CALCULUS II
Learning outcomes of the course unit
The purpose of the course is to provide students with a clear understanding
of the basic ideas of calculus as a solid foundation for subsequent courses
in mathematics and other scientific disciplines.
Course contents summary
Indefinite integration. Integration by substitution, integration by parts. Rational functions.
Definite integration: the Riemann integral. The interpretation of definite integrals. Integrability of monotone functions and of continuous functions. The fundamental theorem of calculus.
Improper integrals. Convergence of integrals of nonnegative functions. Absolute convergence. Comparison tests.
Infinite series. Geometric and harmonic series. Convergence of series of nonnnegative terms, absolute convergence, ratio test. Comparison tests. Alternating sign series. Taylor series.
Differential equations. Slope fields. Separation of variables. Linear first order differential equations. Linear second order constant coefficients differential equations: oscillations.
Recommended readings
C. Canuto - A. Tabacco, Analisi matematica I, Springer Italia
Pagani-Salsa-Bramanti, Matematica. Calcolo infinitesimale e Algebra lineare, Zanichelli
F. Conti, Calcolo, Mc Graw- Hill
