Study-unit MATHEMATICAL AND NUMERICAL METHODS
| Course name | Environmental engineering |
|---|---|
| Study-unit Code | GP004437 |
| Curriculum | Difesa del suolo |
| Lecturer | Ilaria Mantellini |
| Lecturers |
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| Hours |
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| CFU | 5 |
| Course Regulation | Coorte 2022 |
| Supplied | 2022/23 |
| Supplied other course regulation | |
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Sector | 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. |