CODE 56584 ACADEMIC YEAR 2022/2023 CREDITS 12 cfu anno 1 INGEGNERIA MECCANICA 8784 (L-9) - LA SPEZIA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION LA SPEZIA SEMESTER Annual TEACHING MATERIALS AULAWEB OVERVIEW The aim of this course is to provide a practical working tool for students in Engineering or in any other field where rigorous Calculus is needed. The basic focus is on functions of one real variable and basic ordinary differential equations, separation of variables, linear first-order, and constant coefficients ODE. AIMS AND CONTENT LEARNING OUTCOMES The aim is to achieve good knowledge of differential and integral calculus for one or two variables functions. AIMS AND LEARNING OUTCOMES The student will have to acquire a solid ability in Mathematical Analysis, in particular he must know how to study a function of one or more real variables. Moreover he will have to know how to apply the various theorems for the resolution of simple differential equations of the first order and higher order (linear with constant coefficients). PREREQUISITES Elementary algebra: equations and inequalities, trigonometry. TEACHING METHODS 106 hours of lessons. During the theoretical lessons the definitions and the theorems will be presented with many examples and applications. During the other part of the course many exercises will be solved. During the academic year some guided exercises will be carried out. SYLLABUS/CONTENT Real numbers, infimum and supremum, functions of one real variable, elementary functions, limits, infinitesimals and infinities, continuous functions, derivable functions, differentiable functions, Taylor’s formula, expansion of elementary functions, primitives and indefinite integrals, methods of indefinite integration, definite integrals, fundamental theorem of integral calculus, first order differential equations, Cauchy’s problem and theorem, resolution of linear first order differential equations and separable variables equations, linear differential equations with constant coefficients of order n. RECOMMENDED READING/BIBLIOGRAPHY F. Parodi, T. Zolezzi, Appunti di Analisi matematica, ECIG, 2007 R. A. Adams, Calcolo differenziale 1 & 2, Casa Editrice Ambrosiana, 2007 A. Bacciotti, F. Ricci, Lezioni di Analisi Matematica 1 e 2, Levrotto & Bella, 1991. M. Bramanti, C. Pagani, S. Salsa, Analisi matematica 1 e 2 Zannichelli, 2008 M.Baronti-F.De Mari-R.Van Der Putten-I.Venturi: Calculus Problems, Springer TEACHERS AND EXAM BOARD MARCO BARONTI Ricevimento: The teacher is available for explanations one afternoon a week. ROBERTUS VAN DER PUTTEN Ricevimento: The teacher receives students from 11 to 12 a.m. on Wednesday in lecture hall DE118. VALENTINA BERTELLA Ricevimento: Write me an e-mail valentina.bertella@gmail.com Exam Board MARCO BARONTI (President) CLAUDIO ESTATICO ROBERTUS VAN DER PUTTEN (President Substitute) LESSONS LESSONS START https://corsi.unige.it/8784/p/studenti-orario Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The final exam consists of a written test and an oral exam. The student must obtain an evaluation of at least 12/30 in the written test to access the oral exam. ASSESSMENT METHODS During the written test the student will have to solve some exercises concerning the study of functions and the differential problem. During the oral examination the student must highlight critical analytical skills and must be able to apply the main theorems for the solution of easy exercises. Exam schedule Data appello Orario Luogo Degree type Note 16/01/2023 09:30 LA SPEZIA Scritto 10/02/2023 14:00 LA SPEZIA Compitino 13/02/2023 09:30 LA SPEZIA Scritto 06/06/2023 09:30 LA SPEZIA Scritto 10/07/2023 09:30 LA SPEZIA Scritto 12/09/2023 09:30 LA SPEZIA Scritto