Unit MATHEMATICAL ANALYSIS II
- Course
- Mathematics
- Study-unit Code
- 55001909
- Curriculum
- In all curricula
- Teacher
- Tiziana Cardinali
- Teachers
-
- Tiziana Cardinali
- Hours
- 73 ore - Tiziana Cardinali
- CFU
- 9
- Course Regulation
- Coorte 2020
- Offered
- 2021/22
- Learning activities
- Base
- Area
- Formazione matematica di base
- Academic discipline
- MAT/05
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- The goal of Mathematical Analysis II is to continue the study of calculus on the real line, which you started in Mathematical Analysis I, with a focus on functions of several variables: differentiability and integration.
- Reference texts
- The main material introduced during lectures and is contained in Text-book:
1) C. CANUTO, A. TABACCO Analisi Matematica II, Springer-Verlag , 1nd Ed 2008 or 2nd Ed., 2014
or the English version:
1)' C. CANUTO, A. TABACCO Mathematical Analysis II, Springer-Verlag , 2nd Ed., 2015
The lecturer will supply texts about the subject " Lebesgue integration in R^n" (Italian).
Other recommended books:
M. BRAMANTI, C.D. PAGANI, S. SALSA, Analisi matematica 2, Zanichelli, 2009.
M. BRAMANTI, Esercitazioni di Analisi Matematica 2, Ed. Esculapio, Bologna, 2012.
G. BUTTAZZO, V. COLLA, Temi di esame di Analisi Matematica II, Pitagora, 2001.
M. AMAR, A. M. BERSANI, Esercizi di Analisi Matematica per i Nuovi Corsi di Laurea, Progetto Leonardo Ed. Esculapio, 2002. - Educational objectives
- On successful completion of the course, students should be able to:
- to read and understand the definitions and properties about the differential calculus for functions of several variables and Lebesgue integration in R^n,
- to own computational skills to solve various exercises,
- to be able to recognize correct demonstrations and identify incorrect reasoning;
- to think critically, and express mathematical concepts precisely in writing,
- to be prepared to take Mathematical Analysis III,
- to provide themselves a mathematical proof of simple statements,
- to apply the knowledge gained in this course to other situations and disciplines,
- to be able to communicate the mathematical knowledge acquired in the course.
- to apply knowledge and skills acquired in mathematical analysis to analyze and handle novel situations in a critical way.
These competencies are crucial in order to support teachers’ professional development. - Prerequisites
- This course assumes that the student has a good working knowledge of Mathematical Analysis I topics including limits, continuity, derivatives, basic integration and improper integrals on the real line. These prerequisites are concepts that students meet not only in the mentioned basic course of Mathematics but also in their pre-university education.
- Teaching methods
- The course is split into 73 hours (face-to-face traditional lessons on all the arguments of the course (63 hours) in which several exercises are presented to the students (10 hours). In addition to a detailed theoretical expositions, for each argument the teacher will illustrate the relative exercises, which will be the model for the ones proposed in the written exam. (See: https://www.unistudium.unipg.it/unistudium/)
In the tutorial service the students will be followed individually by the teacher.
Some advices for to study the course, the book text and the exam tests:
1. Read the example problems carefully, completing some steps that are left out (ask someone for help if you can't follow the solution to a worked example).
2. Later use the worked examples to study by covering the solutions, and seeing if you can solve the problems on your own.
3. Keep in mind that sometimes an answer could be expressed in various ways that are analitically equivalent, so don't assume that your answer is wrong just because it doesn't have exactly the same form as the answer in the back. - Other information
- The course is divided in 6+2 hours per week and its time schedule is available at the web page :
http://www.dmi.unipg.it/didattica/corsi-di-studio-in-matematica/matematica-triennale/orario-lezioni
Lecture halls (see: http://www.dmi.unipg.it/didattica/corsi-di-studio-in-matematica/matematica-triennale/orario-lezioni) - Dipartimento di Matematica e Informatica.
Attendance of the lectures is warmly recommended.
Tutorial service is given in office hours. Customiced consulting students.
It's desidered a tutorial activity.
The lectures will be companied by exercises sessions.
