Unit MATHEMATICS
- Course
- Geology
- Study-unit Code
- GP004846
- Curriculum
- In all curricula
- Teacher
- Irene Benedetti
- CFU
- 12
- Course Regulation
- Coorte 2021
- Offered
- 2021/22
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa integrata
MATHEMATICS - MOD. 1
| Code | GP004853 |
|---|---|
| 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 |
|---|---|
| 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 |
| 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 (for function in one variable), maximizers and minimizers (for function in one or two variables) and integration of functions in one variable. |
| 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 | The course consists in 42 hours of lessons (face to face). Practical training (face to face). Accompaniment activities are planned. |
| Other information | The beginning and the end of the lectures calendar is available at http://www.fisgeo.unipg.it/joo3x/index.php/it/didattica/corsi-di-laurea-in-geologia/orari-calendari-sessioni-geologia.html Exams calendar is available 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/ https://www.fisgeo.unipg.it/corsidilaurea/GEO/programma-tutorato-I-anno-LT.pdf Classroom will be announced at the beginning of semester. Frequency not mandatory, but highly reccomended. These partial exams are reserved for students who have attended at least 75% of the course lessons . 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. During the written exam are banned mobile phones, computers, iPods, 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, despense the student to do a part of the final exam. So, those who did not pass all partial exams conducted during the year with a grade> = 18 , MUST REPEAT the partial exams that were not sufficient in one of the official appeals, set out in Schedule Exams. The final grade will be calculated by averaging the first two parts (carried out in the in official exam's dates) and then the average between this result and the mark obtained in the third part (carried out in the partial exams or in official exam's dates). Recall that each waiver (or part corresponding to an partial exam) program is evaluated in the following manner: 10 points for each correct answer; 0 points for each non-response; - 2 points for each wrong answer. If the end result is not enough, the student must repeat the entire exam EXCEPT THE PARTIAL EXAMS DURING THE YEAR which she/he has got a vote> = 18. These partial exams are reserved for students who have attended at least 75% of the course lessons . The partial exams with a vote> = 18 are valid until the last call of the session of January / February 2023. In the event that it is necessary according to the University regulations, the exams and the partial exames could take place on the online platform. Students with DSA certification must submit the same at least two weeks prior to the test. Information on support services for students with disabilities and / or DSA see: http://www.unipg.it/disabilita-e-dsa |
| 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). |