Math 671: Asymptotic Methods I
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: Asymptotic sequences and series. Use of asymptotic series. Regular and singular perturbation methods. Asymptotic methods for the solution of ODEs, including: boundary layer methods and asymptotic matching, multiple scales, the method of averaging, and simple WKB theory. Asymptotic expansion of integrals, including: Watson's lemma, stationary phase, Laplace's method, and the method of steepest descent.
Number of Credits: 3
Prerequisites: Math 645 or Math 545, and Math 656 or departmental approval.
Course-Section and Instructors
| Course-Section |
Instructor |
| Math 671-001 |
Professor R. Goodman |
Office Hours for All Math Instructors: Fall 2017 Office Hours and Emails
Required Textbooks:
| Title |
Applied Asymptotic Analysis, Graduate Studies in Mathematics |
| Author |
P. D. Miller |
| Edition |
2006 |
| Publisher |
American Math Society |
| ISBN # |
0-8218-4078-9 |
| Errata |
http://www.math.lsa.umich.edu/~millerpd/pubpages/T1.html |
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:
| Hand-in Homework |
80% |
| Final Exam |
20% |
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. Attendance in all classes is expected. Absences from class may inhibit your ability to learn the material.
Homework Policy: Homework will be assigned in class every few weeks. Because asymptotics problems take a long time to complete, the course grade will be based primarily on the homework.
Exams: The final exam will be take home and will be due whenever NJIT decides to schedule our final exam. It may take the form of a final project, where students pick a problem to work on themselves that uses methods related to those used in class.
| 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
*This outline is approximate and static. More details including assigned readings and homework problems will be posted on the course Moodle page.
| Week |
Topic |
| WEEK 1 |
Overview, basic concepts and notations |
| WEEKS 2-3 |
Asymptotic expansions, basic estimates for sums and integrals |
| WEEKS 4-5 |
Watson's Lemma, Laplace's method, applications |
| WEEKS 6-7 |
Methods of Steepest Descent and Stationary Phase |
| WEEK 8 |
Perturbation Methods for Algebraic Problems |
| WEEKS 9-10 |
Linear second-order ODEs and special functions |
| WEEKS 11-12 |
Singular perturbations, WKB method, boundary layers |
| WEEKS 13-14 |
Miscellaneous Topics |
Updated by Professor R. Goodman- 9/1/2017
Department of Mathematical Sciences Course Syllabus, Fall 2017
