Unit MATHEMATICS
- Course
- Geology
- Study-unit Code
- GP004846
- Location
- PERUGIA
- Curriculum
- In all curricula
- Teacher
- Irene Benedetti
- CFU
- 12
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
MATHEMATICS - MOD. 1
| Code | GP004853 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Irene Benedetti |
| Teachers |
|
| Hours |
|
| Learning activities | Base |
| Area | Discipline matematiche |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Basic concepts of Mathematics. Sequences. Matrix Calculus. For functions in one variable: limit calculus; continuity. |
| Reference texts | - Paolo Marcellini, Carlo Sbordone : Elementi di Calcolo - Versione semplificata per i nuovi corsi di laurea, Ed. Liguori |
| Educational objectives | At the end of the course the student is supposed to be able to handle with limits and derivatives and to study a function in one or two variables with the calculus of the domain, of asymptotes, maximizers and minimizers. Moreover, to solve simple problems arising in applications. |
| Prerequisites | In order to be able to understand and apply the techniques described within the course you must know basic concepts of Mathematics such as: natural, rational and real numbers; equations and inequalities of first and second degree; exponential and logarithmic functions, trigonometric functions. |
| Teaching methods | Face to face and practical training. The course consists in 42 hours of lessons. Accompaniment activities are planned. |
| Other information | The beginning and the end of the lectures calendar is available at https://www.fisgeo.unipg.it/fisgejo/index.php/it/didattica/corsi-di-laurea-in-geologia/laurea-triennale-g/orario-lezioni-tg.html Classroom will be announced at the beginning of semester. Frequency not mandatory, but highly recommended. Visit the webpage https://www.unistudium.unipg.it/unistudium/ for useful informations and additional material such as lessons slides, extra exercises. Don't miss class. Ask questions. Go to office hours as often as necessary. During the written exam are banned mobile phones, computers, tablets, etc.... |
| Learning verification modality | Capability of solving basic exercises, and to correctly answering to multiple choice tests on the above listed topics. The exams consists of a written test. At the end of the two modules will take place the final exam. The written test consists of the solution of some multiple choice tests and some tests with open answer questions. The final exam test has a duration of of no more than four hours. It is designed to evaluate the ability to correctly apply the theoretical knowledge and the understanding of the issues proposed. For the students of the first year course it is possible to do partial exams (multiple choice tests and tests with open answer questions) that, in case of a positive evaluation, dispense the student to do a part of the final exam. |
| Extended program | Basic concepts of Mathematics: Sets, rational and real numbers, maximum and minimum, supremum and infimum. Exponential and logarithmic function. Sequences. Functions in one variable: domain, elementary functions, continuity, composition and inversion of a function. Limit calculus: definition of limit, algebra of limits, asymptotes. Matrix calculus: definition of matrices, determinant, rank, solving methods of linear systems. |
MATHEMATICS - MOD. 2
| Code | GP004854 |
|---|---|
| Location | PERUGIA |
| CFU | 6 |
| Teacher | Tiziana Cardinali |
| Teachers |
|
| Hours |
|
| Learning activities | Affine/integrativa |
| Area | Attività formative affini o integrative |
| Academic discipline | MAT/05 |
| Type of study-unit | Obbligatorio (Required) |
| Language of instruction | Italian |
| Contents | Differential Calculus and Integration for one variable functions. Differential Calculus and Optimization for two variable functions. |
| Reference texts | Paolo Marcellini, Carlo Sbordone : Elementi di Calcolo - Versione semplificata per i nuovi corsi di laurea, Ed. Liguori. The material presented in class and the exercises on the program will be made available on the Unistudium platform. Working students, non-attending students, disabled and / or SLD students are invited to report this to the teacher in charge of the course in order to better interact with the student. |
| Educational objectives | As teaching is the only Mathematics course for the Three-year Degree Course in Geology, it provides the basic mathematical tools useful for understanding the topics covered in the geological courses. The main objective of the course is to provide students with the foundations to approach with a critical spirit the reading of the graphs and formulas present in the textbooks they use during the three-year degree course in Geology. At the end of both modules into which the course is divided, the student will have acquired: - basic knowledge of mathematical analysis, such as, for example, the calculation of limits, derivatives, local and / or global maximums and minimums for functions of one or more variables and the calculation of simple integrals of functions of one variable. Furthermore, he must be able to carry out a complete study of a function of one variable and be able to solve simple optimization problems for functions of one or more variables. - Skills: will know how to apply the methods of mathematical analysis in order to solve problems, even of an applicative nature. - Communication skills: will have the ability to express the fundamental concepts of mathematical analysis with a certain rigor. - Learning skills: the student will acquire the ability to study and learn the notions of mathematical analysis, also in order to use them for solving simple real-world problems |
| Prerequisites | In order to be able to understand and apply the techniques described within the course you must know basic concepts of Mathematics (learned in module I but which are also topics present in upper secondary school programs) such as: - natural, rational and real numbers; - equations and inequalities of first and second degree; - exponential and logarithmic functions, trigonometric functions. For non-attending students, I would like to point out that the prerequisites described above are also present in upper secondary school programs. |
