Unit MATHEMATICAL ANALYSIS III
- Course
- Mathematics
- Study-unit Code
- 55071909
- Curriculum
- In all curricula
- Teacher
- Roberta Filippucci
- Teachers
-
- Roberta Filippucci
- Hours
- 73 ore - Roberta Filippucci
- CFU
- 9
- Course Regulation
- Coorte 2021
- Offered
- 2022/23
- Learning activities
- Caratterizzante
- Area
- Formazione teorica
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Sequences and series of functions. Fourier series and applications. General theory of ODEs and systems of differential equations in the nonlinear and linear cases, with fundamental examples. Integrals on manifolds. Gamma function and some applications.
- Reference texts
- C. Pagani e S. Salsa, Analisi Matematica 2, Seconda edizione Zanichelli, ISBN: 978-88-08-63708-6
A. Ambrosetti e S. Ahmad, Differential Equations, DE Gruyter, 2019
G. Buttazzo e V. Colla, Temi d'esame di Analisi Matematica 2, Pitagora - Educational objectives
- The student should acquire a basic knowledge in mathematical analysis, descriptive statistic and some notions of inferential statistics. The course matter is part of the contents of a standard reformed first level course for Italian three-year degrees in mathematics. Even the setting is reformed, and the textbooks used are rich of examples and counterexamples, and therefore seem to be optimal to achieve a good understanding of the topics starting from exercises, that is from applications.
Main knowledge acquired will be:
- To know the main topics of mathematical analysis and how to apply them to the natural sciences,
- To know the theory of diagnostic tests and some statistical hypotheses tests,
- To know several tools to solve elementary and basilar exercises,
- To read and understand texts of Mathematical Analysis and Statistics,
- To work in teams, but also in autonomy.
The skills listed above are set out in the framework of the professions related to both a traditional Biotechnologist, and a Biotechnologist oriented to technical and/or industrial activities.
Main competence (i.e. ability to apply the main knowledge acquired) will be:
- To apply the theory to the resolution of exercises or problems based on models developed during lessons
- To analyze and treat simple concrete statistical problems by choosing the right statical test to apply,
- To solve some easy mathematical problems in the field of applied mathematics, indipendently. - Prerequisites
- To better understand the topics covered in the course the student should have passed the exams of Mathematical Analysis I and II. Therefore, the prerequisites are concepts that students meet not only in basic courses of Mathematics but, increasingly, also in their pre-university education. Furthermore the student is required to be familiar with the notions of metric spaces, eigenvalues, eigenvectors and to recognize and draw quadrics.
- Teaching methods
- The course is split in theoretical lessons and practical lessons, in these latter several exercises are carried out in class. The course is composed by 73 divided into 43 hours of theory, together with different examples and counterexamples, and 30 hours of practical exercises. A overhead projector is used to project lessons.
In the tutorial service the students will be followed individually by the teacher. - Other information
- The teacher makes available educational materials useful for a better understanding of the course, in order to help and to let the students pass easily the exam, visit UNISTUDIUM. Furthermore all the previous written test can be found in UNISTUDIUM, where also the results of the written test and the date of the relative oral exam can be found.
As an experiment, the course could be done wholly or partly in English, with the agreement of the students attending it. In any case, the oral exam may be conducted in the English language at the request of the student. - Learning verification modality
- The exam includes both a written exam with open answer questions and oral exam.
The written part consists of solving 3 or 4 exercises on topics which cover all the programme in about 3 hours. The written exam is designed to assess the ability of solving concrete or teoric problems. The written test is positively concluded if the grade is greater or equal to 18. Eventually the written test can be replaced by progress assessments.
The oral exam consists of a discussion on three topics one of which divided into several questions and takes about 30 minutes. The oral test is designed to assess the level of knowledge attained by the student on the theoretical contents and on and counterexamples). Finally, the oral examination allows the teacher to verify the performance of the student and his/her ability to organize the presentation in autonomy. - Extended program
- Cauchy sequences and Banach-Cacioppoli Theorem. Sequences and series of functions. Power series. Taylor’s theorem and series expansion. Evaluation of limits by using Taylor expansions. Fourier series and applications. General theory of ODEs and systems of differential equations in the nonlinear and linear cases, with fundamental examples. Integration on manifolds. Gamma function and some applications. For a detailed program and useful training aids and tools see UNISTUDIUM.