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Math 712: Numerical Methods II
Fall 2017 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 finite difference methods. Consistency, stability, convergence, and implementation are considered.

Number of Credits: 3

Prerequisites: MATH 614MATH 331 or departmental approval, and proficiency in a computer programming language (MATLAB). 

Course-Section and Instructors

Course-Section Instructor
Math 712-001 Professor S. Jiang

Office Hours for All Math Instructors: Fall 2017 Office Hours and Emails

Required Textbooks:

Title Difference Methods for Ordinary and Partial Differential Equations Steady State and Time Dependent Problems
Author Randall J. LeVeque
Edition July 2007
Publisher SIAM
ISBN # 978-0898716290

University-wide Withdrawal Date:The last day to withdraw with a w is Monday, November 6, 2017. It will be strictly enforced.

Policies

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 - 40
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 December 15 - 21, 2017

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 lyles@njit.edu. 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: Fall 2017 Academic Calendar, Registrar)

Date Day Event
September 5, 2017 T First Day of Classes
September 11, 2017 M Last Day to Add/Drop Classes
November 6, 2017 M Last Day to Withdraw
November 21, 2017 T Thursday Classes Meet
November 22, 2017 W Friday Classes Meet
November 23 - 26, 2017 R - Su Thanksgiving Break - University Closed
December 13, 2017 W Last Day of Classes
December 14, 2017 R Reading Day
December 15 - 21, 2017 F - R Final Exam Period

Course Outline

Week Lecture Course Topics
1 1-2 Chapter 1 Finite difference methods
2 3-4 Chapter 2 Error, Stability, Consistency and Convergence
3 5-6 Chapter 2 Green’s functions, max-norm stability, Neumann boundary conditions
4 7-8 Chapter 2 Sections 2.14-21
5 9-10 Chapter 3 Elliptic Equations
6 11-12 Chapter 4 GMRES
7 13-14 Chapter 4 Multigrid methods
8 15-16 Review and Midterm
9 17-18 Chapter 9 Diffusion Equations and Parabolic Problems
10 19-20 Chapter 10 Sections 10.1-10.6
11 21-22 Chapter 10 Sections 10.7-10.13
12 23-24 Chapter 11 Mixed Equations
13 25 Introduction to Finite Volume Methods
14 26-27 Introduction to Finite Element Methods
15 28 Review
FINAL EXAM WEEK: DECEMBER 15 - 21, 2017

Updated by Professor S. Jiang - 9/15/2017
Department of Mathematical Sciences Course Syllabus, Fall 2017