. Math 446: Applied Complex Variables (V2)
. Instructor Information
Instructor Information
Barry Walker
NetMath | Department of Mathematics
Contact Information
Last modified: Thursday, December 29, 2022, 1:28 PM
. Math 446: Applied Complex Variables (V2)
. Instructor Information
Instructor Information
Barry Walker
NetMath | Department of Mathematics
Contact Information
Last modified: Thursday, December 29, 2022, 1:28 PM
. Math 446: Applied Complex Variables (V2)
. Course Information
Course Information
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Course Overview
MATH 446 is for students who desire a working knowledge of complex variables. The course covers the standard topics and gives an introduction to integration by residues, the argument principle, conformal maps, and potential fields. Students desiring a systematic development of the foundations of the subject should take MATH 448.
Course Goals
The two main objectives are to develop theory that is useful in applications of complex variables and to introduce to applications of residues and conformal mapping. The former includes evaluating real improper integrals and locating zeros of functions and the latter includes solving boundary value problems in differential equations.
General Information
This is a 3 credit hour course. The course is 16 weeks long and consists of 15 Units. You should dedicate approximately 9 hours per week to work on the course itself, but actual time commitments will vary depending on your input, needs, and personal study habits. It is recommended that you log on to the course website and check your email frequently for updates, news and announcements.
Required and Recommended Texts
James Ward Brown, Ruel V. Churchill. (2014). Complex Variables and Applications. (9th Edition). McGraw-Hill Higher Education.
Course Components
This course will consist of the following components:
Pre-Assignment
The pre-assignment should be completed first. It is used to ensure that you understand the policies, expectations and resources provided in the course. The pre-assignment is worth half the value of one homework assignment.
Each unit begins with an overview and the learning goals you are expected to achieve. These goals should guide your study through the unit. Every unit consists of a homework assignment, lectures,
readings and additional exercises to support these goals. They are designed with the same structure and components unless otherwise specified. The module activities are explained in greater detail below.
Homework Assignments
Each unit contains a homework assignment consisting of several exercises. After clicking the assignment you will see assignment instructions and a link to a PDF file containing these exercises. View the PDF file and complete the exercises. When you are finished, scan or take a picture of your work and submit the file via the assignment link in Moodle.
Each unit contains a list of recorded lectures. Clicking a link to a lecture allows you to view the lecture in its entirety. You will also find links to view specific topics in each lecture.
As the lecture is playing, note that there are PDF slides of what is written on the chalkboard. These can be displayed side by side with the lecture. There are controls in the upper right corner of the video player that allow for viewing of just the lecture, just the slide, or to view both, side by side. You can download these slides and use them to take notes as the lecture plays.
Captions for the video can be displayed by clicking the CC button in the lower right corner of the player. You will find these helpful to clarify any portions of the video where descriptions or audio is not
clear. Note that in most cases, subscripts are identified by a preceding underscore character and superscripts are identified by a preceding ^ character.
Some lectures also include a practice quiz. These are not graded but are a resource to check your understanding.
Each unit contains assigned readings. You are responsible to complete these items. Lectures cover major topics from the readings but do not necessarily include all important information from the readings.
Discussion Forum
Each unit contains a discussion forum. This forum should be used if you have a question about the assignment or content of the unit. Posting questions here allows everyone to benefit from the answer. Most likely, other students also have the same question.
By default, you will receive an e-mail each time a new post is created. To unsubscribe from the forum, go to Forum administration –> Unsubscribe from this forum under the blue Administration block located to the left of the forum.
CS Help, Email: tutorcs@163.com
This course includes three midterm exams and a final exam. Midterm Exam #1, Midterm Exam #3 and the Final Exam are proctored. See the Exam tab for details.
Accommodations
To obtain disability-related academic adjustments and/or auxiliary aids, students should contact both the instructor and the Disability Resources and Educational Services (DRES) as soon as possible. You can contact DRES at 1207 S. Oak Street, Champaign, (217) 333-1970, or via e-mail at
Course Content
1. Complex numbers: Basic algebraic properties, absolute value of a complex number, triangle inequality, complex conjugate, polar form, Euler’s formula, de Moivre’s formula, argument, principal argument, nth roots of complex numbers, regions in the complex plane
2. Analytic functions: Mapping by complex functions, limits, continuity and differentiability, Cauchy-Riemann equations, Cauchy-Riemann equations in polar form, analytic functions
3. Elementary functions: Exponential and logarithmic functions, branches of logarithmic functions, principal branch of logarithmic functions, power functions for any complex exponents, principal branch of power functions, trigonometric functions, zeroes and singularities of trig. functions, hyperbolic functions
4. Integrals: Contour integrals, upper bound of the absolute value of a contour integral, antiderivatives, Cauchy-Goursat theorem, Simply connected domain, Cauchy Integral Formula (CIF) and extended CIF, Liouville’s Theorem and Fundamental Theorem of Algebra, Maximum Modulus Principle
5. Series: Convergence of series, power series, Taylor’s series, Maclaurin series, Laurent series, sums of power series, integration and differentiation of power series, multiplication and division of power series
6. Residues and poles: Isolated singularity, residues, Cauchy’s residue theorem, residue at infinity, classification of isolated singularities (removable singularity, poles, essential singularity), zeros and poles
7. Applications of Resides: Evaluation of real improper integrals, Jordan’s lemma, real definite integrals of rational functions, logarithmic functions, power functions with arbitrary real exponents, rational functions of sine and cosine functions, Argument Principle, Rouche’s Theorem
8. Mapping by elementary functions: Linear transformation, Linear Fractional Transformation, Mappings of upper half-plane, mappings by exponential functions, trigonometric functions, square functions, square root function
9. Conformal mapping: Angle preservation, local inverse, harmonic conjugates, explanation of boundary value problem
10. Applications of conformal mapping: Boundary value problems: Dirichlet problem, Neumann problem, and mixed problem
Grading Distribution
Percentages
Assignments
Final Exam
Course Total
When calculating your final grade, your instructor will look at an average of all your exams. Your final grade cannot exceed this average by more than 10%. For example, if the average grade on all of your exams (weighted equally) is 70%, your final grade cannot exceed 80%.
