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Analisi Matematica 1 (INF)
Mathematics 1
Piero Montecchiari

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

Prerequisites
Basic elements of Calculus and Analityc Geometry

Learning outcomes
The course aims to teach students the methods of mathematical reasoning, and top provide them with the basic elements of differential and integral calculus for real functions of real variable.

Program
Sets, Relations and Functions. Natural, Integer, Rational and Real numbers. Complex numbers, trigonometric and exponential representation. De Moivre Formula. The Induction principle. Modulus and powers. Exponential, logaritmic and angular functions. Limit of real sequences and its properties. Indeterminate forms. Monotone sequences. The Neper's number and related limits. Asymptotic comparison. 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 Formulas. Asymptots and the study of the graphs of functions. Riemann integral and integrability. Definite Integral and its properties. Fundamental Theorem and Formula of the Integral Calculus. Indefinite Integral and integration methods: sum decomposition, by parts and sostitution. Improper integral and convergence tests. Series. The Geometric and Harmonic Series. Convergence tests. Absolute convergence. Leibnitz Theorem. Introduction to Taylor and Fourier series

Development of the examination
LEARNING EVALUATION METHODS
two written tests

LEARNING EVALUATION CRITERIA
It is evaluated the ability in solving exercises in the field of differential and integral calculus in one variable and the capacity of discussing theoretical results

LEARNING MEASUREMENT CRITERIA
The first written test consists of four theoretical questions each with maximum evaluation equal to 8. The second written test consists of five exercises of differential and integral calculus in one variable each with maximum evaluation equal to 6

FINAL MARK ALLOCATION CRITERIA
The final mark averages the results obtained in the two tests.

Recommended reading
F.G. Alessio e P. Montecchiari, ”Note di Analisi Matematica uno”, Esculapio (ristampa 2015)

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