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Math 756: Complex Variables II
Spring 2019 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: A deeper investigation of the theory and applications of complex analysis in several topic areas. The areas chosen for study are to be selected by the instructor from topics such as conformal mapping – including a proof of the Riemann mapping theorem, Picard’s theorems, elliptic integrals, asymptotic evaluation of integrals, Riemann—Hilbert problems and complex dynamical systems.

Number of Credits: 3

Prerequisites: Math 656 or departmental approval.

Course-Section and Instructors

Course-Section Instructor
Math 756-002 Professor D. Blackmore

Office Hours for All Math Instructors: Spring 2019 Office Hours and Emails

Required Textbooks:

Title Complex Variables + Notes
Author Ablowitz & Fokas
Edition N/A
Publisher Cambridge University Press
ISBN # 978-0521534291

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, April 8, 2019. It will be strictly enforced.


Course Objectives

Course Outcomes

Course Assessment: The assessment of objectives is achieved through homework assignments, and the in-class midterm and final examinations.


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 15, 2019
Final Exam Period May 10 - 16, 2019

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 2019 Academic Calendar, Registrar)

Date Day Event
January 22, 2019 T First Day of Classes
February 1, 2019 F Last Day to Add/Drop Classes
March 17 - 24, 2019 Su - Su Spring Recess - No Classes, NJIT Open
April 8, 2019 M Last Day to Withdraw
April 19, 2019 F Good Friday - No Classes, NJIT Closed
May 7, 2019 T Friday Classes Meet/ Last Day of Classes
May 8 & 9, 2019 W & R Reading Days
May 10 - 16, 2019 F - R Final Exam Period

Course Outline

Date Sectopms Topics Assignment
1/22 5.1, 5.2 Conformal Maps Selected Probs.
1/25 5.3 Conformal Maps and Inverses Selected Probs.
1/29 Notes Introduction to Riemann Mapping Theorem (RMT) Selected Probs.
2/1 Notes Normal Families, Montel’s Theorem Selected Probs.
2/5 Notes Proof of the RMT Selected Probs.
2/8 Notes Continuity at Boundary Selected Probs.
2/12 Notes Applications: Elliptic Functions & Picard’s Theorems Selected Probs.
2/15 Notes Elliptic functions & Picard’s Theorems  Selected Probs.
2/19 6.1 Asymptotic Integration: Fundamentals Selected Probs.
2/22 6.2 Laplace Type Integrals: Watson’s Lemma; Laplace’s Method Selected Probs.
2/26 6.3 Fourier Type Integrals: Watson Analog; Stationary Phase Selected Probs.
3/1 6.4 Steepest Descent Selected Probs.
3/5 6.5 Applications Selected Probs.
3/8 6.7 WKB Method Selected Probs.
3/12 ------- Review for Midterm ------------
3/15 ------- MIDTERM EXAM  -----------.
3/17 - 3/24 ------- SPRING BREAK ------------
3/26 7.1 Riemann—Hilbert Problems  Selected Probs.
3/29 7.2 Riemann—Hilbert Problems: Cauchy Type Integrals Selected Probs.
4/2 7.3 Scalar Riemann—Hilbert Problems Selected Probs.
4/5 7.4 Applications of Scalar Riemann—Hilbert Problems Selected Probs.
4/9 7.4, 7.5 Applications of Scalar Problems, Matrix Problems Selected Probs.
4/12 7.5 Matrix Riemann—Hilbert Problems Selected Probs.
4/16 Notes Complex Dynamical Systems Selected Probs.
4/19 ------- Good Friday -----------------
4/23 Notes Complex Dynamical Systems Selected Probs.
4/26 Notes Complex Dynamical Systems Selected Probs.
4/30 Notes Complex Dynamical Systems Selected Probs.
5/3 Notes Complex Dynamical Systems Selected Probs.
5/7 ------- REVIEW FOR FINAL EXAM --------------

Updated by Professor D. Blackmore - 1/21/2019
Department of Mathematical Sciences Course Syllabus, Spring 2019