Integration with Complex Numbers

Description

Integration with Complex Numbers: A Primer on Complex Analysis offers a reader-friendly contemporary balance between idea, proof, and practice, informed by several decades of classroom experience and a seasoned understanding of the backgrounds, motivation and competing time pressures of today's student cohorts.

• Allows as much time as it takes to establish confident facility with fundamental ideas
• Explicitly and accessibly describes the processes by which solutions are discovered, as well as how those discoveries are refined into logically secure mathematical arguments
• Incorporates worked examples and exercises supported by partial solutions or hints to scaffold understanding and reinforce learning
• Includes a companion website with solutions to the problems in the text

About the Author(s)

Brian McMaster, Honorary Senior Lecturer, Queen's University Belfast, and Aisling McCluskey, Professor in Mathematics, National University of Ireland, Galway

Brian McMaster studied at Queen's University Belfast (QUB), UK and has served his alma mater department in various capacities including those of Adviser of Studies, Head of Research, and Associate Director of Education. He has written for over sixty refereed journal articles, mostly in the area of analytic topology but incorporating a smattering of applications in disciplines as diverse as probabilistic metric spaces and decision support theory. In 2018 he received the accolade for Special Recognition for Inspirational Teaching awarded by QUB Students Union. His teaching interests focus around analysis (real and complex) and set theory and their development into various fields, especially that of analytic topology.

Since her appointment at the National University of Ireland Galway in 1992, Aisling McCluskey has established a meaningful and rewarding academic career, maintaining an active research profile whilst holding the teaching and learning of mathematics central to her academic endeavour. She has received several institutional and national awards for excellence in teaching, most recently in 2020 and 2021. She is currently a Governor at NUI Galway and Head of School.

Table of Contents

1:Background Part A: set, sequence, series
2:What are complex numbers?
3:Background Part B: real functions and their limits
4:Complex functions
5:Background Part C: real integration
6:Paths in the complex plane
7:Cauchy's theorem(s)
8:Taylor's theorem
9:Residues
10:Reality from complexity
11:The repair shop for broken promises

Reviews

"Integration with Complex Numbers: A Primer on Complex Analysis offers a reader-friendly contemporary balance between idea, proof, and practice, informed by several decades of classroom experience and a seasoned understanding of the backgrounds, motivation, and competing time pressures of today's student cohorts." - zb Math Open