CODE 56585 ACADEMIC YEAR 2018/2019 CREDITS 12 cfu anno 1 INGEGNERIA MECCANICA 8720 (L-9) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/05 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER Annual TEACHING MATERIALS AULAWEB AIMS AND CONTENT LEARNING OUTCOMES The course aims at providing the student with basic operative knowledge on differential and integral calculus for functions of one and two real variables, with some attention to mathematical rigour. Some of the founding elements of mathematical modeling are developed in the second half of the course, such as the elementary theory of ordinary differential equations. TEACHING METHODS Lectures and practice SYLLABUS/CONTENT Functions of one real variable. Real numbers, the oriented real line. The Cartesian plane, graphs of elementary functions. Operations on functions and their graphical interpretation. Monotonicity. Composition and inversion. Powers, exponentials and logarithms. Supremum and infimunm. Sequences and series: the basic notions and examples. Limits of functions. Infinitesimal and infinite functions. Continuous functions and their local and global, derivative, derivation rules. Derivatives of elementary functions. Sign of derivatives in the study of monotonicity and convexity. The classical theorems of Rolle, Cauchy, Lagrange and de l'Hôpital. Taylor expansions and applications to critical points. Definite and indefinite integrals. Functions of two (or more) real variables. Continuity, directional and partial derivatives, gradient. Differentiability and tangent plane. Level sets. Local minima and maxima: second order derivatives and the Hessian. Schwartz’s theorem. Differential equations. Separation of variables. The existence and uniqueness theorem for the Cauchy problem. Linear first and second order differential equations: solving methods. General solution for the linear equation. RECOMMENDED READING/BIBLIOGRAPHY A. Bacciotti, F. Ricci, Lezioni di Analisi Matematica 1 e 2, Levrotto & Bella, 1991. C. Canuto, A. Tabacco, Analisi Matematica 1 e 2, Springer-Verlag Italia, 2003. F.De Mari, Dispense di Analisi Matematica 1, http://www.dima.unige.it/~demari/DIDA.html TEACHERS AND EXAM BOARD ERNESTO DE VITO Ricevimento: Friday 14-16 MICHELE LATTARULO Exam Board ERNESTO DE VITO (President) MICHELE LATTARULO (President) LESSONS Class schedule MATHEMATICAL ANALYSIS 1 EXAMS Exam schedule Data appello Orario Luogo Degree type Note 14/01/2019 09:00 GENOVA Scritto 13/02/2019 09:00 GENOVA Scritto 14/02/2019 09:00 GENOVA Scritto 14/06/2019 09:00 GENOVA Scritto 01/07/2019 09:00 GENOVA Scritto 17/07/2019 09:00 GENOVA Scritto 10/09/2019 09:00 GENOVA Scritto
