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Analisi Matematica 1 (EA)
Mathematics 1
Francesca Papalini

Seat Ingegneria
A.A. 2015/2016
Credits 6
Hours 72
Period 1s
Language ENG

Prerequisites
Algebric calculus and analytic geometry.

Learning outcomes
The course aims to give basic knowledge as regards linear algebra and analytic geometry, in all aspects directly and indirectly associated with the identification on the plane and in the space of geometric shapes.

Program
Elements of set theory . The set of the real numbers and its properties. Complex numbers. Numerical sequences and definition of limit. Numerical series and their behavior. Functions of one variable: elementary functions. Limit of a function. Continuous functions and their properties. Differential calculus for functions of one variable. Graph of a function. Some optimization problems. Taylor polynomial . Taylor series . Complex exponential. Integral calculus for functions of one variable: primitive of a function. Improper integral and convergence criteria. Sequences and series of functions: pointwise and uniform convergence. Power series and Fourier series.

Development of the examination
LEARNING EVALUATION METHODS
The learning evaluation method consists of two parts: -a written test, consisting in the solution of some exercises on topics covered in the course, to be completed in two or three hours, depending on the type of task; -an oral test, consisting in the discussion on one or more topics covered in the course. The written test is in preparation for the oral exam, for accessing to which the student must have obtained at least an assessment of 15/30 in the written test. The oral examination must be during an appeal of the same session of the written examination. In the case of negative result in the oral exam, the student must also repeat the written test.

LEARNING EVALUATION CRITERIA
To successfully pass the assessment of learning, the student must demonstrate, through the trials described above, to understand the concepts presented in the course, to be able to make comparisons between them, to be able to set up a problem and solve it through the logical-deductive method.

LEARNING MEASUREMENT CRITERIA
For each of the tests specified before it is assigned a score between zero and thirty. The overall grade, thirty, is derived from the comparative evaluation of both tests and may not exceed 6/30 of the marks obtained in the written test.

FINAL MARK ALLOCATION CRITERIA
In order to obtain a positive evaluation, the student must first pass the written test and then achieve a sufficient judgment in the oral test. The highest rating is achieved by demonstrating a thorough understanding of the course. Praise is given to students who, having done all the tests so correctly, have demonstrated a particular brilliance in the oral and in the written assignments.

Recommended reading
Marco Bramanti, Carlo D. Pagani, Sandro Salsa, ”Analisi matematica 1”, Zanchelli

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