Stroethoff, Karel M.

English

University of Montana

University of Montana ScholarWorks at University of Montana University of Montana Course Syllabi, 2021-2025 Spring 2-1-2022 M 472.01: Introduction to Complex Analysis Karel M. Stroethoff University of Montana, Missoula, karel.stroethoff@umontana.edu Follow this and additional works at: https://scholarworks.umt.edu/syllabi2021-2025 Let us know how access to this document benefits you. Recommended Citation Stroethoff, Karel M., "M 472.01: Introduction to Complex Analysis" (2022). University of Montana Course Syllabi, 2021-2025. 723. https://scholarworks.umt.edu/syllabi2021-2025/723 This Syllabus is brought to you for free and open access by ScholarWorks at University of Montana. It has been accepted for inclusion in University of Montana Course Syllabi, 2021-2025 by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact scholarworks@mso.umt.edu. M 472 — Introduction to Complex Analysis Spring Semester 2022CLASS: M Tu W F: 11:10 am – 12:00 noon; CRN: 30046INSTRUCTOR: Karel StroethoffOffice: MA 307; e-mail: karel.stroethoff@umontana.eduPREREQUISITE: M 273 and M 307 (or equivalent)MOODLE PAGE: https://moodle.umt.edu/course/view.php?id=51162Homework assignments and other information pertinent to thiscourse will be posted at this webpage.TEXT: Lecture notes will be provided. We will loosely follow the following recommendedbook (which will be on the moodle page):William T. Shaw, Complex Analysis with Mathematica,Cambridge University Press, 2006. ISBN 978-0-521-83626-5.IMPORTANT DATES: January 17: Martin Luther King Day; HolidayJanuary 18: First day of instructionFebruary 21: Presidents’ Day; HolidayMarch 21–25: Spring BreakMay 9–13: Final Exam WeekFINAL EXAM: Friday, May 13, 10:10 am – 12:10 pm.COURSE DESCRIPTION: Analytic functions, complex integration, singularities and application tocontour integration, harmonic functions, spaces of analytic functions.COURSE OBJECTIVES & LEARNING GOALS:Purpose of the Course: To provide an in-depth introduction to complex analysis techniques and someexposure to rigorous mathematical proofs. To discuss some of the geometrical and topological aspects ofcomplex analysis. The emphasis is on those parts of the subject that emanate from Cauchy’s integral formulaand Cauchy’s residue theorem.Learning Goals: Learning Goals include, but are not limited to:A. Course overarching learning goal: to learn to think independently and write clearly.B. Course specific learning goals:1. to learn the basics of complex analysis (definitions, terminology, concepts, techniques, methods)2. to learn different ways in which analyticity can be defined.3. to understand Cauchy’s theorem and integral formula and some of their applications4. to use complex analytic methods to evaluate real integrals.5. to be able to write a clear proof involving above items.HOMEWORK: There will be regular homework and reading assignments, and part of the assigned home-work will be collected for grading. To help you keep track of the assigned homework I will post a list of allassigned problems (with the dates they are due) on the moodle page for this course.MIDTERM: Tuesday, March 29.GRADING: Your grade for the course will be based on the three assessment components using the followingpercentages: 50% homework, 20% midterm, and 30% final exam.

M 472.01: Introduction to Complex Analysis

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M 472.01: Introduction to Complex Analysis

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