CODE 60503 ACADEMIC YEAR 2024/2025 CREDITS 6 cfu anno 2 INGEGNERIA NAUTICA 8721 (L-9) - LA SPEZIA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION LA SPEZIA SEMESTER 1° Semester MODULES Questo insegnamento è un modulo di: MATHEMATICAL ANALYSIS + MATHEMATICAL PHYSICS TEACHING MATERIALS AULAWEB OVERVIEW The course is directed to second year students which are familiar with basic notions in Calculus and Analytical Geometry. AIMS AND CONTENT LEARNING OUTCOMES Provide basic concepts and more specific mathematical tools to better understand the contents of some nautical engineering courses . AIMS AND LEARNING OUTCOMES The knowledge of mathematical basic tools useful in physical problems modelling. 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. level set, partial derivatives, optimization, line integral, integral in R^2 and R^3 ); 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 Basic notions in Calculus and Analytical Geometry. TEACHING METHODS The course consists of 52 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 Euclidean spaces. Toplology in R^n. Functions of several variables. Level sets. Continuity and differentiability. Directional and partial derivatives. Derivatives of higher order. Schwartz Theorem. Taylor approximation with Peano's and Lagrange's reminder. Quadratic forms. Unconstrained optimization. Necessary first order condition and sufficient second order condition. Change of coordinates. Double and triple integrals. Normal domains in R^2 and R^3. Integration formulas and theorem of change of variables. Lines and Surfaces in R^n and line and surface integral. Lenght of a curve and area of a surface. Barycenter and moment of inertia. Vector fields. Irrotational and conservative vector fields. Gauss - Green formulas and Divergence Theorem. RECOMMENDED READING/BIBLIOGRAPHY C. Canuto, A. Tabacco, "Analisi Matematica II", Springer, 2014. M. Bramanti, C. Pagani, S. Salsa. “Analisi matematica 2”, Zanichelli, 2009. S. Salsa, A. Squellati. “Esercizi di Analisi matematica 2”, Zanichelli 2011. 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 STEFANO VIGNOLO (President) ROBERTUS VAN DER PUTTEN (President Substitute) LESSONS LESSONS START https://corsi.unige.it/8721/p/studenti-orario Class schedule MATHEMATICAL ANALYSIS 2 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 SLD, disability or other regularly certified special educational needs are advised to contact the instructor at the beginning of the course to agree on teaching and examination methods that, in compliance with the course objectives, take into account the individual learning requirements. 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 10/01/2025 14:00 LA SPEZIA Scritto 31/01/2025 09:00 LA SPEZIA Scritto 11/06/2025 09:30 LA SPEZIA Scritto 14/07/2025 09:30 LA SPEZIA Scritto 05/09/2025 09:30 LA SPEZIA Scritto FURTHER INFORMATION The course requires knowledge of the content of Mathematical Analysis 1, Mathematical Analysis 1B and Geometry.