Introduction to the rigorous treatment of mathematical analysis, while developing at the same time the methods of differential and integral calculus in the context of real functions of a real variable.
Traditional: blackboard.
1. The indefinite integral. Integration techniques. Integration of elementary functions. Integration by parts and by substitution. Integration of rational functions.
2. The Riemann integral. Definition and properties of the definite integral. Integrability of continuous and monotonic functions. The oriented integral. The integral mean theorem. Relations between derivation and integration: integral functions, the fundamental theorem of calculus and its consequences. Improper integrals. Convergence criteria.
3. Series. Geometric and telescopic series. Convergence. Series with non negative terms: comparison, root and ratio criteria; condensation, order and integral tests. Alternating series and Leibniz' theorem.
4. Differential equations. Separation of variables. Linear first order equations Second order linear equations with constant coefficients.
A.Bacciotti, F.Ricci - Analisi Matematica I - Liguori Editore
M. Baronti, F. De Mari, R. van der Putten, I. Venturi - Calculus Problems, Springer, 2016
Further readings will be posted on the web page (AULAWEB)
Ricevimento: The teacher is available for explanations one afternoon a week.
Ricevimento: Send a message to ernesto.devito@unige.it
Ricevimento: By appointment
MARCO BARONTI (President)
FILIPPO DE MARI CASARETO DAL VERME
GIOVANNI ALBERTI (President Substitute)
ERNESTO DE VITO (President Substitute)
MATTEO SANTACESARIA (Substitute)
Lessons will start according to the academic calendar.
The exam consists of a written test and an oral test.
Students enrolled in the course of study in Physics are not required to study the proofs of the theorems that will be the object of learning during the second semester.
Students with a certified DSA, disability or other special educational needs are advised to contact the lecturer at the beginning of the course in order to agree on teaching and examination methods that, while respecting the teaching objectives, take into account individual learning methods and provide suitable compensatory tools.
1. Two intermediate written tests will be provided during the year. If a student obtains an average mark greater than or equal to 18/30 and if he scores at least 15/30 in both, the average of the two marks counts as a written test.
2. A written test with a score greater than or equal to 12/30 allows access to the oral test.
3. If a student submits a written test, the intermediate written tests will be considered canceled.
Teaching style: in presence.
