CODE 101117 ACADEMIC YEAR 2022/2023 CREDITS 6 cfu anno 1 MARITIME SCIENCE AND TECHNOLOGY 10948 (L-28) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE English TEACHING LOCATION GENOVA SEMESTER 1° Semester MODULES Questo insegnamento è un modulo di: MATHEMATICS AND ALGEBRA TEACHING MATERIALS AULAWEB AIMS AND CONTENT LEARNING OUTCOMES The aim of this course is to provide a practical working tool for students where rigorous Calculus is needed. The main focus is on the study of functions of one real variable (continuity, derivative, maxima/minima, integration) and a brief introduction to multivariable calculus (oriented towards finding maxima/minima). The last part of the course is oriented towards basic ordinary differential equations (for example separation of variables, linear first-order, and constant coefficients ODE). AIMS AND LEARNING OUTCOMES The aim of this course is to provide a practical working tool for students where rigorous Calculus is needed. The main focus is on the study of functions of one real variable (continuity, derivative, maxima/minima, integration) and a brief introduction to multivariable calculus (oriented towards understanding the objects and finding maxima/minima). The last part of the course is oriented towards basic ordinary differential equations. TEACHING METHODS During the course theory and example classes will be given. During theory classes, definitions, theorems and main proofs will be given, with lots of examples and exercises. In the example classes, exercises will be discussed and solved with the class, aiming to a ameliorate the calculus skills of the students. Working students and students with certified SLD (Specific Learning Disorders), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination arrangements so to take into account individual learning patterns, while respecting the teaching objectives. SYLLABUS/CONTENT Numbers: natural, integer, rational, real numbers. Definitions and first examples of functions; continuity, derivability and theorems about them, study of maxima/minima, integration. Definitions and examples of functions of two variables: various representations. Continuity and differentiability for multivariable functions. Maxima/minima. Ordinary differential equations: separation of variables, constant and nonconstant linear differential equations RECOMMENDED READING/BIBLIOGRAPHY Paolo MARCELLINI, Carlo SBORDONE: Elementi di analisi matematica 1, editore Liguori, Napoli. Marco BARONTI, Filippo DE MARI, Robertus VAN DER PUTTEN, Irene VENTURI: Calculus problems. editore Springer. TEACHERS AND EXAM BOARD LAURA BAZZOTTI Exam Board LAURA BAZZOTTI (President) VALENTINA BERTELLA (President) LESSONS LESSONS START https://corsi.unige.it/10948/p/studenti-orario Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION The exam will consist of a written part and an oral part. The oral part is accessible only if the score in the written test is higher or equal to 14. ASSESSMENT METHODS During the written test, the student will solve exercises mainly concerning limits, integrals, study of functions (possibly of more than one variable) and ordinary differential equations. During the oral examination student must highlight critical analysis, skills and ability to apply the concepts learnt to solve easy exercises, possibly some (guided) applications to the real world. Exam schedule Data appello Orario Luogo Degree type Note 13/01/2023 14:00 GENOVA Scritto 20/01/2023 14:00 GENOVA Orale 03/02/2023 14:00 GENOVA Scritto 10/02/2023 14:00 GENOVA Orale 09/06/2023 14:00 GENOVA Scritto 16/06/2023 14:00 GENOVA Orale 06/07/2023 09:00 GENOVA Scritto 06/07/2023 15:00 GENOVA Orale 08/09/2023 14:00 GENOVA Scritto 14/09/2023 14:00 GENOVA Orale