Residues : Solving Improper Integrals

Use residues to evaluate the improper integral... Please see the attached file for the fully formatted problems.

Residues : Cauchy Principal Values of Integrals

Use residues to find the Cauchy principal values of the integrals {see attachment}.

Residues : Improper Integrals

Use residues to evaluate the improper integrals {see attachment}.

Residues : Improper Integrals

Use residues to evaluate the improper integrals (see attachment).

Residues : Cauchy Principal Values

Use residues to find the Cauchy principal values of the improper integrals {see attachment}.

Indented Contour : Derive Integration Formula and Trigonometric Identity

Derive the attached integration formula. Then, with the aid of the trigonometric identity {see attachment} point out how it follows that ... {see attachment} **See attachment for complete question including diagram.

Use a Function to Derive a Pair of Integration Functions

Use the attached function to derive the pair of integration functions {see attached for functions and diagram}

Indented Path : Integral of Branch of Multiple-Valued Function

Show that... by integrating an appropriate branch of the multiple-valued function... over (a) the indented path in Fig. 97, Sec 75; (b) the closed contour in Fig. 99, Sec. 77. See attachment for equations and diagrams.

Complex Variable Class - Undergraduate 500 Level

The beta function is this function of two real variables... Make the substitution t=1/(x+1) and use the result obtained in the example in Sec. 77 to show that... Please see attachment for equations.

Residues, Singularities and Conjugate Points

Please try to use the example method. 1. F(s) = (2s^3)/((s^4) - 4) Please see attachment for proper format.