Unit MATHEMATICAL AND NUMERICAL METHODS
- Course
- Environmental engineering
- Study-unit Code
- GP004437
- Location
- PERUGIA
- Curriculum
- Difesa del suolo
- Teacher
- Ilaria Mantellini
- Teachers
-
- Ilaria Mantellini
- Hours
- 40 ore - Ilaria Mantellini
- CFU
- 5
- Course Regulation
- Coorte 2023
- Offered
- 2023/24
- 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 1,5/2 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.