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MATHEMATICAL ANALYSIS 1

Degree course: 
Corso di First cycle degree in MATHEMATICS
Academic year when starting the degree: 
2016/2017
Year: 
1
Academic year in which the course will be held: 
2016/2017
Course type: 
Basic compulsory subjects
Credits: 
9
Period: 
First Semester
Standard lectures hours: 
56
Detail of lecture’s hours: 
Lesson (56 hours)
Requirements: 

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

Final Examination: 
Orale
Assessment: 
Voto Finale

Aims and 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.

Program
Number 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.

Teaching methods
Frontal lectures: 56 hours. Exercise sessions: 24 hours.

Textbooks
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
J. Hass, M. D. Weir, G. B. Thomas, Analisi Matematica 1, Pearson

Final examination
Written and oral exam. Access to the oral part is conditioned to having obtained at least 14/30 in the written part.

Professors

SETTI ALBERTO GIULIO
LONGHI ELENA

Borrowers