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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