MA 4291: Applied Complex Variables
C-Term - Spring 2023
Department of Mathematical Sciences
Worcester Polytechnic Institute
C-Term - Spring 2023
Department of Mathematical Sciences
Worcester Polytechnic Institute
Instructor: Prof. B.S. Tilley
Department of Mathematical Sciences
Worcester Polytechnic Institute
Office: SL 405D
Office Hours: T: 3:00-3:50pm;
R: 3:00-4:50pm;
or by appointment.
Phone: (508) 831-6664
e-mail: tilley@wpi.edu
Tilley Home Page
Textbook: Complex Variables and Applications, Eighth Edition, J.W. Brown and R.V. Churchill, McGraw-Hill, ISBN: 978-0-07-305194-9.
Room: MTRF: SH309; W: SH 203.
Time: 12:00-12:50pm
Course Description:
This course provides an introduction to the ideas and techniques of complex analysis that are frequently used by scientists and engineers. The presentation will follow a middle ground between rigor and intuition. Topics covered include: complex numbers, analytic functions, Taylor and Laurent expansions, Cauchy integral theorem, residue theory, and conformal mappings.
Learning Objectives:
Perform complex arithmetic and determine values of functions with multiple branches
Determine continuity, differentiability and analyticity of a function calculate the derivative where it exists.
Apply conformal mapping techniques to applications involving Laplace's equation in two dimensions.
Evaluate contour integrals using parameterization, and using the Cauchy-Goursat theorem over multiply-connected domains.
Articulate the impact of the Cauchy integral formula on Liouville's Theorem, the Fundamental Theorem of Algebra, and the Maximum Modulus Theorem.
Find the Taylor and Laurent series of a function and determin its circle or annulus of convergence.
Compute the residue of a function and use residue theory to evaluate a contour integral or an integral over the real line.
Class Expectations: As an upper-level mathematics course, collaborative learning and active engagement are expected. Collaborative learning meas that students collaborate together to learn the material in the course. Active engagement by students means that students accept the responsibility for their own learning of the material and do not perceive the instructor (professor) as a source of all knowledge.
In order to meet these expectations, the classroom environment must be professional and supportive. Students are expected to treat each other with mutual respect, provide constructive feedback to other students, and to realize that as humans we all need guidance at times.
Students should also be able to communicate the mathematics they are learning, in both written and oral form, to others. Every student in class will have to give a (very short) oral presentation before the class detailing the answer to a homework or quiz question at least once over the term.
Grades: Grades will be determined by the following deliverables
Homework: There will be weekly homework assignments that are due in class the first day of the following week (e.g. 1/17/2023, 1/23/2023, etc.). The assignments should be done in pencil. You are strongly encouraged to work on the homework problems together, but the written solutions should be done individually. Copying homework is cheating, and will be dealt with according to the academic dishonesty policies of WPI. I anticipate seven (7) homework assignments this term.
Quizzes Quizzes will be given on Fridays where there is class and when there are no exams. The quizzes are open book, open notes, but no internet access. The quizzes are to be done individually and students are given 20 minutes to complete the quiz. The material for the quiz are topics from the homework assignments that were collected earlier that week. I anticipate four (4) quizzes this term.
Exams: Both exams will be given in person during lecture/discussion time on 2/3/2023 and 3/3/2023. Prior to the start of each exam, you must place all of your belongings (e.g., cell phone, study materials, etc.) in your backpack and under your desk, so that no items are visible during the exam. All exams this term are closed book, closed notes, and no electronic devices are permitted.
Grade Distribution
Written Homework: 10%
Due the first class of each week.
Quizzes (open book/notes): 30%
On Fridays where there are no exams.
Exams (closed book/notes): 60%
Best score: 35%
Worst Score: 25%
Exam 1 (2/3/2023), Exam 2 (3/3/2023):
Electronics Policy
All lectures (audio and video) are captured through course capture and can be found on the course Canvas page. NO recording of audio or video by students is allowed during lecture or during conference. Laptops, phones, and tables should be turned off during the lecture and conference sessions. If you take notes (typing/stylus only) using these devices during lecture, then you should sit in the back of the room, since screen activity is distracting to your neighbors.
Special Arrangements:
If you need course adaptations or accommodations because of a disability, or if you have medical information to share with me, please make an appointment with me as soon as possible. My office location and office hours are listed above. If you have not already done so, students who believe that they may need accommodations in this class are encouraged to contact the Office of Accessibility Services (OAS) as soon as possible to ensure that these accommodations are implemented in a timely fashion. The OAS is in Unity Hall, (508) 831-4908. Students who need accommodations for exams are required to make the arrangements to take these exams at the Exam Proctoring Center (EPC) on the day of the exam.