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Analisi Matematica 1 (CA)
Mathematics 1
Francesca Gemma Alessio

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

Prerequisites
Basic elements of Calculus and Analytic Geometry

Learning outcomes
Aim of the course is to introduce the students to the basic elements of the Differential and Integral Calculus

Program
Natural, Integer, Rational and Real numbers. The Induction principle. Limit of real sequences and its properties. Indeterminate forms. Monotone sequences. The Neper's number and related limits. Limits of real function of real variale. Properties. Indeterminate forms. Asymptotic comparison. Monotone functions. Continuity; The Weierstrass's and the Intermediate Values Theorems. Derivative and Derivative Formulas. Successive Derivative. The Fermat's, Rolle's, Lagrange's and Cauchy's Theorems. Derivative and monotonicity. Convexity. Primitives. The De L'Hospital's Theorems. Taylor's Formula. Asymptots and study of the graphs of functions. Definite Integral and its properties. Fundamental Theorem and Formula of the Integral Calculus. Indefinite Integral and integration methods: by sum decomposition, by parts and substitution. Improper integral and convergence tests. Numerical series and convergence criteria. Power and Taylor series.

Development of the examination
LEARNING EVALUATION METHODS
The student will be assessed through two written tests and an oral test. The first written test will assess the learning of the theory, the second one the ability to solve problems by using the learned techniques. The oral test will focus on a discussion of the two written tests.

LEARNING EVALUATION CRITERIA
The written tests are passed if the student obtains a mark of at least 15/30 in each test. The student will be admitted to the oral test only if he has reached an average of the written tests of 18/30.

LEARNING MEASUREMENT CRITERIA
At each question (written and oral) proposed to the student is associated a score, so that each test can be assessed with a maximum score of 30/30. Only correct and complete answers will be evaluated with the maximum score.

FINAL MARK ALLOCATION CRITERIA
The final mark will be determined by the average of the sustained tests.

Recommended reading
Alessio-Montecchiari, ”Note di Analisi Matematica Uno”, Esculapio

Courses

• Ingegneria Civile e Ambientale (Corso di Laurea Triennale (DM 270/04))