| Teaching methods | The course consists in 42 hours of lessons (face to face). - the arguments presented are accompanied by examples and counterexamples to achieve a good understanding of the definitions and statements of the theorems. - a strategy used as a support to teaching is the tutoring activity that will be carried out by a capable and deserving student, as established by the Intercorso Council, in additional hours to the lessons. This Tutoring, coordinated by the teacher, will aim to help students in the study and understanding of the topics of the course, with particular attention to the performance of the exercises. - another strategy will be to prepare to prepare two exemption tests that invite students to study the topics in a calibrated way and to also have the possibility with a study distributed throughout the course to be able to take the exam more easily and in the scheduled exam sessions in the current academic year. - the textbook used meets the needs of the course, which are to present the contents indicated for a first level course for the three-year degrees in Geology. - If there are working students, non-attending students or students with disabilities and /or with DSA, the teacher has prepared slides and handouts in Italian, available on the Unistudium platform. In any case, I advise non-attending students to report this to the teacher at the beginning of the lessons to decide together the most suitable strategy to arrive at a good preparation for the exam. |
| Other information | The beginning and the end of the lectures calendar is available at https://www.fisgeo.unipg.it/fisgejo/index.php/it/didattica/corsi-di-laurea-in-geologia/laurea-triennale-g.html The course takes place over 42 hours and each week there are 4 frontal hours on the calendar. The calendar of lessons is available on the web page: https://www.fisgeo.unipg.it/fisgejo/index.php/it/didattica/corsi-di-laurea-in-geologia/laurea-triennale-g.html Frequency: Optional but strongly recommended. Attendance is strongly recommended especially for students who do not pass the entrance test. The exemptions are reserved for students who have attended at least 75% of the lessons of the course. Collective study activities are foreseen in the presence of the teacher and / or a tutor. There are hours of teaching support which are hours of collective study activity. This activity is strongly recommended especially for students who do not pass the entrance test. The student reception for the course is organized according to the timetable indicated on the web page: https://www.fisgeo.unipg.it/corsidilaurea/GEO/programma-tutorato-I-anno-LT.pdf takes place in the teacher's office on the fifth floor of the Department of Mathematics and Computer Science or on the Teams platform. During the reception hours the students will be followed in a personalized way. The exam calendar can be found at: https://www.fisgeo.unipg.it/fisgejo/index.php/it/didattica/corsi-di-laurea-in-geologia/laurea-triennale-g/calendario-degli-esami-tg.html Examining board: T. Cardinali, I. Benedetti (A. Boccuto, R. Filippucci, P. Pucci, P. Rubbioni, A.Sambucini, E. Vitillaro). Course informations see: https://www.unistudium.unipg.it/unistudium/ or https://www.fisgeo.unipg.it/corsidilaurea/GEO/programma-tutorato-I-anno-LT.pdf - Classroom will be announced at the beginning of semester. - During the written test, scientific calculators, cell phones, iPods, etc. are forbidden, under penalty of exclusion from the test. - Material and news relating to the course can be found at: https://www.unistudium.unipg.it/unistudium/ - Advice: Don't miss class. Ask questions. Go to office hours as often as necessary. Clarifications on the program, on the exam or on the topics covered in class will be given by the teacher at his office located in the Department of Mathematics and Computer Science or on the Teams platform. - If there are working students, non-attending students or students with disabilities and / or with SLD, the teacher has prepared slides and handouts in Italian, available on the Unistudium platform. In any case, I advise non-attending students to report it to the teacher at the beginning of the lessons to decide together the most suitable strategy to arrive at a good preparation for the exam. - For the preparation of the written test it is important to actively attend, that is by asking questions about the program carried out and carefully reviewing the exercises presented in class or during the hours of Tutoring, then trying to carry out independently also those inserted by the teacher on the Unistudium page relating to the course in question. object. - The right place for clarification is the hours dedicated to tutoring and the hours dedicated by the teacher to receive students. |
| Learning verification modality | Capability of solving basic exercises on the above listed topics. The exams consists of a written test. At the end of the two modules will take place the final exam. The written test consists of the solution of some open answer questions. The final exam test has a duration of of no more than three hours. It is designed to evaluate the ability to correctly apply the theoretical knowledge and the understanding of the issues proposed. For the students of the first year course it is possible to do partial exams that, in case of a positive evaluation, dispense the student to do a part of the final exam. |
| Extended program | Differential Calculus: definition of derivative, calculus of derivative, derivative of the sum, of the product, of the quotient, of the composition and of the inverse. Mean value Theorem. Maximum and Minimum of a function. De l'Hospital Theorem. Derivative of second order: geometric meaning, convexity and concavity. Integration: definition, geometric meaning of the definite integral. Primitives, Torricelli-Barrow Theorem, immediate integrals. Integration by parts and by substitution. Integration of rational fractions Two variable functions: Plane domains. Partial and directional derivatives, gradient vector and critical points. Second derivatives, Schwarz Lemma, Method of the Hessian. Search of maxima and minima with easy constraints (on compact subsets of the domain). |