Scheda programma d'esame
ANALISI MATEMATICA 1
|ANALISI MATEMATICA 1||MAT/05||LEZIONI||120|
Programma non disponibile nella lingua selezionata
KnowledgeStudent who completes the course successfully will be able to: - use the definitions of limit as they apply to sequences, series, and functions, - determine the continuity, differentiability, and integrability of functions defined on subsets of the real line, - draw the approximate graph of a function, - produce rigorous proofs of results that arise in the context of real analysis, - write solutions to problems and proofs of theorems that meet rigorous standards based on content, organization and coherence, argument and support. Special emphasis is placed on problem solving abilities and autonomous creative reasoning.
Assessment criteria of knowledgeIn the multiple choice test (30 minutes, 16 questions) the student must demonstrate his/her knowledge of the basic course contents and prerequisites. In the written exam (3 hours, 4 problems), the student must demonstrate his/her ability to approach and solve standard problems requiring the tools presented in the course. Solutions are presented in written form. Correctness and clarity of solutions will be assessed. During the oral exam the student's ability to explain correctly the main topics presented during the course at the board will be assessed.
- Final oral exam
- Final written exam
- Periodic written tests
Delivery: face to face
- attending lectures
- individual study
- group work
SyllabusPreliminaries: elementary logic, basic set theory, mathematical induction, elementary functions, real numbers. Limits of sequences and functions. Numerical series. Continuity and uniform continuity in one variable. Intermediate value theorem. Compactness and Weierstrass theorem. Derivatives and differential calculus in one variable. Taylor expansion. Graphs of real functions. Integrals and generalized integrals in one variable. Basic differential equations.
BibliographyStudents are highly recommended to read the course notes (a printout of the lectures). Students are also highly recommended to work on the suggested exercises. Both the notes and the exercises can be easily downloaded from the teacher's home page. Further reading: E. Acerbi, G. Buttazzo, Primo corso di Analisi Matematica 1997, Pitagora Editrice Bologna, ISBN 88-371-0942-3. P. Marcellini, C. Sbordone; Analisi Matematica uno; Liguori Editore.
Ultimo aggiornamento 14/11/2016 17:27