Titlebook: Learning Higher Mathematics; Part I: The Method o Lev Semenovič Pontrjagin Textbook 1984 Springer-Verlag Berlin Heidelberg 1984 Analysis.An

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The Integral Calculusrtain sequence of finite sums. This produces a rigorous proof that the definite integral exists. At the end of the chapter, we present some applications of the definite integral, including the calculation of the length of the graph of a function and of a curve given in parametric form.

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Analytic Functionsn isolated singular point. At the end of the chapter, we analyze the behavior of an analytic function near an essential singularity. We prove that by an appropriate choice of a sequence converging to this singularity, the function can be made to approach any limit we please.