Integration with Complex Numbers: A Primer on Complex Analysis by Brian McMaster

Description: Integration with Complex Numbers by Brian McMaster, Aisling McCluskey 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 todays student cohorts. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description Complex analysis, more than almost any other undergraduate topic in mathematics, runs the full pure/applied gamut from the most subtle, difficult, and ingenious proofs to the most direct, hands-on, engineering-based applications. This creates challenges for the instructor as much as for the very wide range of students whose various programmes require a secure grasp of complex analysis. Its techniques are indispensable to many, but skill in the use of a mathematicaltool is hazardous and fallible without a sound understanding of why and when that tool is the right one to pick up. This kind of understanding develops only by combining careful exploration of ideas,analysis of proofs, and practice across a range of exercises. 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 todays student cohorts. To achieve its aim of supporting and sustaining such cohorts through those aspects ofcomplex analysis that they encounter in first and second-year study, it also balances competing needs to be self-contained, comprehensive, accessible, and engaging - all in sufficient but not in excessivemeasures. In particular, it begins where most students are likely to be, and invests the time and effort that are required in order to deliver accessibility and introductory gradualness. Author Biography Brian McMaster studied at Queens 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. In2018 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 intovarious 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, series2: What are complex numbers?3: Background Part B: real functions and their limits4: Complex functions5: Background Part C: real integration6: Paths in the complex plane7: Cauchys theorem(s)8: Taylors theorem9: Residues10: Reality from complexity11: The repair shop for broken promises Review 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 todays student cohorts. * zb Math Open * Long Description Complex analysis, more than almost any other undergraduate topic in mathematics, runs the full pure/applied gamut from the most subtle, difficult, and ingenious proofs to the most direct, hands-on, engineering-based applications. This creates challenges for the instructor as much as for the very wide range of students whose various programmes require a secure grasp of complex analysis. Its techniques are indispensable to many, but skill in the use of a mathematicaltool is hazardous and fallible without a sound understanding of why and when that tool is the right one to pick up. This kind of understanding develops only by combining careful exploration of ideas, analysis of proofs, and practice across a range of exercises. 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 todays student cohorts. To achieve its aim of supporting and sustaining such cohorts through those aspects of complex analysis that they encounter in first and second-year study, it also balancescompeting needs to be self-contained, comprehensive, accessible, and engaging - all in sufficient but not in excessive measures. In particular, it begins where most students are likely to be, and invests the time and effort that are required in order to deliver accessibility and introductorygradualness. Review Quote "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 todays student cohorts." -- zb Math Open Feature Allows as much time as it takes to establish confident facility with fundamental ideasExplicitly and accessibly describes the processes by which solutions are discovered, as well as how those discoveries are refined into logically secure mathematical argumentsIncorporates worked examples and exercises supported by partial solutions or hints to scaffold understanding and reinforce learningIncludes a companion website with solutions to the problems in the text Details ISBN0192846434 Language English Year 2022 ISBN-10 0192846434 ISBN-13 9780192846433 Format Paperback Publisher Oxford University Press Imprint Oxford University Press Place of Publication Oxford Country of Publication United Kingdom Publication Date 2022-05-02 UK Release Date 2022-05-02 NZ Release Date 2022-05-02 Pages 288 Subtitle A Primer on Complex Analysis Author Aisling McCluskey Alternative 9780192846075 DEWEY 515.9 Audience Professional & Vocational AU Release Date 2022-07-24 We've got this At The Nile, if you're looking for it, we've got it. 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