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 attachmnet}

Derive Integration Formula; 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.

Pair of Integration Functions

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

Complex Variable Class - Undergraduate 500 Level

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.