebraic and differential equations and systems.

Course contents

The course introduces the fundamental tools of numerical analysis applied to problems in civil engineering. Its objective is to provide both theoretical understanding and practical skills for modeling and numerically solving complex problems arising in the study of structures, materials, and physical systems.

By using the Python programming language, students will learn how to implement numerical algorithms and interpret the results obtained. The course covers both classical and modern methods for function and data approximation, the solution of (systems of) equations (linear and nonlinear), numerical integration and differentiation, as well as the numerical simulation of ordinary differential equations. Particular emphasis is placed on computational applications, with attention to the stability, accuracy, and efficiency of the algorithms.

The course covers the following topics:

• Introduction to programming in Python
• Fundamentals of numerical mathematics
• Function and data approximation (polynomial interpolation, least squares)
• Numerical differentiation and integration
• Methods for solving linear systems (direct and iterative approaches)
• Methods for solving (systems of) nonlinear equations and optimization problems
• Computation of eigenvalues and eigenvectors
• Numerical methods for ordinary differential equations (initial value problems, boundary value problems discretized with finite differences and finite elements)

Readings/Bibliography

The course material (slides, lecture notes, exercises, ...) will be made available on Virtuale. Useful textbook:

• A. Quarteroni, F. Saleri, P. Gervasio: Calcolo scientifico. Springer, 2017.

Teaching methods

Frontal lectures, exercise sessions in lecture hall and in computer lab, independent solution of homeworks.

Assessment methods

Final examination assessing the acquisition of both theoretical and practical skills.

Teaching tools

The course includes a computer lab activity, which is an important part of the program, where the Python software will be used.

Office hours

See the website of Michele Ruggeri