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Prerequisite: MATH 5333 or consent of instructor. Description: Complex numbers, holomorphic functions, linear transformations, Cauchy integral theorem and residue theorem. MATH 5350 - Intro To ...

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Functions of a complex variable: continuity, differentiability, analytic functions, harmonic functions; Complex integration: Cauchy’s integral theorem and formula; Liouville’s theorem ...

GATE syllabus for Electronics and Communication Engineering (ECE) 2025 consists of eight sections - Engineering Mathematics, Networks, Signals and Systems, Electronic Devices, Analog Circuits ...

Complex Variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series. Probability and Statistics: Definitions of probability ...

We present an analytical method to calculate the three-loop massive Feynman integral in arbitrary dimensions. The method is based on the Mellin-Barnes representation of the Feynman integral. The ...

In semimetric spaces, the notions of convergent and Cauchy sequences, as well as completeness, can be introduced in the usual way. In this study, we revisit several well-known fixed-point theorems, ...

The analysis relies merely on Cauchy's theorem and integral formula and is valid for systems satisfying some definite sign requirements on its frequency response. Illustrative numerical examples ...