625.703.81 - Complex Analysis

Expanded Course Description

Prerequisites 

Mathematical maturity, as demonstrated by 625.601 Real Analysis, 625.604 Ordinary Differential Equations, or other relevant courses with permission of the instructor. 

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates. 

Course Topics

TBD

Course Goals

TBD

Course Learning Outcomes (CLOs)

• Explain the key definitions and theorems of complex analysis, including various methods of proof.
• Apply complex analysis to solve problems such as: computing and determining the radius of convergence of a power series; computing real and contour integrals using Cauchy’s theorem and residue methods.
• Analyze conformal mappings, mappings by rational functions, and apply concepts such as the reflection principle to solve problems.
• Apply complex analysis to the study of Fourier, Laplace and z-transforms, including in the context of problems in analog and digital signal processing.
• Build upon the learning strategies used in this course to extend their knowledge of the subject and apply complex analysis to other fields.

Textbooks

Required 

Stein, E, & Shakarchi, R. (2003). Complex analysis. Princeton University Press.

ISBN-10: 0691113858 

ISBN-13: 978-0691113852 

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website. 

Optional 

Ablowitz, M, & Fokas, A. (2003). Complex Variables: Introduction and Applications. Cambridge University Press. 

ISBN-13: 9780521534291 

Required Software

Scientific Computing Software 

You will need access to a scientific computing software package. You may use either MATLAB, Mathematica or Python with appropriate libraries. Use of Python does not require a license. A license for MATLAB or Mathematica is provided at no cost to you, through JHU. 

To download this kind of software, visit the JHU IT Services Portal. Log in with your JHED ID and type “Matlab” or “Mathematica” in the search bar. Click on “Matlab for Students” or “Mathematica for Students” in the search results and follow the instructions provided. 

Student Coursework Requirements

It is expected that each module will take approximately 7–10 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2–3 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 1 hour per week), and writing assignments (approximately 4 hours per week). 

This course will consist of the following basic student requirements: 

Module Assignments (30% of Final Grade Calculation) 

Assignments will include quantitative problem sets, proofs, or computer problems. All figures and tables should be captioned and labeled appropriately. When specified in the problem, proper justification and clear steps of mathematical derivation must be provided. 

All assignments are due according to the dates in the Calendar. Refer to the Assignment Guidelines for specific grading and policy information. 

Mini Projects (15% of Final Grade Calculation) 

In the second half of the course, there will be a few extended problem sets that focus on more advanced topics and integrating material from multiple modules. These “mini-projects” will be more open-ended in nature and tied to various applications in signal processing. 

The Mini-Projects will include the need to use scientific computing software, for example to generate graphs. MATLAB, Mathematica or Python may be used, at the student’s discretion. The code must be submitted with the assignment. 

All mini projects are due according to the dates in the Calendar. Refer to the Min-Project Guidelines for specific grading and policy information. 

The Mini-Projects are evaluated by the following grading elements: 

1. Correctness of the response to each part. Even when there is no unique solution, the solution provided must be technically correct and provide a proper response to the question posed. (40%) 
2. Proper justification and steps for mathematical derivation are provided, at a level commensurate with graduate academic work. (40%) 
3. Organization of the response, including clarity of exposition. For portions of the assignment that involve using scientific computing software, the code is properly commented and reflects good programming techniques. (20%) 

Exams (55% of Final Grade Calculation, combined from 40% for Midterm and 15% for Final) 

The Midterm Exam will be assigned in Module 7 and the Final Exam will be available in Module 12. The Exams will have a mix of problems similar to the type that would appear in the Module Assignments; thus, doing the Module Assignments will help prepare students for the Exams. There will also be some short-answer questions where students need to demonstrate that they are familiar with key definitions and theorems. The Midterm will cover Modules 1-6 and the Final will cover Modules 7-11. You will have one week to complete the exams. You may use the course materials (lecture notes and videos) as well as the course text to complete the exams.

The exams are evaluated by the following grading elements: 

1. For problems for which no justification is asked to be provided (e.g., short answer questions), the grading is based on correctness of the response. (100%) 
2. For problems for which justification or step by step derivation is asked to be provided: 
   1. Correctness of the answer. (50%) 
   2. Proper justification and clear steps for mathematical derivation are provided, at a level commensurate with graduate academic work. (50%) 

Grading Policy

Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Calendar or the Assignments in the corresponding modules. We will post grades one week after assignment due dates. 

We generally do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted without comment. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade. 

A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week. 

A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course. 

100-90 = A 

89-80 = B 

79-70 = C 

69-63 = D 

62-0 = F 

Final grades will be determined by the following weighting: 

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.