Grades are essentially straight scale:
Grades are not curved. You have an opportunity to earn 1% extra credit by completing the survey at the end of the course. After completing the final, you will receive an email with instructions to complete the survey.
Additional Important Information
In addition to the information found on this page, the following pages contain essential information about this course:
Instructor Information
Policies
Course Schedule
Assignment Instructions and Grading
Last modified: Thursday, December 29, 2022, 2:46 PM
. Math 446: Applied Complex Variables (V2)
. Policies
Accommodations
To obtain disability-related academic adjustments and/or auxiliary aids, students should contact both the instructor and the Disability Resources and Educational Services (DRES) as soon as possible. You can contact DRES by phone at (217) 333-1970 or via email at
Participation: Student Commitment
By registering for this online course, you commit to self-motivated study, participation in online course activities, and timely submission of all assignments. Furthermore, you commit to accessing the course website, your Nexus student dashboard and checking e-mail frequently, as well as to devoting at least 9 hours weekly to preparing for each module and completing the required assignments and readings.
Extensions
Eligible students may purchase up to two 1-month extensions. Each extension costs $350.
To be eligible for an extension students must demonstrate satisfactory progress in their course. Students must take the first Midterm Exam and complete all homework assignments leading up to this exam to qualify for the first extension. Students must complete the second Midterm Exam and submit all homework assignments leading up to this exam to qualify for the second extension.
The following criteria also apply:
You are submitting your extension request form at least seven (7) business days (Mon – Fri; 8:30am – 5:00pm) before your course end date.
Extension requests received after a course has expired will not be processed.
You do not have a financial hold on your account.
To apply for an extension, follow the instructions in your Nexus dashboard. Once approved, extension fees must be paid before the extension is processed.
When calculating your final grade, your instructor will take an average of all your exams. Your final grade cannot exceed this average by more than 10%. For example, if the average grade on all of your exams (weighted equally) is 70%, your final grade cannot exceed 80%.
Once you complete your exam, you will receive a 0 on any homework leading up to that exam that has not been submitted. Under special circumstances, students may request that they be allowed to submit these assignments. This is left to the discretion of the course instructor.
Communications
Instructor Feedback Turnaround Time
Instructors are expected to respond to student communications and grade homework assignments in a timely manner. Observed Campus Holidays, illness, personal obligations, or other circumstances outside the instructor’s control may affect normal grading and response time. If you experience consistent and significant delays, please contact with your concerns.
Instructors will grade up to three submitted assignments per week. Under special circumstances, students may request that additional assignments be graded. This is left to the discretion of the course instructor.
Daily Contact
Your daily contact should be via the discussion forums and via e-mail.
Course Questions
Questions pertaining to the course should be posted in the discussion forums. Posting questions here allows everyone to benefit from the answers. If you have a question, someone else is probably wondering the same thing. Participants should not hesitate to answer questions posed by peers if they know the answers and the instructor has not yet responded. This not only expedites the process but also encourages peer interaction and support.
Personal and Grade-related Questions
Grade-related questions should first be sent to the instructor’s e-mail address:
Course Announcements
The Announcements forum serves as a way for your instructor and University of Illinois administrators to make announcements within the virtual learning environment. Announcements posted here will also be sent to your Illinois e-mail address, so be sure to check your e-mail or the Announcements forum frequently to see whether any new announcements have been made.
Instructor E-mail: General Inquiries:
Proctoring Questions:
Main Office Phone: (217) 265-0439
Phone hours: Monday – Friday, 9am – 12pm & 1pm – 4pm CST
Academic Integrity
Expectations
Academic dishonesty will not be tolerated. Examples of academic dishonesty include the following:
Cheating
Fabrication
Facilitating infractions of academic integrity
Plagiarism
Bribes, favors, and threats
Academic interference
Examination by proxy
Grade tampering
Non-original works
Guidelines
Should an incident arise in which a student is thought to have violated academic integrity, the student will be processed under the disciplinary policy set forth in the Illinois Academic Integrity Policy.
If you do not understand relevant definitions of academic infractions, contact the instructor for an explanation within the first week of class.
