Complex Variables and Applications (8E) - Brown/Churchill Ex 3, Sec81: Residues/Improper Integrals скачать в хорошем качестве

Complex Variables and Applications (8E) - Brown/Churchill Ex 3, Sec81: Residues/Improper Integrals

Complex Variables and Applications (8th Ed) - James Ward Brown and Ruel V. Churchill Ch 7: Applications of Residues 80: Improper Integrals from Fourier Analysis 81: Jordan's Lemma Remark: Note that different textbooks adopt different notations. In this textbook, arg z is the argument of the complex number z and Arg z is the principal value of the argument of z defined in (-pi, pi]. And log z is the multiple-valued logarithmic function and Log z is the principal branch of log z defined in (-pi, pi]. The relations arg z = Arg z + 2n pi, log z = Log z + i(2n pi), where n ranges over all the integers. Ex 3: Use residues to evaluate the improper integral: \int_{0}^{infinity} cos(ax)/(x^2 + b^2)^2, where a, b are positive real numbers.