MATHEMATICAL ANALYSIS 1

Degree course: 
Corso di First cycle degree in MATHEMATICS
Academic year when starting the degree: 
2013/2014
Year: 
1
Academic year in which the course will be held: 
2013/2014
Course type: 
Basic compulsory subjects
Credits: 
9
Period: 
First Semester
Standard lectures hours: 
56
Detail of lecture’s hours: 
Lesson (56 hours)
Requirements: 

Prerequisites:

Basic knowledge of high school algebra, trigonometry and analytic geometry.

Assessment: 
Voto Finale

Teaching objectives and expected learning outcomes:

The course aims at introducing students to the fundamental methods and techniques of Mathematics, and in particular to the differential and integral calculus of one real variable and to sequences and series. A further goal is to train students in applying analytic techniques to other sciences. Students will know the fundamental of differential and integral calculus of real functions of one real variable. In particular they will be able to study the qualitative graph of elementary function, to solve elementary ordinary differential equations, to determine the convergence of sequences and series; they will be able to state and prove the basics theorems of Analysis.

Course program:

Numerical sets. Real and complex numbers. Topology of the real line. Limits of sequences and series.. Limits of functions and continuity. Continuous functions and topology. Differentiable functions and their properties. Differentiation rules. Fundamental theorems of the differential calculus. Taylor formula and second order conditions to determine the nature of a stationary point. Convexity. Study of the graph of a function. Riemann integral: definition of integrable function and properties of the integral. Classes of integrable functions. The fundamental theorem of calculus. Integration methods and computation of definite integrals. Improper integrals.

Type of didactic activities: Lectures: 56 hours Exercise sessions: 24 hours

Texts and teaching materials:

Analisi Matematica 1 lecture notes available at the page: http://www.matapp.unimib.it/~demichele/libro.pdf E. Giusti, Analisi Matematica 1, Boringhieri E. Giusti, Complementi di Analisi Matematica 1, Boringhieri

Verification of learning skills:

Written examination with an exercise part and a part on the theory, followed by an oral exam consisting in the discussion of the written test, and in further questions on the theory. The access to the oral part is conditioned to having obtained a score of at least 14/30 in the written part.