CODE 115468 ACADEMIC YEAR 2024/2025 CREDITS 6 cfu anno 1 INGEGNERIA INFORMATICA 8719 (L-8) - IMPERIA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE English TEACHING LOCATION IMPERIA SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW The course provides the basic tools of Mathematical Analysis concerning functions of one real variable. AIMS AND CONTENT AIMS AND LEARNING OUTCOMES The knowledge of mathematical basic tools useful in physical problems modeling. The skill of setting up and solving problems by using intuitive and deductive reasoning as well as recognizing and using the suitable mathematical tools in solving problems in a physical setting. At the end of the course the student will be able 1. to state the concepts ( theorems and definitions ) introduced during the course ( f.i. integral , Existence and Uniqueness theorems for differential problems ); 2. to give physical and geometric interpretation of the basic concepts of Mathematical Analysis; 3. to set up problem solving with an intuitive approach; 4. to select the suitable mathematical tools in problem solving; 5. to solve problems with deductive reasoning. PREREQUISITES Differential calculus for functions of one real variable, i.e. the content of Mathematical Analysis Module 1 course. TEACHING METHODS The course consists of 60 hours of lectures and practices. In the lectures the topics of the syllabus are explained with definitions and theorems and some proofs which can be useful for the comprehension of the topics and to develop the logical and deductive skills. Every theoretical topic is explained with easy examples and some exercises. In the practices, many exercises are solved with the aim of going into the knowledge of theoretical topics treated in the lectures and preparing the student for the exam. Some guided practices will be held to help the student to valuate one's preparation. Several intermediate tests are provided. Students have several exercises at their disposal on Aulaweb SYLLABUS/CONTENT Antiderivatives. Riemann integral : definition and basic properties. Mean value Theorem. The Fundamental Theorem and Formula of Integral Calculus. Areas of plane regions. Changes of variable: the method of substitution. Integration by parts. Integrals of rational and trigonometric functions. Integral functions. Improper Integral. Ordinary differential equations : the method of separation of variables and Existence and Uniqueness Theorems for the Cauchy Problem. Ordinary linear differential equations : structure of the general solution in the Homogeneous and not homogeneus case. Solving methods for n order linear equations with constant coefficients and first order linear equations with continuous coefficients. Systems of linear differential equations. RECOMMENDED READING/BIBLIOGRAPHY Theory C. Canuto – A. Tabacco : Analisi Matematica 1. Pearson. 2021. M.Bramanti - C.D.Pagani - S. Salsa : Analisi Matematica 1. Zanichelli, 2008. T. Zolezzi : Dispense di analisi matematica I e II. F. Parodi – T. Zolezzi : Appunti di analisi matematica. ECIG, 2002 R. Adams : Calcolo differenziale I. Funzioni di una variabile reale. Casa ed. Ambrosiana, 1992. P. Marcellini – C. Sbordone : Analisi Matematica II. Liguori Editori Exercises M. Baronti – F. De Mari – R. van der Putten – I. Venturi : Calculus Problems. Springer 2016 M. Pavone: Temi svolti di analisi matematica I. Marcellini-Sbordone : Esercitazioni di matematica, I volume S. Salsa – A. Squellati : Esercizi di Matematica, volume 1. TEACHERS AND EXAM BOARD ROBERTUS VAN DER PUTTEN Ricevimento: The teacher receives students on a day in the week at the office located at the degree course building. The day will be fixed on February 2025. The e - mail address is : robertus.van.der.putten@unige.it Exam Board ROBERTUS VAN DER PUTTEN (President) ALBERTO DAMIANO ANGELO MORRO (President Substitute) LESSONS LESSONS START The lessons start on Febraury 17, 2025 https://easyacademy.unige.it/portalestudenti//index.php?_lang=en Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The exam consists in a written and oral examination. The written examination consists in two problems concerning the topics treated. The students have two / three hours at their disposal. After the written examination, the students who obtained a grade higher than 13/30 may take the oral examination. Two intermediate examinations will be held which may substitute the written examination. Students with certification of Specific Learning Disabilities (SLD), disabilities, or other special educational needs must contact the instructor at the beginning of the course to agree on teaching and examination methods that, while respecting the course objectives, take into account individual learning styles and provide appropriate compensatory tools. It is reminded that the request for compensatory/dispensatory measures for exams must be sent to the course instructor, the School representative, and the “Settore serviziper l'inclusione degli studenti con disabilità e con DSA” office (dsa@unige.it) at least 10 working days before the test, as per the guidelines available at the link: https://unige.it/disabilita-dsa” ASSESSMENT METHODS The aim of the examination is verifying the skills acquired by the student. The problems proposed in the examination call for the choice and the application of suitable mathematical tools, besides their solution needs the skill of constructing a logical connection applying theoretical topics treated. The student must solve the exercises justifying the most important passages recalling theorems and definitions and underlying the physical and geometric interpretation of the problem. The final evaluation depends also on the quality of the written exposition and on the ability of reasoning. Exam schedule Data appello Orario Luogo Degree type Note 16/06/2025 09:00 IMPERIA Scritto + Orale 11/07/2025 09:00 IMPERIA Scritto + Orale 15/09/2025 09:00 IMPERIA Scritto + Orale Agenda 2030 - Sustainable Development Goals Quality education