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Mathmatical Analysis II Integral Calculus by Server Angel Popescu


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Mathmatical Analysis II Integral Calculus written by Server Angel Popescu This is an other great mathematics book cover the following topics.

  • Indefinite integrals (Primitives, Antiderivatives)
    Definitions, some properties and basic formulas, Some results on polynomials, Primitives of rational functions, Primitives of irrational and trigonometric functions, Problems and exercises

  • Definite integrals
    The mass of a linear bar, Darboux sums and their applications, Lebesgue criterion and its applications, Mean theorem. Newton-Leibniz formula, The measure of a figure in Rn, Areas of plane figures bounded by graphics of functions, The volume of a rotational solid, The length of a curve in R3, Approximate computation of definite integrals., Problems and exercises 101

  • Improper (generalized) integrals
    More on limits of functions of one variable, Improper integrals of the first type, Improper integrals of the second type, Problems and exercises

  • Integrals with parameters
    Proper integrals with parameters, Improper integrals with parameters, Euler’s functions gamma and beta, Problems and exercises

  • Line integrals
    The mass of a wire. Line integrals of the first type, Line integrals of the second type, Independence on path. Conservative fields, Computing plane areas with line integrals, Supplementary remarks on line integrals, Problems and exercises

  • Double integrals
    Double integrals on rectangles, Double integrals on an arbitrary bounded domain, Green formula. Applications, Change of variables in double integrals. Polar coordinates, Problems and exercises

  • Triple integrals
    What is a triple integral on a parallelepiped?, Triple integrals on a general domain, Iterative formulas for a general space domain, Change of variables in a triple integral, Problems and exercises

  • Surface integrals
    Deformation of a 2D-domain into a space surface, Surface integral of the first type. The mass of a 3D-lamina, Flux of a vector field through an oriented surface, Problems and exercises

  • Gauss and Stokes formulas. Applications
    Gauss formula (divergence theorem), A mathematical model of the heat flow in a solid, Stokes Theorem, Problems and exercises

  • Some remarks on complex functions integration
    Complex functions integration, Applications of residues formula, Problems and exercises

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