Titlebook: Single Variable Differential and Integral Calculus; Mathematical Analysi Elimhan Mahmudov Textbook 2013 Atlantis Press 2013 Derivative.Inte

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Sequences and Series,In this chapter we give the basic properties of monotone, strictly monotone, and Cauchy sequences in detail. In particular, we treat the convergence tests of Cauchy, D’Alembert, Leibniz, and Raabe. As examples, we consider the harmonic series, the geometric series, and products of series.

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The Definite Integral,In this chapter we define Newton’s and Riemann’s integrals. We investigate the conditions under which they are equal. Necessary and sufficient conditions for the existence of the Riemann integral are formulated in terms of a partition of a given interval of the real line.