Student Content
Participants in University of Illinois courses retain copyright of all assignments and posts they complete; however, all materials may be used for educational purposes within the given course. In group projects, only the portion of the work completed by a particular individual is copyrighted by that individual. The University of Illinois may request that students’ materials be shared with future courses, but such sharing will only be done with the students’ consent. The information that students submit during a course may, however, be used for the purposes of administrative data collection and research. No personal information is retained without the students’ consent.
Non-Student Content
Everything on this site and within University of Illinois courses is copyrighted. The copyrights of all non-student work are owned by the University of Illinois Board of Trustees, except in approved cases where the original creator retains copyright of the material. Copyrights to external links are owned by or are the responsibility of those external sites. Students are free to view and print material from this site so long as
The material is used for informational purposes only.
The material is used for noncommercial purposes only.
Copies of any material include the respective copyright notice.
These materials may not be mirrored or reproduced on non-University of Illinois websites without the express written permission of the University of Illinois Board of Trustees. To request permission, please contact the academic unit for the program.
Student Behavior
Student Conduct
Students are expected to behave in accordance with the penal and civil statutes of all applicable local, state, and federal governments, with the rules and regulations of the Board of Regents, and with University regulations and administrative rules.
Netiquette
In any social interaction, certain rules of etiquette are expected and contribute to more enjoyable and productive communication. The following are tips for interacting online via e-mail or discussion board messages, adapted from guidelines originally compiled by Chuq Von Rospach and Gene Spafford (1995):
Remember that the person receiving your message is someone like you, deserving and appreciating courtesy and respect.
Be brief; succinct, thoughtful messages have the greatest effect.
Your messages reflect on you personally; take time to make sure that you are proud of their form
and content.
Use descriptive subject headings in your e-mails.
Think about your audience and the relevance of your messages.
Be careful when you use humor and sarcasm; absent the voice inflections and body language
that aid face-to-face communication, Internet messages are easy to misinterpret.
When making follow-up comments, summarize the parts of the message to which you are
responding.
Avoid repeating what has already been said; needless repetition is ineffective communication.
Cite appropriate references whenever using someone else’s ideas, thoughts, or words.
Emergencies
If you have an emergency that will keep you from participating in the course, please notify your instructor. Provide callback information in your e-mail (if necessary).
You can also call the NetMath office:
Main Office Phone: (217) 265-0439
Phone hours: Monday – Friday, 9am – 12pm & 1pm – 4pm CST
Last modified: Thursday, December 29, 2022, 1:34 PM
. Math 446: Applied Complex Variables (V2)
. Course Schedule
Course Schedule
This course is not like a traditional course in which the students and instructor meet face-to-face every week. With the exception of weekly office hours, all of the learning activities and communication in this course are asynchronous, meaning that individual students are working on different parts of the course at any given time. This arrangement makes it possible for you to do your coursework when it’s most convenient for you. However, with this increased freedom and flexibility comes more personal responsibility. Without the structure of regular class meetings, it is up to the student to create a schedule and complete assignments on time. NetMath will try to help you create and work with your course timeline, but it is ultimately up to you to remain on schedule and finish the course on time.
The course consists of 15 units to be completed over a 16-week period. To stay on schedule, it is recommended that you complete at least one unit per week. This will give you time to study for each midterm exam and the final exam. Instructors will grade up to three submitted assignments per week. Under special circumstances, students may request that additional assignments be graded. This is left to the discretion of the course instructor.
Last modified: Thursday, December 29, 2022, 1:38 PM
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. Math 446: Applied Complex Variables (V2)
. Assignment Instructions and Grading
Assignment Instructions and Grading
Assignment Instructions
Each unit contains a homework assignment consisting of several exercises. After clicking the assignment you will see assignment instructions and a link to a PDF file containing these exercises. View the PDF file and complete the exercises. When you are finished, scan or take a picture of your work and submit the file via the assignment link in Moodle.
If you are not sure how to go about completing the assignment, post your question to the Unit Forum. Here your classmates and the instructor are encouraged to help you understand the assignment.
Submission Directions
Submit your assignment using the following naming convention: lastname_446HW##.
File formats accepted: pdf, doc, docx, jpeg
To submit your work, click on the Submit Assignment link.
Homework Grading Rubric
Each assignment is scored out of 20 points, 10 points for correctness and 10 points for explanation. To receive full credit for an assignment, you must provide clear explanation for each problem that demonstrates your solution process. Having only numbers and/or formulas for a solution is worth half of the credit. If there are graphics that need to be included, they should be detailed and recognizable.
Inadequate
Improvement
Mathematical
Almost all of
the steps and
solutions are
incorrect,
incomplete,
Most of the
solutions are
incorrect,
incomplete,
Most of the
solutions are
complete, and
Almost all of
the steps and
solutions are
complete, and
mathematical
mathematical
mathematical
mathematical
Explanation
Explanation or the solution process is difficult to understand and is missing several components OR was not included.
Explanation
process is a
difficult to
understand
but includes
components.
Explanation
process is
Explanation
process is
detailed and
Last modified: Wednesday, May 6, 2020, 7:09 PM