CALCULUS II
cod. 13592

Academic year 2007/08
1° year of course - Second semester
Professor
Academic discipline
Analisi matematica (MAT/05)
Field
Discipline matematiche
Type of training activity
Basic
32 hours
of face-to-face activities
4 credits
hub:
course unit
in

Integrated course unit module: CALCULUS I - CALCULUS II

Learning objectives

<br />The purpose of the course is to provide students with a clear understanding <br />of the basic  ideas of calculus as a solid foundation for subsequent courses <br />in mathematics and other scientific disciplines. <br /><br />

Prerequisites

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Course unit content

<br />Indefinite integration. Integration by substitution, integration by parts. Rational functions. <br />Definite integration: the Riemann integral. The interpretation of definite integrals.  Integrability of monotone functions and of continuous functions. The fundamental theorem of calculus. <br />Improper integrals. Convergence of integrals of nonnegative functions. Absolute convergence. Comparison tests. <br />Infinite series. Geometric and harmonic series. Convergence of series of nonnnegative terms, absolute convergence, ratio test. Comparison tests. Alternating sign series. Taylor series. <br />Differential equations. Slope fields. Separation of variables. Linear first order differential equations. Linear second order constant coefficients differential equations: oscillations.    <br /> 

Full programme

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Bibliography

C. Canuto - A. Tabacco, Analisi matematica I, Springer Italia <br />Pagani-Salsa-Bramanti, Matematica. Calcolo infinitesimale e Algebra lineare, Zanichelli <br />F. Conti, Calcolo, Mc Graw- Hill 

Teaching methods

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Assessment methods and criteria

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Other information

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