Portale di Ateneo - En.Unibs.it

Other Courses of the Study Programme

Course year: 1

ADVANCED SOLID AND STRUCTURAL MECHANICS - 9 credits - Related/Supplementary
DESIGN OF BUILDING SERVICES - 9 credits - Characterising
DYNAMICS OF STRUCTURES - 9 credits - Characterising
GEOTECHNICAL ENGINEERING - 9 credits - Characterising
NUMERICAL ANALYSIS - 9 credits - Related/Supplementary
STRUCTURAL DESIGN - 9 credits - Characterising
WATER SUPPLY AND WATER DRAINAGE SYSTEMS - 9 credits - Characterising

Course year: 2

ADVANCES IN FORENSIC PRACTICE - 3 credits - Student's own choice
COMPUTATIONAL NONLINEAR STRUCTURAL MECHANICS - 9 credits - Characterising
Construction of Roads, bridges and small structures
Attendance grouping
9 credits - Raggruppamento di frequenza
DESIGN OF REINFORCED AND PRESTRESSED CONCRETE STRUCTURES 2 - 9 credits - Characterising
DESIGN OF SEISMIC RESISTANT STRUCTURES - 9 credits - Characterising
Design of Steel and Timber Structures
Attendance grouping
9 credits - Raggruppamento di frequenza
ETHICS OF ENVIRONMENTAL SUSTAINABILITY - 3 credits - Student's own choice
FINAL THESIS - 12 credits - Language/Final Examination
FORENSIC PRACTICE - 6 credits - Student's own choice
FOUNDATIONS - 9 credits - Characterising
MECHANICS OF SMART MATERIALS AND STRUCTURES - 6 credits - Student's own choice
STRUCTURAL REHABILITATION - 9 credits - Characterising
SUMMER SCHOOL - 3 credits - Student's own choice
TRAINING ACTIVITY/INTERNSHIP 6 CREDITS - MASTER LEVEL - 6 credits - Student's own choice
TRAINING ACTIVITY/INTERNSHIP 9 CREDITS - MASTER LEVEL - 9 credits - Student's own choice
TRANSPORTATION TECHNIQUES AND ECONOMICS - 9 credits - Characterising

NUMERICAL ANALYSIS

Note

Information unavailable, as the teaching activity currently displayed will be provided in a subsequent academic year.

Single discipline educational activity

Course Sheet

Course code:

703507

Academic Year of enrolment:

2019/2020

Academic Year of provision:

2019/2020

Type of Course:

Related/Supplementary

Degree:

Master's Degree Programme in CIVIL ENGINEERING

Disciplinary Sector:

Numerical Analysis

Language:

Italian

Grouping type:

Credits:

Programme Year:

Professor and Collaborators:

GASTALDI Lucia Professor

Cycle:

First semester

Hours of classroom activity:

Hours of individual study:

135

Analisi Matematica I, Analisi Matematica II, Algebra e Geometria

Educational Goals

The Scientific Calculus is a very important tool in the design of structures and buildings since it allows to compute with sufficient precision the behavior of structures undergoing external forces. The aim of the course is the introduction of basic methods of the numerical analysis. In particular the following problems will be considered: solution of linear and nonlinear systems, computation of the eigenvalues of a matrix, approximation of functions and data, numerical differentiation and integration, and solution of ordinary differential
equations and numerical approximation of boundary value problems. The convergence and the properties of the numerical methods are discussed. An important feature of the course is the use of MATLAB® in order todevelop some programs to solve simple problems and verify the theoretical results.

Content

Programming with Matlab
Computer arithmetic
Solution of linear systems of equations
Iteration methods for the solution of linear systems of equation
Eigenvalue problems
Nonlinear systems of equations
Optimization
Approximation of functions and data
Numerical differentiation and integration
Ordinary differential equations
Numerical methods for boundary value problems

Extended Syllabus

Programming with Matlab
* Scalar variables and arrays
* Arithmetic operations and operations with arrays
* Functions and graphical elements
* Branching and loops
Computer arithmetic
* Number representation
* Floating point number systems
* Rounding error
* Arithmetic in floating point number systems and error propagation
Solution of linear systems of equations
* LU factorization and Gauss method
* Choleski factorization
* Error analysis
* Condition number
Iteration methods for the solution of linear systems of equation
* Classical iteration methods and convergence analysis
* Stopping criteria
* Jacobi, Gauss-Seidel and Richardson methods
* Conjugate gradient
* Preconditioning
Eigenvalue problems
* Introductory remarks
* Localization of eigenvalues
* Eigenvalues and eigenvectors of symmetric positive definte matrices
* Power methods
* Rayleigh quotient
* QR algorithm
Nonlinear systems of equations
* Bisection method
* Newton and secant methods
* Extension to the solution of nonlinear systems
* Convergence analysis
Optimization
* Unconstrained optimization
* Newton and line-search method
Approximation of functions and data
* Interpolation by polynomials
* The interpolation error
* Spline functions
* Least square methods for data approximation
Numerical differentiation and integration
* Numerical integration
* Quadrature by interpolation formulas
* Adaptive Simpson formula
* Finite differences
Ordinary differential equations
* The Cauchy problem
* Euler and Cranc-Nicolson methods
* Theory for one-step methods
* Absolute stability region
* High order methods
* Systems of ordinary differential equations
Numerical methods for boundary value problems
* Finite differences approximation of boundary value problems for
stationary partial differential equations
* Finite differences approximation of time dependent problems
* Finite element method
* Discretization of Laplace equation, heat equation and wave equation