CODE 98340 ACADEMIC YEAR 2021/2022 CREDITS 9 cfu anno 1 INGEGNERIA NAUTICA 8721 (L-9) - LA SPEZIA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION LA SPEZIA SEMESTER Annual MODULES Questo insegnamento è un modulo di: MATHEMATICAL ANALYSIS + GEOMETRY TEACHING MATERIALS AULAWEB OVERVIEW The course is directed to first year students which are familiar with basic notions in elementary Mathematics AIMS AND CONTENT LEARNING OUTCOMES The course aims to provide the basic knowledge preparatory to other courses that require mathematical methods and tools. AIMS AND LEARNING OUTCOMES The course provides basic notions about Functions of one variable, integration of continuous functions and first order ODE’s in view of applications in Physics and Nautic Engineering. PREREQUISITES Basic notions in elementary mathematics. TEACHING METHODS 90 hours of lectures . Distance lectures until the end of sanitary emergency an subsequently frontal lectures. SYLLABUS/CONTENT 1) Real numbers and the real line. Cartesian coordinates in the plane. Functions and their graphs. Limits and continuity. Theorems about continuous functions. The derivative. Differentiation rules: product, reciprocal, quotient and chain rule. Monotone functions: the inverse function theorem. Derivatives of some elementary functions. Theorems about differentiable functions: Rolle, Lagrange, Cauchy. Higher order derivatives. Extreme values, convexity and inflection. Sketching the graph of a function. 2) Integration. Sums and sigma notation. Areas as limits of sums. The definite integral. Properties of the definite integral. The fundamental Theorem of Calculus. Changes of variable: the method of substitution. Areas of plane regions. Integration by parts. Integrals of rational functions. 3) L’Hopital’s rule. Taylor’ formula and its applications. 3) Ordinary differential equations. First order equations: separable equations, linear equations. Cauchy problems: existence and uniqueness theorem. Linear ODE’s with constant coefficients. RECOMMENDED READING/BIBLIOGRAPHY R.A. Adams, Calcolo Differenziale 1 Casa Editrice Ambrosiana. Notes & Exercises in aulaweb ( a.a. 10/11 and the following) TEACHERS AND EXAM BOARD DANILO PERCIVALE Ricevimento: Until the end of the health emergency, a special Teams channel will be set up and students can post their requests. Periodically the teacher will post the answers on Stream Exam Board DANILO PERCIVALE (President) VALENTINA BERTELLA SERGIO DE MICHELI MARIA VIRGINIA CATALISANO (President Substitute) LESSONS LESSONS START https://corsi.unige.it/8721/p/studenti-orario Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION A written test is required which could be followed by another confirmation test ASSESSMENT METHODS Outcome of written test and its confirmation. Exam schedule Data appello Orario Luogo Degree type Note 10/01/2022 09:00 LA SPEZIA Scritto 24/01/2022 09:15 GENOVA Scritto 07/02/2022 14:30 LA SPEZIA Scritto 08/06/2022 09:00 LA SPEZIA Scritto 08/07/2022 09:00 LA SPEZIA Scritto 07/09/2022 09:00 LA SPEZIA Scritto FURTHER INFORMATION Professor will receive students by appointment.