The teacher will distribute educational material on the argument : Lebesgue integration (in italian) useful for a better understanding of this topic.
Some tips:
Don't miss class. Ask questions. Go to office hours as often as necessary.
The final exam may be conducted in the English language at the request of the student.
Some suggestions for the exam:
You need to know the terminology used throughout this course.
Finally, many of the problems in this course will have multiple solution techniques and so you’ll need to be able to identify all the possible techniques and then decide which will be the easiest technique to use.
All cell phones and electronic devices that transmit wirelessly must be turned off during the written exam. Vibrate or silence modes are not allowed. Laptops, iPods, language translators, or any devices that can receive a wireless signal are not allowed.
8 exams. The written exam dates are available at the web: http://www.dmi.unipg.it/didattica/corsi-di-studio-in-matematica/matematica-triennale/calendario-esami
Examining board: T. Cardinali, I. Benedetti (A. Boccuto, R. Filippucci, P. Pucci, P. Rubbioni, A. Sambucini, E. Vitillaro).
The final written exam is not given in the usual classroom. You will find the room assignments at
http: //www.segreterie.unipg.it/self/gissweb.home
There is a Web page which contains this course description as well as other information related to this course. Point your Web browser to:
https://www.unipg.it/personale/tiziana.cardinali/didattica
News on:
https://www.unistudium.unipg.it/unistudium/
Per informazioni sui servizi di supporto agli studenti con disabilità e/o DSA visita la pagina
http://www.unipg.it/disabilita-e-dsa - Learning verification modality
- The final exam consist: written exam with open answer questions and oral exam.
- the written exam consists of three exercises one of which divided into several questions and takes three hours. The calculus abilities and knowledge are verified.
- the oral exam consists of a discussion on three topics one of which divided into several questions and takes about 30/40 minutes.
It is possible to do partial exams that, in case of a positive evaluation (with a grade> = 18), despense the student to do the final written-exam.
The partial exams are valid until the last call of the session of January / February 2023.
The oral exam is designed to verify the level of knowledge attained by the student on the theoretical contents and on the methodologies of the course. Moreover, the oral examination allows the teacher to assess the performance of the student and his/her ability to organize the presentation in autonomy. The method, the language and the theoretical knowledge of the matter are verified. It is necessary that the student will need to know all definitions introduced in the course. Moreover, the student will need to understand them, how they work, and more importantly whether they can be used or not.
You can take the oral test in the same appeal of the written test of whether the latter has achieved a higher vote than or equal to 15/30. You can take the oral examination in appeals after the date on which the written exam is supported if on the latter it has achieved a higher vote than or equal to 18/30. If the oral examination is not enough, the teacher will decide if the written test is necessary to repeat (it depends on the reasons that have led to an assessment not enough of the oral test).
In the event that it is necessary according to the University regulations, the exams and partial exams could take place on the online platform.
Students with DSA certification must submit the same at least two weeks prior to the test.
Valutation (it is advisable to take the oral exam with an evaluation> 14/30):
- Written test score < 18/30 and the oral exam is SATISFACTORY ALSO AS REGARDS THE PART OF THEORY,
the final mark of the exam can be at most rated 23/30.
- Written test score = o > 18/30 and < 20/30 and the oral exam is SATISFACTORY ALSO AS REGARDS THE PART OF THEORY, the final mark of the exam can be at most evaluated 28/30 .
- Written test score = o > of 20/30 and the oral exam is SATISFACTORY ALSO AS REGARDS THE PART OF THEORY,
the final mark of the exam can be at most 30/30 and honors.
Information on support services for students with disabilities and / or DSA see: http://www.unipg.it/disabilita-e-dsa - Extended program
- Vector functions and curves. Functions of several variables: continuity, partial derivability, directional derivability, differentiability, maximums and minimums with and without constraints. Lagrange Multipliers. Chain Rules. Implicit functions. Lebesgue integration in R^n. Polar coordinates in R2, cylindrical coordinates spherical coordinates. Integrals on curves. Differential forms and their integration. Gauss and Green's theorem, divergence theorem, Stokes' theorem in R^2.