Unit MATHEMATICAL AND NUMERICAL METHODS

Course
Environmental engineering
Study-unit Code
GP004437
Curriculum
Difesa del suolo
Teacher
Ilaria Mantellini
Teachers
  • Ilaria Mantellini
  • Loris Faina
Hours
  • 40 ore - Ilaria Mantellini
  • 10 ore - Loris Faina
CFU
5
Course Regulation
Coorte 2022
Offered
2022/23
Learning activities
Affine/integrativa
Area
Attività formative affini o integrative
Academic discipline
MAT/05
Type of study-unit
Obbligatorio (Required)
Type of learning activities
Attività formativa monodisciplinare
Language of instruction
Italian
Contents
Introduction to Fourier Analysis and applications to linear and quasi linear partial differential equations. Numerical methods for partial differential equations
Reference texts
Some didactical materials given by the teachers . For insights see the book
C. Ray Wylie - L.C. Barrett, Advanced Engineering Mathematics, McGraw-Hill, 1995
Educational objectives
From experience in previous academic years , students acquire the basic theoretical knowledges (mathematical concepts, theorems, etc) given in the course , which can be helpful for practical subjects, and in particular acquires the ability to set up mathematical models based on the theory of partial differential equations ( diffusion problems, problems concerning vibrating structures , simple Dirichlet problems, etc ) .
Prerequisites
Of fundamental importance is the knowledge of the topics for the courses of Mathematics 1 , Mathematics 2 and Geometry , given in the three-year degree
Teaching methods
Didactical methods consist in theoretical lessons, in which the basic topics of the course are developed, and laboratory exercises aimed at practical application of numerical models , also through the use of computer programs .
Other information
The attendance at classes is not obligatory, but strongly suggested.
Learning verification modality
The exam is based on an individual written test of 1,5 hours in which questions are presented to students both theoretical and of calculation type ( regarding the two different part of mathematical and numerical methods) , which serve to highlight the descriptive skills acquired by the student and their use for solving differential equations which model practical problems in Engineering Sciences.
Extended program
Power series and Fourier series. Fourier transform. First order partial differential equations: linear and quasi-linear equations.
Characteristic curves. Second order partial differential equations: classifications. Wave equation, heat equation,
Dirichlet problems on simple domains. Separation of the variables, applications of the Fourier Transform.
Numerical methods for partial differential equations: finite differences, finite elements. Applications to the wave equation, the heat
equation and to the Laplace equation.
Condividi su