Syllabi Header

Math 713: Advanced Scientific Computing
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: Numerical methods for the solution of initial - and boundary-value problems for partial differential equations, with emphasis on spectral methods.

Number of Credits: 3

Prerequisites: MATH 614, MATH 712 or departmental approval, and proficiency in a computer programming language such as Matlab.

Course-Section and Instructors

Course-Section Instructor
Math 713-002 Professor S. Jiang

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

Required Textbooks:

Title Spectral Methods in Matlab
Author Lloyd N. Trefethen
Edition ---
Publisher SIAM
ISBN # 978-0898714654

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


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 40%
Midterm Exam 25%
Final Exam 35%

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

A 90 - 100 C 60 - 69
B+ 85 - 89 D 50 - 59
B 75 - 84 F 0 - 49
C+ 70 - 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 TBA
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

Lecture Section HW Problems
1 1-2 Chapter 1: Differentiation Matrices
2 3-4 Chapter 2: Unbounded Grids – The Semi-Discrete Fourier Transform
3 5-6 Chapter 3: Periodic Grids – The DFT and FFT
4 7-8 Chapter 4: Smoothness and Spectral Accuracy
5 9-10 Chapter 5: Polynomial Interpolation and Clustered Grids
6 11-12 Chapter 6: Chebyshev Differentiation Matrices
7 13-14 Chapter 7: Boundary Value Problems
8 15-16 Chapter 8: Chebyshev Series and the FFT
9 17-18 Chapter 9: Eigenvalues and Pseudospectra
10 19-20 Chapter 10: Time-Stepping and Stability Regions
11 21-22 Chapter 11: Polar Coordinates
12 23-24 Chapter 12: Integrals and Quadrature Formulas
13 25-26 Chapter 13: More About Boundary Conditions
14 27-28 Chapter 14: Fourth-Order Problems
15 1-29 Review
FINAL EXAM WEEK: May 4 - 10, 2018

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