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Math 656: Complex Variables I
Spring 2018 Graduate Course Syllabus

NJIT Academic Integrity Code: All Students should be aware that the Department of Mathematical Sciences takes the University Code on Academic Integrity at NJIT very seriously and enforces it strictly. This means that there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the University Code on Academic Integrity, students are obligated to report any such activities to the Instructor.

Course Information

Course Description: The theory and applications of analytic functions of one complex variable: elementary properties of complex numbers, analytic functions, elementary complex functions, conformal mapping, Cauchy integral formula, maximum modulus principle, Laurent series, classification of isolated singularities, residue theorem, and applications.

Number of Credits: 3

Prerequisites: Math 545 or Math 645 or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 656-002 Professor D. Blackmore

Office Hours for All Math Instructors: Spring 2018 Office Hours and Emails

Required Textbooks:

Title Complex Variables
Author Ablowitz, Fokas
Edition ---
Publisher Cambridge University Press
ISBN # 978-0521534291

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 2, 2018. It will be strictly enforced.

Course Goals

Course Objectives

Course Outcomes

Course Assessment:


DMS Course Policies: All DMS students must familiarize themselves with, and adhere to, the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly.

Grading Policy: The final grade in this course will be determined as follows:

Homework 15%
Midterm Exam 35%
Final Exam 50%

Your final letter grade will be based on the following tentative curve.

A 88 - 100 C 62 - 67
B+ 82 - 87 D 55 - 61
B 75 - 81 F 0 - 54
C+ 68 - 74

Attendance Policy: Attendance at all classes will be recorded and is mandatory. Please make sure you read and fully understand the Math Department’s Attendance Policy. This policy will be strictly enforced.

Exams: There will be one midterm exam held in class during the semester and one comprehensive final exam. Exams are held on the following days:

Midterm Exam March 9, 2018
Final Exam Period May 4 - 10, 2018

The final exam will test your knowledge of all the course material taught in the entire course. Make sure you read and fully understand the Math Department's Examination Policy. This policy will be strictly enforced.

Makeup Exam Policy: To properly report your absence from a midterm or final exam, please review and follow the required steps under the DMS Examination Policy found here:

Cellular Phones: All cellular phones and other electronic devices must be switched off during all class times.

Additional Resources

Accommodation of Disabilities: Disability Support Services (DSS) offers long term and temporary accommodations for undergraduate, graduate and visiting students at NJIT.

If you are in need of accommodations due to a disability please contact Chantonette Lyles, Associate Director of Disability Support Services at 973-596-5417 or via email at The office is located in Fenster Hall, Room 260.  A Letter of Accommodation Eligibility from the Disability Support Services office authorizing your accommodations will be required.

For further information regarding self identification, the submission of medical documentation and additional support services provided please visit the Disability Support Services (DSS) website at:

Important Dates (See: Spring 2018 Academic Calendar, Registrar)

Date Day Event
January 16, 2018 T First Day of Classes
January 22, 2018 M Last Day to Add/Drop Classes
March 11 - 18, 2018 Su - Su Spring Recess - No Classes/ University Closed
March 30, 2018 F Good Friday - No Classes/ University Closed
April 2, 2018 M Last Day to Withdraw
May 1, 2018 T Friday Classes Meet - Last Day of Classes
May 2 - 3, 2018 W - R Reading Days
May 4 - 10, 2018 F - R Final Exam Period

Course Outline

Date Sections Topics Assignment
1/16 1.1, 1.2 Complex Numbers and Functions Selected Probs.
1/19 1.2, 1.3 Complex Functions and Derivatives Selected Probs.
1/23 2.1, 2.2 Analytic Functions and Integration Selected Probs.
1/26 2.3, 2.4 Analytic Functions and Integration Selected Probs.
1/30 2.5, 2.6 Complex Integration: Cauchy’s Theorem and Formulas Selected Probs.
2/2 2.6 Liouville, Morera and Maximum Modulus Theorems Selected Probs.
2/6 3.1, 3.2 Series and Singularities for Complex Functions Selected Probs.
2/9 3.2, 3.3 Taylor and Laurent Series Selected Probs.
2/13 3.3,  3.4 Laurent Series and Singularities Selected Probs.
2/16 3.4, 3.5 Singularities and Continuation Selected Probs.
2/20 3.5, 3.7 Singularities and Painlevé Equations Selected Probs.
2/23 3.7, 3.8 Computations and Applications for Singularities Selected Probs.
2/27 3.8+Notes Complex Functions: Representations  Selected Probs.
3/2 Notes More on Complex Functions Selected Probs.
3/6 ------- Review for Midterm ------------
3/9 ------- MIDTERM EXAM  -----------.
3/11 -  3/18 SPRING BREAK
3/20 4.1 Residue Calculus: Cauchy’s Theorem Selected Probs.
3/23 4.2, 4.3 Applications of Residue Theory: Definite Integrals Selected Probs.
3/27 4.4 Applications of Residue Theory: Argument Principle Selected Probs.
3/30 ------- Good Friday --------------
4/3 4.4 Applications of Residue Theory: Rouché’s Theorem Selected Probs.
4/6 4.4, 4.5 More Applications: Fourier and Laplace Transforms Selected Probs.
4/10 4.1 – 4.6 Overview of Residue Theory and Applications Selected Probs.
4/13 5.1, 5.2 Conformal Maps and Their Inverses Selected Probs.
4/17 5.3, 5.4 Conformal Maps and Their Applications Selected Probs.
4/20 5.5, 5.6 Riemann Mapping and Schwarz—Christoffel Theorems Selected Probs.
4/24 5.1 - 5.6 Overview of Conformal Maps Selected Probs.
4/27 Notes More Conformal Maps- Riemann Mapping Theorem Selected Probs.
5/1 ------- REVIEW FOR FINAL EXAM --------------

Updated by Professor D. Blackmore - 1/18/2018
Department of Mathematical Sciences Course Syllabus, Spring 2018