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Analisi Matematica 1 (MECC) (M/Z)
Mathematics 1
Cristina Marcelli

Seat Ingegneria
A.A. 2015/2016
Credits 9
Hours 72
Period I
Language ENG

Prerequisites
Algebric calculus and analytic geometry in the plane.

Learning outcomes
Knowledge of the language of Mathematical Analysis. Knowledge of basic elements of differential calculus for functions of one variable and applications.

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 solving some exercises on topics of the course, within two or three hours,according to the type of the task; -an oral test, consisting in the discussion about some topics of the course. In order to take the oral examination, it is mandatory to achieve an assessment not less than 18/30 in the written test. The written test should be developed, partially or interely, by means to texts online. The oral examination can be taken within three weeks from the date of the written test. In the case of negative result in the oral exam, the student has to repeat the written test too

LEARNING EVALUATION CRITERIA
To successfully overcome the assessment of learning, the student is required to 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 and solve a problem through the logical-deductive method.

LEARNING MEASUREMENT CRITERIA
or each of the tests specified before it is assigned a score between zero and thirty. The overall grade is derived from the comparative evaluation of both tests and it is not greater than 6/30 in addition to the assessment achieveed in the written test.

FINAL MARK ALLOCATION CRITERIA
n order to obtain a positive evaluation, the student must 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
ass-Weir-Thomas, ”Analisi Matematica 1”, Pearson

Courses

• Ingegneria Meccanica (Corso di Laurea Triennale (DM 270/04))